Physics of the urban production of algae in photo-bio reactors for the utilization in vertical farms

Diploma Thesis 2012 113 Pages

Physics - Biophysics




0.1 English
0.2 Deutsch

1 Introduction
1.1 Brief history of fertilizer utilization
1.2 Resources used in today’s agriculture . .
1.3 Concept for the urban food supply chain of tomorrow

2 Ecological Stoichiometry

3 About the Utilization of Light
3.1 Photosynthesis by algae
3.2 Total sunlight irradiance
3.3 Reflections on the reactor surface
3.4 Absorption in algal culture
3.5 Photosynthetically active radiation
3.6 Solar conversion efficiency
3.7 Biomass yield
3.8 Calculations-Summary

4 Nutrients
4.1 Carbon dioxide
4.2 Recycling nutrients from waste water treatment plants

5 Temperature
5.1 Photosynthetically non active radiation and inhibition .
5.2 Photosynthetic inefficiency
5.3 Total heat produced
5.4 Ensuring culture temperature for maximum yield
5.5 Calculations-Summary

6 Getting Energy Self-sufficient, A Harvesting Method
6.1 Raising algal density
6.2 Biogas as a joint product
6.3 Final treatment
6.4 Net energy of the harvesting process

7 Estimating Algal Fertilizer Production in Vienna
7.1 Total net energy
7.2 Costs, fertilizer value and other benefits

8 Conclusions
8.1 Sensitivity analysis
8.2 Food for thought

A Spreadsheets

B Glossary

C Paper and Poster presented on BC&E 2012

List of figures

List of tables





„Physics of the urban production of algae in photo-bio reactors for the utilization in vertical farms “

„Authors “

Schipfer Family, Matzenberger Julian, Hitzenberger Regina, Brenner Veronika and Schlögl Marianne

Thank you for „writing“this thesis with me!

Thank you Lukas Kranzl for your positiv input.

Special thanks to Prof. Haas and Prof. Rumpf for making this cooperation possible.

Thank you Sonnleitner Andrea and Dina Bacovsky from Bioenergy2020 for an entire library of literature! Thanks also to Vincent Garcia for the LaTeX template.

§ 0.1 English

Todays agricultural food production highly depends on the availability of non-renewable resources like crude oil, natural gas and phosphor rocks. To- morrow’s food security can only be ensured by reducing this dependency.

There are open questions concerning the methods that can be used for the production of renewable sources in order to achieve this goal. Is it technically and economically feasible, for instance, to produce micro-algal fertilizer in photo-bio reactors to recycle N and P from waste water streams? Is this furthermore possible by avoiding the combustion of non-renewable energies to become energy self-sufficient?

Relevant examples from literature will be used to investigate the micro- algal potential to extract nutrients from urban waste water streams for the re-injection into the food chain of the population. The production of algae and heat will be described in a bio-physical way to calculate the mass- and energy flux in photo-bio reactors, attached to walls of buildings in Vienna. It will be suggested to decompose the generated bio material through anaer- obic digestion to increase the N - and P share on one hand and to produce methane as an energy carrier on the other hand. The calculation model will be used to estimate the costs of producing a micro-algal fertilizer in Vienna. Furthermore a possible utilization of the generated fertilizer in vertical farms will be discussed.

About 271 t micro algae per year could be produced on a 100 m * 100 m wall in Vienna. The combustion of the produced biogas could meet the entire heat- and electrical-energy demand of the production process. By demonstrating the technical feasibility of every single part of the energy self-sufficient pro- duction chain, the technical feasibility of the whole concept is ensured. The costs of this product, however, would be nine times higher than the costs of commercial fertilizer. The bio-refinery in question still has a great po- tential when it comes to saving a high amount of non-renewable resources, thus making it an attractive alternative to the exclusive use of biomaterial as an energy carrier. This can be further shown by comparing the sunlight irradiation on a photo-bio reactor with the calorific value of the produced micro algae: This calculation yields an energy conversion efficiency of about 4% which could be surpassed by the electricity production of every available photovoltaic system.

§ 0.2 Deutsch

Die heutige Lebensmittelindustrie verlangt nach einer großen Menge nicht erneuerbarer Ressourcen wie Rohöl, Erdgas und Phosphatgestein. Um die Ernährungssicherheit der kommenden Generationen zu garantieren ist es notwendig diese Abhängigkeiten zu minimieren. Dabei stellen sich die Fra- gen, welche Technologien zur Gewinnung von erneuerbaren Energieträgern dafür genutzt werden könnten. Ist es zum Beispiel gro ß technisch undöko- nomisch möglich Algendünger in Photobioreaktoren zu produzieren und so N und P aus dem Abwasser zu recyceln? Ist es des Weiteren möglich diesen Prozess energieautark zu gestalten um so die Verwendung von nicht erneuer- baren Energieträgern zu vermeiden?

Anhand von Beispielen aus der Literatur untersucht diese Arbeit das Po- tential von Mikroalgen, städtischem Abwasser Nährstoffe zu entziehen um diese wieder in den urbanen Lebensmittelkreislauf zurück zu führen. Eine biophysikalische Beschreibung der Algen- und Hitzeproduktion in Photo- bioreaktoren an Wiener Hausfassaden dient zur Berechnung des Masse- und Energieflusses. Die Verfaulung der produzierten Biomasse wird vorgeschla- gen um deren Düngereffizienz zu steigern und um gleichzeitig CH 4 als En- ergieträger zu gewinnen. Die Ergebnisse des Rechenmodells werden zur Abschätzung der Kosten für eine Algendüngemittelproduktion in Wien ver- wendet. Der mögliche Einsatz des Biodüngers in vertikalen Farmen wird diskutiert.

In Wien könnten an einer 100 m * 100 m Hausfassade jedes Jahr 271 t Mikroal- gen wachsen. Die Verbrennung des produzierten Biogases könnte dabei den Heiz- und Strombedarf decken. Da die einzelnen Glieder dieser energieau- tarken Prozesskette bereits existieren, ist diese Art der Biodüngerproduk- tion mit Hilfe von P BRs technisch realisierbar. Das Produkt wäre jedoch selbst nach optimistischer Abschätzung neun mal so teuer wie kommerzieller Dünger. Dieses Konzept einer Bioraffinerie birgt jedoch ein enormes Ein- sparungspotenzial für Rohöl, Erdgas und Phosphorgestein und ist damit der alleinigen Nutzung von Biomasse als Energieträger einen Schritt vo- raus. Bestätigt wird das durch die Berechnung des Wirkungsgrades für die Umwandlung von Sonneneinstrahlung zu Algenbiomasse für eine direkte Verbrennung: Mit knapp 4% liegt dieser weit unter dem moderner Photo- voltaikanlagen für die Stromproduktion.

Chapter 1 - Introduction

§ 1.1 Brief history of fertilizer utilization

About 12 , 000 years ago, in the neolithic revolution the way of human living changed more and more from a hunting- and gathering- into an agriculture- and settlement-kind of lifestyle [Flannery, 1973, p.276]. By ob- serving acreage and crop yield, different cultivation methods for edible plants have been developed and optimized over time. Even though food security could largely increase for a larger number of consumers because of technical and organizational progress, most questions about the biological processes that are important for plant growth and thus for agriculture stayed unan- swered for a long time. One of these questions gives an ancient controversy about the source of nutrients which are used by plants for the accumulation of mass: Is it the dead organic material that is rotted to humus that pro- vides the necessary matter for plant growth or is it possible, that minerals unrelated to any living thing are in charge of this business?

This dispute was mainly settled in the 19 th century by three German sci- entists: Albrecht Thaer (1752-1828), a former medic, developed the humus theory and can be seen as the founder of phytotrophology - the science of plant nutrition. His own student Carl Sprengel (1787-1859) disproved this theory around 1826 by showing that the fertilizing effect of humus relies in its embodied mineral nutrient content. Justus von Liebig (1803-1873) finally gave the mineral theory its scientific acceptance. He composed several fertil- izers by using the knowledge of his own scientific field: Chemistry. With his profound systematical investigations Liebig stands for the beginning of agri- cultural chemistry. He still had to fight a long time against the supporters of humus theory who thought that only organic materials can assist plant growth. This fight reenforced his ambitions to bring his theses to perfection. While he initially talked about the need of an artificial addition of phospho- rus (P) and potassium (K) to the farmland, he had to admit at a later date that also nitrogen-scarcity (N) can be the reason for a poor harvest.

The need for N was proven through the greater success of Guano than Liebig ’ s patented fertilizers. Guano is a natural resource containing an av- erage amount of 15% N, 9% equivalent phosphoric acid and 3% potassium. It can be found in dry climates and consists of bird and bat feces. Even though ancient cultures in South America, especially in Peru, knew about its fertilizing value earlier, Guano first became important for Europe in the middle of the 19 th century. Its import displaced several professional guilds and industries that where in charge of collecting and recycling resources for the fertilizer production and also the production of explosives.

The robber economy of the Europeans led to a climax denoted as ” peak- Guano” in the early 20 th century. Two important developments drew off attention from this resource before its supplies could have been exhausted totally: The production of industrial superphosphate fertilizer out of phos- phor rocks (PR) mined in Maraca plus the invention by Fritz Haber and Carl Bosch to synthesize ammonia out of air. Although both processes asked for a high amount of electrical and thermal energy they appeared to give in- exhaustible sources for the production of N - and P -fertilizer. This made it possible that world population could grow to over seven billion people living on Earth today.

§ 1.2 Resources used in today’s agriculture

It is a sad fact that nearly one eighth of the world population do not have enough to eat [FAO, 2010, p.4]. It is important to note this. Although this topic will not be further discussed in this work, it should always be kept in mind. The food security of the industrialized countries highly de- pends on three non-renewable resources: Crude oil, methane (CH 4) and PRs. With about 95 EJ year thefoodsectoraccountsforaround30 %ofthe world’s total energy consumption [FAO, [2011]a, p.11 ]. More than one per cent is used solely for the production and distribution of N -, P - and K - fertilizers [Dawson and Hilton, 2011, p.17]. The burning of worldwide reserves of crude oil and natural gas provides most of this energy. A simple shift to renewable energy sources is necessary but would not entirely free food production from the dependence on fossil fuels.

The Haber-Bosch process for example was developed at the beginning of the 20 th century and was improved over years reaching a today’s energy consumption close to the theoretical minimum [Appl, 1997, p.25]. The formation of ammonia (N H 3) requires hydrogen (H 2). H 2 -stripping out of CH 4 is the best available technology, making this resource highly important for fertilizer industries. [Dawson and Hilton, 2011, p.21] estimate that if all reserves of natural gas would only be used for ammonia production, the demand could be satisfied for thousands of years.

Furthermore oil refinery is the basis of many different economic sections. Amongst others it is the main producer of sulphur. Sulphur is further burned to get sulphur dioxide. Sulphur dioxide is water-soluble and pro- duces sulphuric acid, which is ”...the ’acid of choice’ for the dissolution of PR...” [Dawson and Hilton, 2011, p.19]. Thus it becomes evident, that there is a double dependence on crude oil: It is needed for the extraction of sulphur as well as for the burning of the latter. [FAO, 2008, p.35] gives a forecast for phosphate fertilizer supply for 2011 / 2012 of about 45 * 106 tonnes P 2 O 5. The origin of this phosphate is mainly PR, thus making world reserves of this mineral highly interesting. About 42% of these reserves are assumed to lie under Moroccan territory [Cohen, 2007]. Related to the up- coming oil peak a so-called peak phosphorus is expected in the next decades [White and Cordell, 2009]. Better technologies to dissolve P 2 O 5 out of the residues saved from todays PR -mining could prolong the reserves’ lifespan but would not change the fact that this resource is finite. According to [Cohen, 2007] and [Dawson and Hilton, 2011, p.18] a consumption rate re- lated to today’s lifestyle could only be ensured for the next 100-400 years.

Another large part of the mentioned 30% of the world’s total energy con- sumption is used for the transportation, processing, retailing and produc- tion of food [FAO, 2011a, S.49]. Energy is mainly provided by fossil fuels. Combined with CH 4 released into the atmosphere from livestock farming, food production contributes a large share in global green house gas (GHG)- emissions. Growing consumption increases the amount of emissions as well as the land and water used for food production. In 2008 about 11% of the world’s ground surface was used for crop production and 70% of all water withdrawn from aquifers, streams and lakes were used for irrigation. [FAO, 2011c, p.13]. Several concepts to work against these trends have been developed. [FAO, 2011a] predicts that a change to diets including ”...the use of more fresh and local foods...” is indispensable. This would also reduce food losses and the demand for energy, water and land. In fact one third of the food is lost during production, processing and distribution today [FAO, 2011b, p.4]. This does not take into account that only a small share of used fertilizer can be found in food meant for the consumer. N and P are also lost at the prae-harvesting stage through erosion into lakes and rivers and finally into the ocean thus causing eutrophication changing ecological systems.

Alternative methods for the production of high quantities of food are quite common in less developed countries and strictly forbidden in Europe because of their destructive impacts on nature and consumers. One is known as the technique of slash and burn: Large parts of forests are slashed every year around the world before the dry seasons. In times with less rainfall the wood can dry and is burned afterwards to release its nutrients into the subjacent soil. This gives a short-term boost of soil fertility which is exhausted after a few crops because of high erosions. When harvest turns out badly the farmer moves to another part of the forest to repeat the procedure, leaving behind land which cannot be reafforested easily. The negative impact on ecosystems and the often-occurring non reversibility of the soil condition is well known and is still caused by between three and seven per cent of the world population who use this technique [Cornell, 2011], most often because of the lack of other possibilities.

Another common method is the direct use of human feces from waste wa- ter streams. According to the World Health Organization (WHO, cited by [Eichenseher, 2010]) nearly 700 * 106 people are reliant on a food supply, produced using human fecal fertilizers, triggering diarrhoea related diseases such as cholera killing 2 . 2 * 106 every year. Although this is yet another proof of bad conditions in these countries, recycling of nutrients from sewage could be an option for the rest of the world as well. The International Water Man- agement Institute (IWMI) argue that ”...the social and economic benefits of using untreated human waste to grow food outweigh the health risks.” The ”...dangers can be addressed with farmer and consumer education...” (IWMI, cited in [Eichenseher, 2010]). The author of this thesis suggests that an advanced technology for the recycling of essential elements could reduce the first world’s dependence on the fertilizer industry and in that context on fossil fuels and PRs.

§ 1.3 Concept for the urban food supply chain of tomorrow

The world population prospect of the UN’s department of economic and social affairs (ESA) released different growth forecasts for the upcoming decades. Their overall conclusion is that the number of people living on this planet will increase until 2050 to a value between 8 and 12 billion [ESA, 2010]. About 9 billion people would need a 70%-increase in food supply compared to the 2005-07 period [FAO, 2009, p.2]. Looking at the previous paragraphs shows that a concept developed to meet this food de- mand has to consider also how to save water, land and non-renewable re- sources at once:

[Despommier, 2010] discusses the idea of a fully controlled agriculture. In so-called vertical farms, food could be produced minimizing cultivated area and shifting production into town at the same time. Many models have been developed in regards to the architecture and function of such farms. All of them are following the same guidelines: Multi-storeyed build- ings hosting different cultivation methods should produce the nutrient de- mand of the citizens living within a short radius around the location of pro- duction. Different well-known techniques could ensure a year-round harvest in perfectly controlled environments. [Despommier, 2010, p.162ff] predicts that pythotrophology is advanced enough to create healthy food in an artificial environment. Some of the numerous advantages are listed below (after [Despommier, 2010, p.145ff]):

- Year-round crop production
- No weather-related crop failures
- Use of 70-95% less water
- Greatly reduced food miles
- More control over food safety and security

If demand is covered by this kind of ”indoor” agriculture, conventional farming could be abandoned, thus allowing the ecosystems to recover. After shrubs and bushes have regained territory, growing trees would bind atmosphere’s carbon dioxide (CO 2) building a serious opponent against GHG emissions. Another advantage would consist in the low consumption of N - and P -fertilizers because of the erosion prevention. How to provide vertical farms with the still needed amount of N and P without the use of nonrenewable resources will be further discussed:

As mentioned in the last paragraph, recycling of essential elements (in this work focusing on N and P) out of urban wastewater will be necessary in the future. Algae have been the object of research for the purpose of recy- cling since the middle of the previous century [Golueke and Oswald, 1963]. Because some algal strains also generate a high amount of lipids, the pro- duction of algae showed promises for the competition against petroleum in- dustries. Looking at the undesired effects of eutrophication in water bodies contaminated by sewage, the need for a controlled combination of wastew- ater treatment and algal production leaps to the eye. This thesis wants to give a thought-provoking impulse how to utilize the product of this artifi- cial eutrophication process. About 60 years after M.K. Hubbert defined the meaningful expression of peak oil [Hubbert, 1956], many scientists make an effort for two different achievements: One group tries to substitute fossil fuels and the other optimizes processes to minimize energy demand. Using algae as fertilizer which contain N and P from urban wastewater could help to save that one percent of world’s energy demand consumed by the fertilizer industry today (paragraph 1.2). The prior condition for a process concerning this efficiency enhancement would be a minimum use of non-renewable resources, as well as a minimum use of land and water.

Different methods for the cultivation of algae have been developed in the last decades. Most of them rely rather on the production of micro algae than macro algae such as seaweed. Depending on the strain, micro-algal growth can be accomplished by photoautotrophic, heterotrophic or mixotrophic cul- tivation. While in heterotrophic cultivation, algae are fed a carbon source, such as sugar, and grow without light, photoautotrophic cultivation strategies use large surfaces to capture photons for photosynthetic plant metabolism [Rittmann and McCarty, 2001, p.29]. As the name says mixotrophic cultivation uses both, photoautotrophic and heterotrophic techniques. For large scale applications only solar radiation (compared to artificial lighting) is considered feasible as a photon source for photoautotrophic cultivation. Lit- erature gives plenty of data about this method of algal production in sev- eral systems including photobioreactors (PBR ’ s), open pond - and race way - systems. In contrast to immobilized cultures, where algae grow on a thin film [Zhang et al., 2008] these systems contain high amounts of water in which micro algae can move and are mobile. Medium with sufficient sun- light for photoautotrophic algal growth is called photoactive volume (PAV). Therefore PAV directly stands for the system’s sunlight utilization efficiency. Because of their architecture highest PAVs mixed with the smallest ground surface area possible can be found in modern PBRs:

A young Austrian company called Ecoduna predicts that their specially designed vertical flat plate photobioreactors can offer 100% of PAV [Mohr and Emminger, 2012]. In their system micro algae sediment down a long thin transparent pipe to reach the entrance on the bottom of the next pipe where CO 2 and air is pumped in. The rising gas carries along the organic particles to the top where they can access the next neighboring sedimentation tube. Many of these pipes together form a flat transparent plate hence it is called a flat plate PBR. Because algae need carbon dioxide for their metabolism this method kills two birds with one stone: To avoid that micro algae bind together, which would negatively affect PAV and functionality of the reactor, algae have to stay mobile while accumulating CO 2. Twelve flat plates are fixed together and their surface normal is always adjusted with 90 o to the incident sunlight. This ensures an uniformly dis- tributed photon flux inside the PAV, avoiding too high sunlight intensities which could harm micro-algal growth. Harvesting and production should be carried out in the same velocity. With this continuos cultivation method, micro-algal concentration can be held constant in the reactor ensuring the highest production rate possible.

Next to sunlight and CO 2 micro algae need N, P and other trace elements to grow. In the rest of this work these essential elements will be called nu- trients. As mentioned above and acknowledged by [Hingsamer et al., 2011], these nutrients should be delivered from wastewater streams not only for ecological but also for economical reasons. The produced biomass can fur- ther be converted to fertilizer [Collet et al., 2011, p.210]. If urban sewage is used for this process and the product is fed into vertical farms, a closed city- internal nutrient cycle could be achieved. Figure 1.1 shows the suggested system and its boundary.

illustration not visible in this excerpt

Figure 1.1: The urban nutrient cycle

Chapter 2 - Ecological Stoichiometry

To calculate the productivity of PBRs it is necessary to illuminate the process of algal growth. Therefore several principles have to be investigated. Many of them are obvious and well known, yet it is the formulation of them that make these laws into powerful tools:

Plants, animals and humans mostly are built up of carbon (C), oxygen (O) and H. The composition differs from species to species and so does the amount of trace elements. If the elemental compositions of different individ- uals of one species are compared, a common proportion can be found. Since life obeys this law of constant compositions it is useful to look at micro al- gae expressed by a fixed stoichiometry. [Park et al., 2011, p.39] mentioned a typical relation between the main elements of micro-algal biomass as follows:

illustration not visible in this excerpt

The relation of N to P is 16 : 1 on an atomic scale. This proportion has a greater meaning than one would primarily expect. Alfred C. Redfield (1890- 1983), an oceanographer from Harvard found the same relation empirically by analyzing dissolved P -and N - contents in ocean water, sampled from different regions of this planet [Redfield, 1958]. His theory called the pythoplankton into account for this relation. Pythoplankton like micro algae form the bottom of the oceanic food chain. Their elemental composition determines an entire mass flow of the largest habitat based on a globally constant proportion that did not change much over time.

This so-called Redfield-ratio (N: P = 16 : 1) is a molar relation. To use this relation for any kind of mass flow calculation modification is necessary. Through multiplication with the atomic masses of the compounds a mass ratio of N: P = 7 : 1 is achieved. The same modification is furthermore applied on the H -, O - and C - content given by formula 2.1. This produces an average mass distribution for micro algae that will be used in the following chapters. Table 2.1 lists the molar relation, the atomic masses of the compounds and the resulting mass relation.

Table 2.1: Mass distribution

illustration not visible in this excerpt

Following the law of conservation of matter this mass has to be accumu- lated from the environment - either algae are grown in the sea or cultured in PBRs. Because micro algae ”are what they eat”, their reproduction is determined by the following principle: Liebig ’ s law of the minimum defines the scarcest nutrient as the limiting one, not allowing biomass to grow fur- ther and neither change the ratio. Energy for the metabolism is provided through photosynthesis. This is shown in formula 2.2 by the last part where Planck’s constant (h in [J*s]) is multiplied by the frequency of the light (ν in [[1] s ]).Thisleadstoanenergycontentthrough Einstein ’ sequation.The variable x gives the number of photons that are used for the photosynthetic process. As it will be discussed later on, not every frequency found in sun- light is suited to play a role in micro-algal reproduction.

[Narasimhan, 2010] gives a stoichiometric overview of the production and destruction of a certain micro-algal species. The calculation was modified to fit to the stoichiometric formula 2.1. The discussed principle of mass con- servation can be easily identified. Energy delivered by photons is written in parentheses in this formula and has only the symbolic meaning described above. Because the overview consists of stoichiometric formulas, the in- accuracy of the energy utilization can be ignored but should at least be indicated.

illustration not visible in this excerpt

Algae and dioxide are formed out of water, CO 2, and minerals through the utilization of light via photosynthesis. In the absence of photons, algae can use chemically stored energy to survive. This process is called dark respi- ration because CO 2 is produced. This ”energy-sapping” leads to a loss of micro-algal mass.

Furthermore algae can contain trace elements like S, K, Fe, Ca, Mg, Mn, Mo, Cu, Zn or V. Even if these elements mostly play a micro nutrient role some algal species can use them as macro nutrients. Special Chlorella -forms require sulfur for cell division or P-deficient Scenedesmus -algae cells can ac- cumulate sulfur as a substitute for P as described by [O’Kelley, 1968, p.89]. This topic should be considered when focusing on certain algae strains in nutrient-limited environments.

Well-studied strains of unicellular micro algae for example are Chlamy domonas reinhardtii, Chlorella or Dunaliella salina

[Rittmann and McCarty, 2001, p.21]. Literature searches produced an unconfirmed picture, that for example the genus Chlorella vulgaris is a desired object of investigation. Wastewater experiments also use a species called Scenedesmus obliquus or Scenedesmus rubescens. This thesis will provide no further specialization in a certain algal strain.

Chapter 3 - About the Utilization of Light

This chapter investigates the utilization of sunlight as a limiting factor for micro-algal growth. Therefore it is necessary to illustrate the quite complex process of photosynthesis. The profundity of this process makes it hard to trim the explanation to just a few pages. It is also noteworthy that the author of this thesis is no biologist. The content is pictured and understood only to such a depth as needed for the following estimation of biomass production which is the true focus of this chapter.

§ 3.1 Photosynthesis by algae

An international team, including Austrian scientists, recently found evidence for the origin of today’s plants to be an endosymbiotic process more than one billion years ago: An eukaryote, a simple organism with at least one cell enclosed by a membrane, united with a certain bacterium. This combination had the great advantage to permit photosynthesis and use its products for the rest of the cell. Finding an ancient link to this special bacterium in the genomes of different plants today makes a single event responsible for the whole evolution of the eukaryote supergroup Plantae including every single plant we know today. [Price et al., 2012]

The knowledge of the principles of this effective process of ”light-harvesting” is indispensable for a solid estimation of micro-algal biomass production. Even if micro algae do not belong to the Plantae -group, their photosyn- thetic process is similar as found in simple C-3 plants:

The handicap of C-3 plants compared to C-4 plants like maize and sug- arcane is dark respiration. As explained in chapter 2, dark respiration has the negative effect of the depletion of the plant’s own biomass. It takes place when the plant has to struggle with too high temperatures and/ or too low light irradiance. On the other hand C-3 plants do have a simpler structure thus making the light-harvesting process easier to understand.

Algae contain chloroplasts with membranes, the thylacoid membranes sur- rounding the thylacoid lumen isolating it from the thylacoid stromen. These membranes are filled with pigments, chlorophyll or carotenoids, with spe- cific light absorption rates. In case of absorbing a photon (h ν) an electron (e −) gets transited to a higher state. The e − now has two possibilities: Ei- ther it relaxes back to its ground state by emitting a photon or its energy gets transferred to another adjacent and similar molecule by excitation of an e − of the neighboring chlorophyll. This excitation/energy-transfer takes place as long as the neighboring chlorophyll has the same or lower energetic requirements for the excitation as the first one. This so called antenna cen- ter transports the energy to the reaction center which consists simply of a chlorophyll molecule with the lowest energy level for the excited state. Due to this difference the e − of the last antenna center chlorophyll now has the possibility to relax back not to his own ground state but to get conducted to the excited state of the reaction center. This last step, a quasi radiation-less e − -transfer, produces an anion and leaves a cation, a photooxidized chloro- phyll, behind. For further steps two different photosystems must now be distinguished:

The antenna chlorophyll pigments of Photosystem II (PSII) absorb light with a wavelength of 680 nm hence they are called P680. The created cation chlorophyll (P 680+) attracts an e − from the so called water oxidizing complex. To oxidize two molecules H 2 O, it is necessary to extract four e − and four protons. The oxidization forms one molecule O 2 and four H + ions which are released to the thylakoid lumen.

The extra e − from the anion chlorophyll of PSII gets (indirectly) further transported to a cation chlorophyll of Photosystem I (PSI). There it can sub- stitute an e − that was excited by light with the wavelength of 700 nm and transferred to the reaction center of PSI. This reaction center is happy to give its extra e − to a nicotinamide adenine dinucleotide phosphate (N ADP +). This N ADP + will be reduced to a N ADP H 2 by four e −. N ADP + as well as adenosine diphosphate ADP are dropped by the carbon reactions pathway. They are used as ”energy carriers”. Mainly because of the water oxidizing complex a H + excess emerges in the lumen. The so generated PH-gradient between lumen and stromen is furthermore the driving force to reduce ADP to AT P thus ”refilling” this ”energy carrier” for the reuse in the carbon reactions pathway.

In the carbon reactions pathway, also called the Calvin Cycle, CO 2 diffuses into the stromen to be metabolized in different steps by Ribulose-1.5- biphosphate (RuBP) to Glycerinaldehyd-3-Phopshate (G 3 P), the pre-stage of sugar. Five G 3 P are reused for the Calvin Cycle while one is the plant’s profit that leaves the carbon reactions pathway.

To process one molecule of CO 2 in the Calvin Cylce two N ADP H 2 and three AT P s are necessary [Zhu et al., 2008, p.154]. To provide two N ADP H 2 eight electrons are used thus eight photons are consumed. Six molecules of CO 2 can be converted to one molecule of glucose (C 6 H 12 O 6). Therefore a minimum of 48 photons are processed to provide the energy for this mass ac- cumulation. This calculation will be a part of the estimation of the biomass production in paragraph 3.7.

§ 3.2 Total sunlight irradiance

The sunlight irradiance depends on several well understood factors:

The zenith angle (ξ) of the shafts of direct sunlight depends on time and location on the earth’s surface as well as the day of the year. This angle can be further used to calculate the optical path length (m (ξ)) between the top of the atmosphere (TOA) and the earth’s surface. Therefore the altitude of TOA and the elevation of the location give the optical path length for the sun at zenith (m o).

illustration not visible in this excerpt

These factors should be enough to estimate which part of the solar irradiance available at TOA can really reach the location of the PBR. This assumption proves to be quite useful on a day with clear sky and without air pollution. Yet on most days the result is highly influenced by weather conditions. This makes it impossible to compute the solar irradiation for any chosen period and place on earth’s surface.

Measured data from meteorological stations can put things right:

Primarily to provide a tool for the estimation of photovoltaic (PV) en- ergy generation in European countries [Suri et al., 2007] collected the data of solar irradiance at a 1 km * 1 km resolution in 30 European Union and candidate countries. The combination of this data with a geographical in- formation system (GIS) can be found as an interactive map on the website of the photovoltaic geographical information system [PVGIS, 2010].

For the estimation of incident solar irradiance on PBRs the values of PVGIS for twelve days, each representing an average day of every month in a year, are further used for this work. The irradiance in [illustration not visible in this excerpt] isgivenbythe global irradiance (G) as well as the diffuse irradiance (G d), because particles in the atmosphere scatter sunlight and bring solar irradiance into corners where no direct light can get. PVGIS provides these values for horizontal surfaces averaged on a fifteen minutes basis under a real sky.

The next step investigates which part of this incident light can reach the surface of the PBRs:

Paragraph 3.6 will highlight the reason why it is beneficial to avoid di- rect sunlight irradiance on the reactor’s surface. To achieve this avoidance the surface of the reactor plates can be turned with the changing azimuth. This method can constantly avoid direct sunlight on the main surface of the reactor plates. G d reaches the reactor walls from every direction because it is diffuse. As it is given in watt per horizontal square meter it is assumed that 50% of this part of the solar irradiance is lost through the conversion to vertical square meter [Slegers et al., 2011, p.3349]. Direct irradiance and G d add up to G. Direct irradiance can be reflected by objects located near the PBRs. If the utilization of urban area should be optimized, such a reflect- ing object could be the cladding of a skyscraper on which the reactors are mounted. Change of the light intensity through reflection can be manipu- lated by using the optimal painting for the wall. It is assumed, that a rough white wall acts like a Lambertian reflector when irradiated. Incident light is scattered in every direction from 90 o to +90 o around the surface normal weighted by the factor cos(α). α is the observation angle; i.e. the angle between the area vector and the ”observer”. The direct irradiance that is scattered by such a type of wall also becomes diffuse. Its light intensity can be averaged over the full range of scattering angles ( 90 o < α < +90 o) if the entire irradiance can further reach the reactor’s surface. This calculation gives an intensity reduction of around 36% for the sunlight that shines at the wall.

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For the irradiance on the surface of a flat-panel PBR mounted on a white wall it is assumed, that 50% of G d, 64% of (G − G d) and another wall- reflected share of G d (0 . 5 * 64% * G d) play a role. Thus a surface irradiance (I PBR) on the PBRs is calculated as given by the following formula:

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This formula could further be improved by including the transformation of direct irradiance measured horizontally to a direct irradiance on a vertical surface.

§ 3.3 Reflections on the reactor surface

Photons reaching the reactor’s surface are confronted with different refrac- tive indices. Due to that change, a part of the irradiance is reflected and another part transmitted. The irradiance values resulting from this reflex- ion and transmission are given by the Fresnel equations. They depend on the refractive indices (η) of the different media, the incident angles (θ) and the polarization (two possibilities: s- or p-polarization) of the light rays [Slegers et al., 2011, p.3351].

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The refractive indices of the considered media are given by η i, for the medium of the incident light, and η t, for the medium of the transmitted light.

Assuming that glass is quite too heavy for the construction of PBRs, re- flections were computed with the refractive indices of Polymethyl methacry- late (PMMA, Acrylic glass) with a value of η = 1 . 49. After the transmission into the transparent wall a second change of medium -from PMMA to water- leads to further Fresnel reflections of the transmitted light. The following table 3.1 shows the refractive indices for the two media that light has to pass to reach the inside of the PBRs: All values are obtained from [Ciddor, 1996]. Furthermore the angle of transmission θ t is given by the incident angle θ i:

Table 3.1: Refractive indices

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