Modeling Microalgae Productivity in Industrial-Scale Vertical Flat

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Modeling Microalgae Productivity in IndustrialScale Vertical Flat Panel Photobioreactors Christian Hermann Endres, Arne Roth, and Thomas Bartholomaeus Brück Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b05545 • Publication Date (Web): 29 Mar 2018 Downloaded from http://pubs.acs.org on March 30, 2018

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TITLE

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Modeling Microalgae Productivity in Industrial-Scale Vertical Flat Panel Photobioreactors

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AUTHORSHIP

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Christian H. Endresa,b,*, Arne Rotha, Thomas B. Brückb

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AFFILIATIONS

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a

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Bauhaus Luftfahrt, Willy-Messerschmitt-Str. 1, 82024 Taufkirchen, Germany, Tel. +49-

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89307484948, E-mail: [email protected]

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b

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Werner Siemens-Chair of Synthetic Biotechnology, Department of Chemistry, Technical

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University of Munich, Lichtenbergstraße 4, 85748 Garching, Germany

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ABSTRACT

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Potentially achievable biomass yields are a decisive performance indicator for the economic

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viability of mass cultivation of microalgae. In this study, a computer model has been

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developed and applied to estimate the productivity of microalgae for large-scale outdoor

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cultivation in vertical flat panel photobioreactors. Algae growth is determined based on

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simulations of the reactor temperature and light distribution. Site-specific weather and

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irradiation data are used for annual yield estimations in six climate zones. Shading and

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reflections between opposing panels and between panels and the ground are dynamically

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computed based on the reactor geometry and the position of the sun. The results indicate that 1 ACS Paragon Plus Environment

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thin panels (≤ 0.05 m) are best suited for the assumed cell density of 2 g L-1 and that reactor

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panels should face in north-south direction. Panel spacings of 0.4 – 0.75 m appear most

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suitable for commercial applications. Under these preconditions, yields of around 10 kg m-2 a-

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1

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have to be expected, as extreme reactor temperatures limit overall productivity.

are possible for most locations in the U.S. Only in hot climates significantly lower yields

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TOC ABSTRACT

34 35 36

INTRODUCTION

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Microalgae have attracted substantial interest as feedstock for a broad range of value added

38

products, encompassing pharmaceuticals, pigments, proteins and biofuels

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show high growth rates, by far exceeding those of terrestrial plants

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cultivation does not depend on arable land and can be operated using seawater

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waste water 11 as growth medium.

1–5

. Microalgae

1,6–9

. In addition, 10

or even

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Various reactor designs for mass outdoor cultivation of microalgae are currently

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pursued. In principle, microalgae can be cultivated in open systems or closed photobioreactors

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(PBRs)

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engineering, closed PBRs offer high controllability of growth conditions, albeit at the cost of

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increased system complexity

12

. While open systems, particularly open ponds, tend to require less elaborate

9,13,14

. Vertical flat panel PBRs, an example of closed reactor

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15–19

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systems, represent a popular reactor concept for academic research

and commercial

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activities 20–22 and has therefore been selected as cultivation system for our study.

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Despite of the widely acknowledged potentials of microalgae as feedstock for the

50

production of fuels and other bioproducts, large-scale cultivation, harvesting and processing

51

of algae biomass are mostly immature technologies. With regard to the economic viability of

52

algae production, the achievable biomass yield represents a crucial performance indicator.

53

However, experiences on microalgal biomass yields are usually based on scientific

54

experiments at laboratory scale

55

for industrial-scale cultivation systems, due to the small number of operational production

56

plants and the lack of publicly-available information on these facilities.

23,24

, while only little knowledge exists about potential yields

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In the absence of an empirical knowledge base on microalgae biomass yields,

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computational simulations are indispensable to assess potential biomass productivities, to

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screen potential cultivation sites and to evaluate optimum reactor geometries and reactor field

60

configurations

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and on the temperature of the culture medium. Consequently, it is crucial for any

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computational assessment of algae productivity to thoroughly model light and temperature as

63

a function of local external conditions 27–29.

25,26

. The growth of algae fundamentally depends on the availability of light

64

Only a limited number of simulations of outdoor cultivation of microalgae in large-

65

scale facilities has been reported to date. Most of this work has been devoted to open pond

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systems, which are easier to describe mathematically in a computer model

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few studies exist that cover yield estimations for closed PBRs under industrially relevant

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cultivation conditions. In two such studies, algae growth was simulated in arrayed tubular

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and flat panel PBRs 25. The light distribution was dynamically modeled based on the position

70

of the sun and the reactor geometry. Furthermore, shading caused by the reactors was taken

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into account. A major drawback of these studies is the fact that the influence of the reactor

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temperature on algae growth has been completely neglected. In contrast, in another study

30–34

, while only

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temperature as well as light were dynamically simulated for a bubble column reactor

.

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However, as only a single reactor was considered, effects like mutual shading and radiation

75

transfer were not taken into account. Consequently, the results of this study are only of

76

limited relevance for industrial applications.

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In summary, to the best of our knowledge, no simulation of the productivity of

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microalgae cultivated in arrayed closed PBRs has been reported to date that includes a

79

detailed temperature model. The work presented here closes this gap: For the first time, a

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sophisticated temperature model is combined with an elaborate simulation of light availability

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to assess potential biomass yields for microalgae cultivation in an arrayed set-up of vertical

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flat panel PBRs. Shading effects and first-order reflections are taken into account; the light

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propagation within the reactors is dynamically simulated based on the actual angles of

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incidence and on the geometry and relative arrangement of reactor panels. Site-specific data

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on weather and solar irradiation are used to simulate microalgae growth and to estimate

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potential biomass yields for a complete year of cultivation at six U.S. locations in different

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climate zones. Important design parameters for industrial-scale cultivation of microalgae in

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vertical flat panels PBRs are discussed.

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The presented productivity model provides a valuable tool to assess potential

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microalgae yields at any given location under local growing conditions and to select the most

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suitable set-up of the reactor panel field, based on the site-specific economic boundary

92

conditions.

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METHODOLOGY

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Examined Cultivation System. The examined cultivation system consists of vertical

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flat plate PBRs that are arranged in parallel panel rows (see abstract graphic). Panels at the

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edges of an array are neglected since they are exposed to higher levels of irradiation and are

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thus not representative for the majority of the reactors. The loss of accuracy associated with 4 ACS Paragon Plus Environment


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this simplification is only small, considering that even for a small field of 100 m × 100 m and

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a panel width of 2 m, a panel distance of 0.5 m and a panel thickness of 0.05 m, only about

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5% of all panels would be located at the edges of the field. Furthermore, only the back and

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front surfaces of the reactor panel are considered for light capture and heat transfer. The areas

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at the sides, the top and the bottom of the reactor are neglected as they are small in

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comparison to the total surface area of the reactor. In addition, the respective areas are often at

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least partially blocked by the ground (bottom), adjacent reactors (sides), equipment or an

106

attachment to a frame (top), further reducing light input through these areas. The impact of

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neglecting these small areas on the reported outcomes is therefore considered small.

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Reactor panels of different thicknesses are examined, while the width and height of the

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reactors are kept constant at 2 and 1 m, respectively. However, yields generated for this

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standard reactor can be transferred with good approximation to reactors of different

111

dimensions, given that the new reactor shows the same ratio of panel height to panel distance

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and is identical with respect to panel thickness (Supporting Information, Section 2.2). For this

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case, yields per panel are directly proportional to the reactor’s surface area (front and back).

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Yields per panel of a reactor system that is 2 m high with a panel distance of 1 m is, for

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example, twice as high as yields corresponding to reactors that are 1 m high with a panel

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spacing of 0.5 m. Areal yield can be calculated from yields per panel by simply dividing the

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latter by the occupied ground area ((panel distance + panel thickness) × panel width). Hereby,

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the panel distance is defined as the distance between two opposing panel surfaces of adjacent

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panel rows (see also length d in Figure S7, Supporting Information).

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The culture medium is continuously mixed by pneumatic aeration. Temperature

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gradients within the reactor are therefore assumed to be negligible. A constant cell

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concentration of 2 g L-1 is assumed throughout this. Quasi-constant cell concentrations can,

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for example, be reached by dynamically harvesting the algae according to the current biomass

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productivity. 5 ACS Paragon Plus Environment

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General Approach. The calculation of microalgae productivity for outdoor

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cultivation plants comprises three steps (Figure 1). First, cultivation temperature is simulated

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as a function of local climate, reactor geometry and solar irradiation. Second, based on the

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reactor geometry and solar irradiation, the light distribution within the reactors is determined.

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Third, microalgae productivities are obtained from the cultivation temperature and local light

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intensities by applying a mechanistic growth model.

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133 134

Figure 1. Basic approach for calculating algae biomass yields in closed PBRs.

135 136

Details Regarding Temperature and Light Simulation. The implemented 36

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temperature model is described in detail in a previous publication

138

calculation of the heat balance in the reactors as a function of the geometry, distance and

139

orientation of reactor panels, of local climatic conditions and irradiation (including all first-

140

order reflections) and thermal radiation from the ground. Importantly, mutual shading is

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calculated as a dynamic function of the sun’s position. The original temperature model has

142

been slightly adapted to integrate it into the comprehensive model presented here.

. It is based on the



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Specifically, the fixed biomass fixation rate simplistically used in the original model has now

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been replaced by a mechanistic growth model, as described in the Supporting Information

145

(Section S.1.1).

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For an infinite array of flat panel PBRs, the light distribution does not change along

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the panel rows. The light distribution therefore is only determined for two dimensions, i.e. the

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cross section of a single panel (panel thickness × height). This cross section is divided by a

149

fine grid into cells of 10 mm in height and 0.5 mm in width. The light intensity is determined

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at the center of each cell. Six components are taken into account to determine local light

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intensities: direct and diffuse sunlight as well as the respective reflections of sunlight at the

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panels and the ground. Basic assumptions and principles regarding the calculation of local

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light intensities are described in the following. For more detailed information and underlying

154

equations, please refer to the Supporting Information (Section S1).

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Light attenuation in the reactor is calculated using a modified version of the Lambert37

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Beer law

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usually independent of the concentration of the considered substance and represents only light

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absorption. The modified law, however, also accounts for the scattering effect of algae. As a

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result, the influence of the cell concentration has to be considered. For the simulation, an

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extinction coefficient of 100 m2 kg-1 is used for a cell concentration of 2 g L-1. This value is in

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accordance with experimentally derived values for Chlorella vulgaris at high cell densities 37.

162

. The expression “modified” here refers to the extinction coefficient, which is

Reflection losses at the panel surfaces are calculated by applying Snell’s law assuming

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refractive indices of 1.0 for air 38, 1.5 for the panel wall (glass, plastic)

39–41

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culture medium 38. The reflectivity of the ground was assumed to be 0.3 corresponding to dry

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sandy soil without vegetation 42,43. Most natural soils show albedos between 0.1 and 0.45. The

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selected value thus represents an intermediate with respect to this range. The impact of the

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ground’s reflectivity on biomass yields is illustrated and discussed in the Supporting

and 1.3 for the


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Information (Section S3.4). Shading of the panels is dynamically computed based on the

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sun’s position, panel geometry and orientation of the panels.

170 171

Translation of Temperature and Light into Cell Growth. A wide variety of

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mechanistic growth models exists. Research in this field has been comprehensively reviewed

173

28,44

174

can be used to determine algae productivity. For the simulation of industrial-scale outdoor

175

cultivation, however, several criteria should be met. Cultivation temperature has a strong

176

effect on algae growth. A respective productivity model should therefore take the cultivation

177

temperature into account. In contrast, the influence of nutrient concentrations can be

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neglected for most commercial applications, assuming that nutrients are added in an optimum

179

amount. Incoming sunlight can be considered by using a spatially resolved light distribution

180

or by using average or incident light intensities. Growth models using the latter options,

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however, do not allow the assessment of various reactor dimensions and reactor field

182

configurations as their utilization is generally limited to a specific reactor geometry. For the

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present work, thus a model is selected that allows productivity simulations based on the

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distribution of light that is individually modeled for the respective reactor geometry. Lastly, a

185

model for simulating outdoor cultivation should comprise a term for endogenous cell

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respiration, to account for biomass losses in poorly illuminated areas of the reactor and during

187

the night.

188

; other growth models have been introduced recently 45,46. In principle, any growth model

The growth model introduced by Béchet et al.

37

includes all of the above mentioned

189

aspects and was therefore adopted for the present study. Specific growth parameters for the

190

microalgae Chlorella vulgaris were provided in the same publication. The respective wild

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type strain (GenBank rbcL sequence: EF589154), which was isolated in New Zealand, is very

192

robust and grows over a wide range of temperatures. The strain is therefore an ideal candidate



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for outdoor applications. Validations of the growth model were conducted in laboratory 37 and

194

in outdoor experiments 26.

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The total productivity, P, of algae within a reactor panel is determined by integrating

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local productivities, µloc, over the reactor volume, VR, and by multiplying them by the cell

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concentration, X (Equation 1).

198 (1) 199 200

Iloc is the local light intensity and TR the reactor temperature. The calculation of µloc is

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described in the Supporting Information (Section S1.3).

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Béchet et al. reported positive cell growth for the examined Chlorella strain in the

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temperature range between 0 and 42.1 °C. However, it was not reported to which extent the

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cell culture is harmed at temperatures exceeding 42.1 °C. Lee et al. observed Chlorella-

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cultures resisting peak temperatures of 49 °C in outdoor PBRs 47. Other eukaryotic microalgae

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were reported to survive even higher temperatures 48. Based on these references, the following

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assumptions are made for the applied productivity model: Algae cells survive temperatures

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between 42.1 to 50 °C; however, biomass production is stopped for the time the algae are

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exposed to these temperatures. If exceeding 50 °C, massive cell death is expected, resulting in

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a collapse of the cell culture. As a consequence, production is put to a halt for seven days after

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the occurrence of temperatures above 50 °C, representing the time algae cells need to recover

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or a new culture needs to reach the original cell concentration. If temperatures exceed 50 °C

213

again while still in recovery, the phase of zero biomass production is extended by further

214

seven days.

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Subzero cultivation temperatures are not covered by the model, as this case does not

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represent a practical application. In the model, the cultivation temperature is therefore 9 ACS Paragon Plus Environment

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artificially kept at 0 °C, even though the thermal balance could result in ice formation. When

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conditions improve, the reactor temperature starts to rise again from 0 °C.

219 220

Selected Cultivation Sites and Input Data. Six U.S. locations have been selected as

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cultivation sites for productivity simulation (Table 1). The selected locations represent distinct

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climate zones that can also be found at other places worldwide. Meteorological and solar

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irradiation data used for the simulation originates from the National Solar Radiation Data

224

Base

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locations in different climate zones within the U.S. and provides the required data in a

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consistent quality for all selected locations.

49

. The database is specifically intended for solar conversion systems covering various

227 228

Table 1. U.S. locations selected as cultivation sites for productivity simulations with

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respective climate classification and average air temperature (Tavg, annual average; Tcold,

230

average coldest month; Thot, average hottest month). Location

Forks, WA

Climatea

Temperate; without dry

Tavg

Tcold

Thot

[°C]

[°C]

[°C]

9.6

5.0

15.2

10.6

-3.0

23.4

15.5

7.5

23.5

season; warm summer

Boston, MA

Cold; without dry season; warm/hot summer

Sacramento, CA

Temperate; dry and hot summer

Phoenix, AZ

Arid; desert; hot

23.8

11.7

35.6

New Orleans, LA

Temperate; without dry

20.4

9.9

30.0

23.1

21.7

24.6

season; hot summer Hilo, HI

231

a

Tropical; rainforest

According to Köppen-Geiger climate classification 50.



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Computation Details. All models were developed, implemented and executed in

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MATLAB® (The MathWorks®, Inc., Natick, MA). The calculations of algae productivity (as

235

well as of temperature and light distribution) were performed for every minute of a complete

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year. The time needed for simulating a complete year of cultivation amounts to approximately

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30 min (Intel Core i5 2.70 GHz, 4 GB RAM).

238 239

RESULTS AND DISCUSSION

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Characterization of Light Distribution and Local Biomass Production. A cross

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sectional cut of the reactor is generated to provide a visual impression of the light distribution

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and corresponding local biomass production (Figure 2). For this purpose, an exemplary

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reactor situated in Sacramento, CA is examined. Reactor panels face in north and south

244

direction. The distance between the panels is set to 0.5 m and the thickness of the panels to

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0.05 m. The images show a day in late spring (day 100) at noon (12:00).

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Figure 2. (A) Distribution of light and (B) biomass production in the PBRs at noon (12:00).

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Different scalings of the vertical and horizontal axes are used to adequately display light and

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productivity distributions (for both subfigures: location, Sacramento, CA; panel distance,

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0.5 m; panel thickness, 0.05 m; orientation, north-south; considered day of the year, 100).

252 253

The light distribution is dominated by direct irradiation which enters the reactor on the

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left side of the panel (Figure 2A). The significant change of light intensity 0.2 m above

255

ground is caused by shading from the opposing panel row. Diffuse irradiation is most intense

256

at the upper edges of the reactor; however, it is only visible in the right corner of the image, as

257

it is superimposed by direct irradiation in the left corner. Direct light reflected at the opposing

258

panel wall can be seen in the lower third on the right side of the panel. Other types of

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irradiation cannot be recognized in the illustration as the respective light intensities are too

260

small. The respective irradiation types are nevertheless still considered for productivity

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simulations. The major fraction of incoming sunlight is absorbed close to the panel wall and 12 ACS Paragon Plus Environment


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its intensity quickly decreases when moving towards the center of the reactor. As a

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consequence, large areas of the reactor are poorly illuminated. It therefore could be concluded

264

that algae growth is limited to the edges of the reactor and, furthermore, that the selected

265

panel thickness of 5 cm is far too large for efficient biomass production.

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This assumption, however, has to be corrected when looking at the image showing the

267

local biomass production (Figure 2B). As can be seen, algae growth is not limited to the

268

edges, but stretches far deeper into the reactors. Even areas appearing not to be illuminated at

269

all can significantly contribute to the overall productivity. The reason for this lies in the

270

relation between growth and light intensity. Algae are very efficient at low irradiation values

271

and convert a relatively large fraction of incoming photons suitable for photosynthesis into

272

biomass 51. At high light intensities, algae usually enter a state of light saturation. At this state,

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light conversion is very inefficient. Even higher light intensities may cause photoinhibition;

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however, this aspect is not covered by the model.

275

Based on the presented results, it has to be noted that even light sources weakly

276

contributing to the overall solar energy received by the reactors can significantly enhance

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overall productivity (see diffuse irradiation and reflected direct irradiation). Biomass

278

production is further not limited to highly irradiated areas close to the panel wall but stretches

279

far deeper into the reactor. Only in the center of the reactor light intensity is too weak and cell

280

respiration results in a net loss of biomass productivity (Figure 2B, area of negative net

281

productivity). For the presented example at the given point in time, the total loss of biomass

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productivity in this specific area of the reactor amounts to 0.09 g min-1. 2.61 g min-1 are

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produced in the parts of positive biomass production, resulting in an overall productivity of

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2.52 g min-1 for the whole panel.

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In terms of productivity, dark zones are not the only criterion for optimizing reactor

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design and plant layout. Thick panels are less prone to temperature fluctuations and in

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particularly reduce the risk of algae being exposed to extremely high reactor temperatures 13 ACS Paragon Plus Environment

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during summer. Losses that result from operating reactors in an unfavorable temperature

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regime may thus exceed those associated with to dark zones in the reactor. For these

290

considerations, however, biomass yields must be analyzed on a yearly basis with respect to

291

panel distance and thickness, as discussed in detail further below.

292 293

Impact of the Various Types of Irradiation on Microalgae Productivity. The

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results described in the previous section indicate that even though direct irradiation may

295

dominate an irradiation profile, weaker types of irradiation may still have a significant

296

influence on the overall productivity. The impact of various irradiation types on the overall

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productivity is therefore further examined (Table 2). One year of cultivation is selected as

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time frame for the analysis. The reactor configuration is identical with the one described in

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the previous section (location Sacramento, CA; panel distance, 0.05 m; panel thickness, 0.5

300

m; orientation, north-south).

301

In a first step, the shares of various irradiation types in the total amount of absorbed

302

solar energy are examined (Table 2, second column). For this purpose, a certain type of light

303

is neglected and the remaining received solar energy is quantified. The comparison clearly

304

shows that direct irradiation dominates the yearly energy input. Neglecting direct irradiation

305

consequently results in a reduction of 60% of captured sunlight. This is followed by diffuse

306

irradiation which covers around 30% of incoming sunlight. Reflections of direct and diffuse

307

light at opposing panels and the ground cover the residual 10%. Of the total available sunlight

308

(7.1 GJ panel-1 a-1) only about two thirds (4.4 GJ panel-1 a-1) are actually captured by the

309

reactors of the given geometry. Factors responsible for this loss, are light absorbed by the

310

ground as well as reflections at the ground/panels that are not captured by another panel. In

311

addition, the top surfaces of the reactors are not accounted for in the model as described in the

312

methodology section. A comprehensive analysis of captured light as a function of panel

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spacing and thickness is presented in our previous publication 36. In general, it has to be noted 14 ACS Paragon Plus Environment


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that the limited efficiency of light capture represents a drawback of vertical systems that must

315

be outweighed by their advantages compared to other reactor systems.

316 317

Table 2. Impact of neglecting specific types of irradiation on total captured solar energy and

318

annual biomass yield. Values in brackets indicate the relative decrease of captured solar

319

energy and productivity with respect to the case of regular irradiation (location, Sacramento,

320

CA; panel distance, 0.5 m; panel thickness, 0.05 m; orientation, north-south). Neglected irradiation type

Captured sunlight

Yieldsa

[-]

[GJ panel-1 a-1]

[kg panel-1 a-1]

None (regular irradiation)

4.4

9.0

Direct

1.8 (-60.0%)

4.0 (-55.6%)

Diffuse

3.1 (-29.7%)

3.0 (-66.8%)

Direct refl. by panels

4.4 (-2.0%)

8.6 (-5.1%)

Diffuse refl. by panels

4.4 (-1.2%)

8.8 (-2.8%)

Direct refl. by ground

4.2 (-5.0%)

8.1 (-9.9%)

Diffuse refl. by ground

4.4 (-2.1%)

8.5 (-5.2%)

All reflections

4.0 (-10.4%)

6.8 (-24.1%)

321

a

322

do not add up to 100%. For the same reason, production losses corresponding to the case that all reflections are

323

neglected cannot be determined from the sum of losses corresponding individual neglected reflections.

Please note that due to the non-linear relationship between light intensity and algae growth, production losses

324 325

In a second step, a sensitivity analysis is performed to quantify the significance of the

326

various types of irradiation on annual biomass yields (Table 2, third column). For the case of

327

regular irradiation, 4.4 GJ of captured sunlight (full solar spectrum) translates into 9.0 kg of

328

algae biomass. Assuming a heating value of 22 MJ kg-1, this corresponds to an overall

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photosynthetic efficiency of 4.5%, which is in good correspondence to values cited for

330

microalgae

52,53

and plant leaves 54. The most striking result of the sensitivity analysis relates 15 ACS Paragon Plus Environment

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to the different impacts of direct and diffuse irradiation: While far more light energy is

332

received by direct irradiation than by diffuse irradiation, diffuse irradiation has a stronger

333

influence on annual biomass yields. Neglecting diffuse irradiation leads to a drop of

334

productivity by approximately 67%, while neglecting direct sunlight only results in a drop of

335

56%. This can be explained by the fact that direct light typically illuminates only a small

336

fraction of the reactor’s surface, albeit with high local intensities of the incident radiation.

337

High light intensities, however, cannot be processed efficiently by microalgae due to light

338

saturation

339

expected. For comparison, diffuse irradiation represents a weaker source of energy, but the

340

incident light fully covers both sides of the panel. The broader spatial distribution of diffuse

341

light explains the strong influence on biomass yields.

51

. This is the reason why biomass yields related to direct sunlight are lower than

342

Reflected light illuminates areas in the reactor that are only poorly reached by direct

343

and diffuse irradiation, i.e. close to the ground. Reflections thus substantially contribute to a

344

more homogenous distribution of light in the reactor. Consequently, reflections have a

345

stronger impact on annual biomass yields (yield reductions of 24%) than might be anticipated

346

from their limited contribution to the total energy input (10% of captured sunlight).

347

Yield simulations for other panel distances and locations lead to similar results

348

(Supporting Information, Section S3.1). Therefore, it can be concluded that diffuse and

349

reflected light generally play a more important role for algae growth than could be expected

350

from their share in the total solar energy captured per reactor panel. This aspect must be kept

351

in consideration for future simulations and the process of integrated reactor and plant design.

352 353

Trade-Off Between Area-Specific Yield and Yields per Reactor Panel. The annual

354

yield with respect to the ground area (Figure 3, black lines) is a measure of how much

355

biomass can be produced on a certain area of land. The higher this area-specific yield, the less

356

land has to be acquired to produce a given quantity of biomass. Furthermore, piping systems 16 ACS Paragon Plus Environment


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357

and infrastructure can be designed in a compact way for plants with high areal biomass

358

outputs, thus reducing investment costs. Alternatively, microalgae yield can be related to the

359

number of reactor panels in which it is achieved (Figure 3, green lines). A higher panel-

360

specific yield implies that fewer reactors are required for producing a certain amount of

361

biomass. By reducing the total number of required reactors, significant reductions of capital

362

costs can be expected.

363

364 365

Figure 3. Annual areal biomass yields (left y-axis, black lines, filled markers) and panel-

366

specific biomass yields (right y-axis, green lines, empty markers) as function of panel distance

367

and thickness. Square, circle, diamond and triangle markers indicate panel thicknesses of

368

0.025, 0.05, 0.1 and 0.15 m (location, Sacramento, CA; orientation, north-south).

369 370

High areal yields are achievable at small distances below 1 m. At larger panel

371

distances more and more light falls on the ground between the panel rows and is lost for

372

biomass production if not reflected back to the panels. Areal productivity therefore decreases

373

with increasing panel distance. For very small panel distances (< 0.3 m) a sharp decline in

374

areal productivity can be observed. Two major reasons are responsible for this decline. First, 17 ACS Paragon Plus Environment

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375

even though more light with respect to the ground area is received by the panels, the available

376

light is distributed among a larger number of reactors. The individual reactor may therefore

377

receive only very little light turning large areas in the reactor virtually black. Algae cells in

378

these areas are not capable of producing biomass via photosynthesis but rather consume

379

biomass via cell respiration. As a result, areal yields are declining even though a large fraction

380

of incoming sunlight is captured by the panels. The second reason for the abrupt decline of

381

areal productivity is related to a simplification made in the model: Light input through the top

382

surface area is neglected for the simulation. The reason for this simplification is a reduced

383

model complexity and the fact that the top surface may be blocked for incoming light by

384

equipment or by the attachment to a frame. Small panel distances in the range of the panel

385

thickness, however, represent a case usually not relevant for industrial applications, as very

386

small panel distances correspond with a large number of reactors, implying high investment

387

costs.

388

With increasing panel distance the exposure to sunlight increases for the individual

389

reactor, typically resulting in higher productivities per panel. The impact of the increasing

390

panel distance on biomass yield per panel is strongest at small panel distances and loses

391

influence at larger panel distances. From a panel distance of approximately 2 m onwards,

392

productivity gains are often negligible. The major reason for this behavior is the fact that at

393

large panel distances only little additional light capture can be expected with increasing panel

394

distance. In addition, reactors can reach very high temperatures at large panel distances,

395

caused by a lack of shading

396

temperatures negatively impact biomass productivity of algae. As a consequence, maximum

397

productivities per panel are not necessarily found at the highest panel distance examined (5

398

m), where irradiation is strongest for an individual panel.

36

, in particular if located in a warm climate. Very high

399

For commercial applications, both, high areal yields and high yields per reactor unit,

400

are desirable. Therefore, a trade-off is necessary with respect to panel distance. Based on our 18 ACS Paragon Plus Environment


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401

results, panel distances in the range of 0.4 to 0.75 m appear most promising. This range offers

402

also the highest potential in case of the other examined locations, as shown in the Supporting

403

Information (Figure S22). However, for a specific determination of the optimum

404

configuration of the production plant, a detailed techno-economic assessment is required,

405

based on, i.a., information regarding costs for land and reactor acquisition. Such an economic

406

analysis is beyond the scope of the present work.

407 408

Optimal Thickness and Orientation of the Reactor Panels for High Biomass

409

Outputs. When concentrating on the optimal panel thickness, thin panels (0.025 m, 0.05 m)

410

appear most favorable for Sacramento (square and circle markers, Figure 3) as well as for the

411

other locations examined in this work (Supporting Information, Figure S22). For the present

412

study, an algae concentration of 2 g L-1 with a corresponding extinction coefficient of 100 m2

413

kg-1 was assumed. Under these conditions, light cannot penetrate very far into the reactor

414

(light intensity is reduced by 95% after 0.015 m). Nevertheless, thicker panels can be of

415

interest, if focus lies on maximizing yields per panel. For this case, increased panel distances

416

are required to enable a sufficient light exposure of the panels and to minimize dark zones

417

within the cultivation medium, however at the expense of reduced areal productivity. At the

418

same time, thicker panels are less prone to overheating. When going on to greater panel

419

thicknesses (above 0.1 m), however, biomass production rates are strongly reduced due to

420

poor light availability in large parts of the reactor volume.

421

In this context it has to be noted that the correlation of biomass productivity with

422

thickness and distance of the reactor panels depends on the optical density of the algae

423

suspension, as given by the cell density and the specific extinction coefficient. While we

424

generally used a fixed optical density for our simulations, the impact of algae cell

425

concentration on annual biomass yields was examined in a sensitivity analysis for the case of

426

cultivation in Sacramento, CA (Supporting Information, Section S3.4). It shows that a higher 19 ACS Paragon Plus Environment

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427

cell concentration of 3 g L-1 generally results in lower or unchanged yields, compared to the

428

standard concentration of 2 g L-1. In contrast, a reduced cell concentration of 1 g L-1 enables

429

higher yields in thicker panels (0.05 m and more), as a consequence of reducing dark zones

430

and the associated biomass degradation through cell respiration. For example, a rise by 120%

431

of the annual yield per panel is observed for a panel thickness of 0.1 m and a panel distance of

432

1 m. For future work in this field it would be interesting to analyze biomass productivities for

433

optimal combinations of cell density and panel thickness. Such an optimal combination would

434

depend on the location, the orientation of the panels, the season of the year and other

435

conditions. However, it has to be noted that lower cell concentrations can negatively affect

436

downstream processing, e.g. cell harvest. In any case, a careful techno-economic assessment

437

is required to identify the most suitable combination of panel thickness, panel distance and

438

optical density of the algae suspension for the given site-specific physical and economic

439

boundary conditions.

440

The influence of the orientation of reactor panels on biomass yields are examined for

441

all selected U.S. locations (Supporting Information, Figure S22). Reactors are assumed to face

442

east and west or north and south. The analysis shows that for the considered locations and

443

ranges of panel thickness and distances, a north-south orientation of reactors tends to result in

444

higher annual biomass yields. The reasons for this finding are complex and relate to the

445

duration of light exposure, local light intensities, temperature regimes and seasonal variations.

446

Even though a general superiority of a north-south orientation was observed for the studied

447

locations, a thorough assessment of the most suitable orientation is required for any specific

448

plant set-up and local conditions of a potential cultivation site.

449 450

Influence of Geographic Location. Knowledge of the influence of the geographic

451

location on biomass yield is particularly important in the planning phase of a commercial

452

cultivation plant. Thus, biomass yields were analyzed for six U.S. locations in different 20 ACS Paragon Plus Environment


Page 22 of 32

453

climate zones (Table 1). Results of this analysis are presented in Table 3 for panel distances

454

between 0.4 and 0.75 m, a panel thickness of 0.025 m and north-south orientation of the

455

panels. These design parameters are considered most suitable for commercial algae

456

cultivation as described above. Biomass yields simulated for a wider spectrum of design

457

parameters can be found in the Supporting Information (Figure S21).

458 459

Table 3. Simulated algae biomass yields for different geographic locations and various panel

460

distances, d (panel thickness, 0.025 m; orientation, north-south). Location

Areal yield

Yield per panel

[kg m-2 a-1]

[kg panel-1 a-1]

d = 0.4 m

d = 0.5 m d = 0.75 m

d = 0.4 m

d = 0.5 m d = 0.75 m

Forks, WA

9.9

9.6

8.4

8.4

10.1

13.0

Boston, MA

10.3

9.4

7.7

8.8

9.9

12.0

Sacramento, CA

11.5

10.0

6.6

9.8

10.6

10.3

6.7

5.5

3.8

5.7

5.6

6.0

New Orleans, LA

10.1

9.3

6.9

8.5

9.8

10.7

Hilo, HI

11.3

10.7

8.1

9.6

11.3

12.6

Phoenix, AZ

461 462

With the exception of Phoenix, areal yields of about 10 kg m-2 a-1 in combination with

463

yields per panel of around 10 kg panel-1 a-1 can be achieved at all of the examined locations.

464

Biomass yields in Phoenix are substantially lower compared to other locations, as the hot and

465

arid climate leads to overheating of the reactors. With extremely high reactor temperatures,

466

production is brought to halt for elongated periods during summer, indicating that microalgae

467

cultivation in closed PBRs is not a suitable option in such climates (exemplary temperature

468

and productivity profiles are displayed in the Supporting Information, Section S3.3).


Page 23 of 32


469

In contrast, it is astonishing that northern locations, such as Forks and Boston, offer

470

the potential for comparably high biomass yields. This observation is also linked to the local

471

prevailing climates. The Köppen-Geiger climate classification

472

Forks as temperate with warm summers, while the climate in the Boston area is classified as

473

cold with warm/hot summers. Under these climatic conditions, winter is not long enough to

474

severely reduce annual biomass output. During summer, however, northern locations such as

475

Boston and Forks experience long periods of daylight with reactors being exposed to

476

moderately warm ambient temperatures, posing a low risk of overheating of the cultivation

477

medium. In this context, it is important to point out that the used mechanistic growth model is

478

based on specific growth parameters of an algae strain that maintains relatively high growth

479

rates even at cultivation temperatures below 15 °C

480

growing under cold conditions, yield expectations have to be reduced for northern locations.

37

50

describes the climate in

. For strains that are less adapted to

481

The probably most suitable locations for algae cultivation correspond with tropical

482

(Hilo, HI) and Mediterranean climates (Sacramento, CA) with potential biomass yields

483

exceeding 11 kg m-2 a-1.

484 485

Implications for Commercial Algae Cultivation in PBRs. In the present work,

486

potential biomass outputs for microalgae grown in vertical flat panel PBRs were analyzed for

487

a wide variety of plant designs and climate zones. Realistic large-scale outdoor cultivation

488

conditions were simulated in high detail.

489

The results show that areal microalgae yields of around 10 kg m-2 a-1 (100 t ha-1 a-1)

490

and more can be potentially achieved. This by far exceeds biomass yields of land-based

491

energy crops, for example of fast growing trees cultivated in short-rotation coppice

492

plantations in Europe (5 to 18 t ha-1 a-1) 55, North America (10 to 12 t ha-1 a-1) 56 or Brazil (20

493

to above 30 t ha-1 a-1) 57. To make use of these potentials, producers should limit the thickness

494

of the reactor panels to 0.05 m and use a panel spacing of 0.4 to 0.75 m (other panel distances 22 ACS Paragon Plus Environment


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495

might be required if the reactor height deviates from the standard height of 1 m used

496

throughout this study; please refer to the Methodology section). Our results also indicate that

497

a north-south orientation of reactor panels is preferable to an east-west orientation for most

498

locations.

499

The reactor temperature is critical for outdoor biomass generation. Even in moderately

500

warm areas, reactor temperature can repeatedly exceed 40 °C during one year of cultivation.

501

Thus, it is mandatory to focus on temperature-robust strains or even thermophilic species. Hot

502

and arid areas are often considered promising for algae cultivation, as they offer cheap land

503

that is not used for food production, coupled with high levels of solar irradiation. Our results,

504

however, indicate that overheating of the reactors may substantially reduce biomass yields in

505

these areas. Active cooling of reactors, e.g. spray cooling, represents an option to avoid

506

overheating and mitigate yield losses. However, the installation of heat exchangers, pipes and

507

pumps would significantly impact the economic viability. Pumping of the required volumes

508

of cooling medium would affect the energy balance of cultivation, and the increased

509

consumption of fresh water would pose severe environmental and social risks, particularly in

510

arid regions where water is scarce and the need for cooling is most urgent. We analyzed the

511

effect of active cooling, limiting reactor temperatures to 40 °C, for the locations Sacramento,

512

CA, and Phoenix, AZ (Supporting Information, Section 3.6). The analysis shows that yields in

513

Phoenix, representing a location in a hot and arid region, can be strongly increased through

514

cooling especially when maximizing yields per panel. The effect of cooling is less

515

pronounced for Sacramento, as the risk of overheating is substantially lower at that location.

516

In the context of the potential benefit of cooling, we note that conclusions regarding the

517

environmental, economic and social sustainability of cooling can only be drawn on the basis

518

of a detailed life cycle analysis and cost assessment, which is beyond the scope of the present

519

work.


Page 25 of 32


520

As the developed simulation tool has been shown to be a valuable asset in the process

521

of integrated plant design, future work should be directed to the refinement of the model. In

522

this context, the model should be extended to cover further promising reactor types and algae

523

species. Most importantly, the simulation tool should be validated against experimental data.

524

We did not have access to a suitable reactor array in the course of the present study. An

525

experimental validation of the model, however, would add to the value of the generated

526

results and may lead to further refinements. The experimental validation should consequently

527

be the next step in future research efforts.

528 529

ASSOCIATED CONTENT

530

MATLAB model can be obtained from the corresponding author upon request; Supporting

531

Information: Description of the productivity model; validation; additional results

532 533

ACKNOWLEDGEMENTS

534

We gratefully acknowledge the financial support by the German Federal Ministry of

535

Education and Research (Project: Advanced Biomass Value, 03SF0446C) and the support

536

granted by the TUM Graduate School. We further thank Christoph Falter, Valentin Batteiger

537

and Andreas Sizmann for their advice and many fruitful discussions.

538 539

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