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A Thermal Reactor Model for Large-Scale Algae Cultivation in Vertical Flat Panel Photobioreactors Christian Hermann Endres, Arne Roth, and Thomas Brück Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b05414 • Publication Date (Web): 07 Mar 2016 Downloaded from http://pubs.acs.org on March 13, 2016

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Environmental Science & Technology

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TITLE

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A Thermal Reactor Model for Large-Scale Algae Cultivation in Vertical Flat Panel

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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, 85521 Ottobrunn, Germany, Tel. +49-

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89307484948, E-mail: [email protected]

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b

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Division of Industrial Biocatalysis, Department of Chemistry, Technische Universität

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München, Lichtenbergstraße 4, 85748 Garching, Germany

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ABSTRACT

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Microalgae grow significantly faster than terrestrial plants and are a promising feedstock for

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sustainable value added products encompassing pharmaceuticals, pigments, proteins and most

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prominently biofuels. As the biomass productivity of microalgae strongly depends on the

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cultivation temperature detailed information of the reactor temperature as a function of time

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and geographical location is essential to evaluate the true potential of microalgae as an

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industrial feedstock. In the present study a temperature model for an array of vertical flat plate 1 ACS Paragon Plus Environment


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photobioreactors is presented. It was demonstrated that mutual shading of reactor panels has a

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decisive effect on the reactor temperature. By optimizing distance and thickness of the panels

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the occurrence of extreme temperatures and the amplitude of daily temperature fluctuations in

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the culture medium can be drastically reduced, while maintaining a high level of irradiation

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on the panels. The presented model was developed and applied to analyze the suitability of

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various climate zones for algae production in flat panel photobioreactors. Our results

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demonstrate that in particular Mediterranean and tropical climates represent favorable

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locations. Lastly, the thermal energy demand required for the case of active temperature

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control is determined for several locations.

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TOC ABSTRACT

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INTRODUCTION

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Microalgae grow significantly faster than terrestrial plants and can accumulate large quantities

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of lipids.1–5 Additionally agricultural land or freshwater is not necessarily required for algae

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cultivation.4–8 Therefore, microalgae are considered a promising sustainable feedstock for a

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broad range of value added products encompassing pharmaceuticals, pigments, proteins and,

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most prominently, biofuels.1,9–12 Various concepts for cultivating microalgae are currently

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under development, generally classified as either closed photobioreactors or open ponds.

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While open pond cultivation is normally characterized by a simple system configuration,

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

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increased system complexity.2,13,14

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The crucial aspect of algae cultivation from an economic perspective is the biomass yield in

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relation to the required effort and investments. One of the most important parameters

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effecting the yield is the temperature of the cultivation medium (in addition to solar

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irradiation and nutrient availability).15,16 A typical range for algae cultivation is 10 °C to

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40 °C. Temperatures below 10 °C usually result in very low growth rates. At subzero

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temperatures ice formation in the reactor and at instrumentations poses an additional problem.

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Temperatures above the 40 °C-threshold are only tolerated by few thermophilic algae and

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may lead to cell death in case of less adapted species. It is therefore mandatory to keep algae

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within a favorable temperature regime, preferably close to the optimum temperature of the

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respective strain, to guarantee high biomass production rates.

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In a laboratory environment temperature can easily be controlled. This cannot be applied to

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the same extent in an industrial-sized plant, as temperature regulation would require the

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installation of heat exchangers, pumps and pipes, thus substantially adding to capital and

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energy costs. However, without active temperature control, closed photobioreactor systems

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may overheat during hot days with reactor temperatures reaching values up to 55 °C.17

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Consequently, it is crucial to evaluate the time-dependent reactor temperature profile already 3 ACS Paragon Plus Environment


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in the planning phase of a commercial microalgae cultivation plant. In this respect an accurate

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process simulation allows the assessment of the economic potential with reference to a given

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geographical location and plant design.

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Recently, several studies reported on the development of temperature models and

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complementary research involving various types of microalgae cultivation systems.18–23 Those

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studies differ widely in terms of scope (e.g. type of reactor system) and levels of accuracy.

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One of the most advanced temperature models for a closed photobioreactor system has been

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reported by Béchet et al.18,19 Their model computes the reactor’s heat balance as a function of

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various static and dynamic parameters for a bubble column reactor concept, a system mostly

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used in laboratory-scale experiments. One current limitation of this important study is that

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only a single, stand-alone reactor was considered. The reported approach thus neglects

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shading effects that naturally occur in larger applications. To date, shading effects on reactor

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temperature have only been taken into account by a single study.23 However, in the respective

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publication shading was only examined as a static parameter, neglecting the effects of the

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sun’s position with respect to the orientation and geometry of the panels.

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In our study, we now introduce a dynamic temperature model for a complete array of flat

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panel photobioreactors providing a new framework for the economic assessment of algae

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processes under industrial relevant conditions. We have selected flat panel reactors because

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they represent one of the most commonly used closed photobioreactor systems for academic

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research13,21,24–26 and commercial activities alike.27,28 In our model the heat balance is

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calculated as a function of a broad range of parameters such as reactor geometry (e.g. panel

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thickness), inter-panel distance, orientation of reactor panels (north-south vs. east-west) as

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well as local climatic conditions and irradiation. All first order reflections are taken into

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account and a detailed multilayer ground model is introduced allowing for an accurate

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calculation of its thermal radiation. Both features represent significant advances with respect

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to the current literature. Most importantly, mutual shading of the reactor panels, calculated as 4 ACS Paragon Plus Environment

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a dynamic function of the sun’s position and reactor dimensions is taken into account for the

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first time. The functionality of the proposed model is demonstrated in an extensive parameter

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study for various locations in the U.S. Trade-offs between parameters are identified and

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discussed. It is demonstrated that shading has a massive impact on both, reactor temperature

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and the amount of available light for photosynthesis.

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The temperature model introduced in this paper therefore represents a substantial step forward

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relative to the work conducted in this field so far and provides a valuable basis for the site-

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specific estimation of microalgae productivities, and thus for the assessment of the economic

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and environmental performance.

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METHODOLOGY

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Photobioreactor Characteristics. The cultivation system selected for this work is an array of

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vertical flat plate photobioreactors. The single reactors are arranged in long parallel lines. An

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illustration of the concept can be found in the supplementary information (Fig. S1). Reactors

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at the borders of the array are neglected as they receive higher levels of irradiation not being

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representative for the majority of reactors in the field. Each single reactor is defined by its

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dimensions (panel thickness, height and width) and the distance to the opposing panels. The

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reactor volume is given by the respective reactor dimensions. Within this study the width and

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height of the reactor are kept constant at 2 m and 1 m, respectively. Even though a fixed panel

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height is used throughout the publication, the presented results can be easily transferred to

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other reactor heights, provided that the ratio between reactor height and panel distance is kept

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constant (Fig. S8, supplementary information). Thus the thermal behavior of a reactor that is 1

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m high and 0.5 m apart from the next panel is basically identical to a reactor of 2 m in height

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with a panel distance of 1 m.

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For heat exchange only the back and front surfaces of the reactor panel are considered and the

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small areas at the edges of the reactor are neglected. The culture medium is continuously 5 ACS Paragon Plus Environment


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homogenized (pneumatic agitation), therefore temperature is assumed to be constant over the

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reactor volume at a certain point in time. As the reactor wall is thin, the temperature of the

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wall is considered to be identical to the temperature of the culture medium. Site-specific

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meteorological and irradiation data were adopted from the National Solar Radiation Data

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Base.29 The provided data sets describe a typical meteorological year and are specifically

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intended for computer simulations of solar energy conversion systems.

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Temperature Modeling Approach. The calculation of the reactor temperature is based on a

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balance of all relevant heat fluxes, which can be expressed by the following equation

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Equation 1 R R R 2 − 1 = ∙ ∆,

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with the reactor volume VR, the density ρR (997 kg m-3) 30 and the specific heat capacity of the

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culture medium cpR (4181 J kg-1 K-1) 30T1 and T2 are the reactor temperatures at the beginning

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and the end of the considered time interval, ∆t, and Q̇i represents heat fluxes affecting the

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reactor.

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Solving the equation for T2, the temperature at the end of each interval can be calculated from

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the temperature of the previous time step, provided that all heat fluxes are known. Using

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MATLAB® (The MathWorks®, Inc., Natick, MA) as software environment for the simulation,

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the reactor temperature and heat fluxes are updated every minute, resulting in 525 601 data

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points for a complete year. The time to generate a single temperature profile amounts to

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approximately 12 min (Intel® Core™i5 2.53 GHz, 4 GB RAM). The starting temperature for

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the culture medium was set to 20 °C and the following heat fluxes are considered in the

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model: 6 ACS Paragon Plus Environment

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- Direct sunlight

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- Diffuse sunlight

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- Atmospheric long-wave irradiation

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- Heat radiation from the reactor panels

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- Heat radiation from the ground

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- Reflections of direct, diffuse and thermal radiation at the reactor panels

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- Reflections of direct, diffuse and thermal radiation at the ground

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- Heat transfer through natural air convection

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- Heat transfer related to the aeration of the reactor panels

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Calculation Details of Heat Fluxes. In the following fundamental assumptions and details

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regarding the calculation of the heat fluxes are explained. For a complete mathematical

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description please refer to the supporting information.

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The amount of direct sunlight contributing to increase the reactor temperature depends on the

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angle the sun beams make with the reactor surface. This angle of incidence is calculated for

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every data point.31 Part of the incident sunlight is lost for the reactors due to reflections at the

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reactor wall. The reflection losses are calculated with the Fresnel equation, assuming the

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reflectivity index of air, the reactor wall (glass, plastic) and the culture medium (water) being

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1, 1.5 and 1.33, respectively. In contrast to the case of an isolated reactor, an array of flat plate

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photobioreactors causes shading, and thus reduces the amount of light reaching the panel

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surface. The equations used in this study to determine this heat flux are based on published

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literature32.

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Not all sunlight reaching the surface of the reactor is converted into heat, but part of it is

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scattered/reflected back by the algae cells. Béchet et al.18 approximated the absorptivity of

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algae biomass based on Kirchhoff’s law of thermal radiation that states that for a given 7 ACS Paragon Plus Environment


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wavelength, emissivity and absorptivity of a material are identical. However, the emissivity is

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often measured for wavelengths in the far infrared and is therefore not suited to determine the

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absorptivity in the visible spectrum of light. This becomes obvious when looking at the

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emissivity of water, which has a value of around 0.9 for a temperature of 273 K.33 Assuming

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that the emissivity determined for infrared radiation equals the absorptivity in the visible

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spectrum of light, water would absorb 90 % of the incoming light. As most of the light is

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absorbed, water would appear as very dark body. In the present study the emissivity is only

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used for radiation in the far infrared, while the albedo is utilized as a measure for the

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reflectivity of the algae cells in the visible spectrum of light. For dense algae cultures an

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albedo of 0.3 is used. This value is in accordance with typical values for thick, plant leaves.34.

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As we assume that light is either absorbed or reflected by the opaque algae culture,

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transmission through the panels is zero and not considered in the temperature model. The

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influence of the albedo on central outcomes of the temperature simulation is further discussed

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in the supporting information (Sec. S2.2).

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Atmospheric longwave radiation is thermal radiation from the air layers above the cultivation

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plant. Therefore, this heat flux can be expressed by the Stefan-Boltzmann-law. The emissivity

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of the atmosphere depends on factors such as the humidity of the air and cloud coverage. In

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our model the Brutsaert-Equation35 in combination with the cloud cover model by Crawford

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and Duchon36 is used to calculate this emissivity.

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Analogous to atmospheric radiation, heat radiation of the ground is calculated with the Stefan-

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Boltzmann equation. The temperature of the top soil layer is determined with a multilayer

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ground temperature model. The heat exchange between different soil layers is taken into

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account as well as the property of the ground to store thermal energy. The first, top layer is

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exposed to the environment and thus affected by irradiation and convection. Additionally, all

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ground layers exchange thermal energy via heat conduction. In total the model consists of 13

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layers of varying thickness and reaches down 16.4 m. The first layer is 2 mm thick and 8 ACS Paragon Plus Environment

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thickness doubles for every further layer. Very fine layers near the top soil are required to

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display daily temperature fluctuations. With increasing depth these fluctuations are less

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pronounced and therefore thicker layers are considered in order to reduce computing time. At

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a depth of 16.4 m the temperature is considered constant during the year, which is in

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accordance with actual measurements of the soil temperature.37,38

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As in particular deep soil layers are capable to store thermal energy for a long time, it is

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essential to choose realistic ground temperatures as starting condition for the simulation. In

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order to determine these temperatures, an iterative procedure is used, where the ground

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temperatures of the last time step in December form the starting condition of the next

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iteration. A detailed description of the ground layer model can be found in the supporting

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information.

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First order reflections between the panels and between panel and ground are considered in the

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model (see supporting information). The heat exchange between the air and a vertical flat

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plate is calculated based on equations for natural convection.33 For simplification it is

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assumed that convection at a panel surface is not influenced by convection at the ground or

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other panels. Forced convection caused by wind is neglected for two reasons. Firstly, wind

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speed is generally measured 10 m above the ground, thus wind speed near the ground would

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be substantially lower. Secondly, the array of vertical flat plate photobioreactors provides

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protection from wind.

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The last heat flux considered in the model is heat exchange caused by aeration of the

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photobioreactors. Various elements contribute to this heat flux. First, heat is exchanged due to

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the different temperatures of the instreaming gas bubbles and the culture medium. Second,

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during their way through the reactor, gas bubbles are saturated with water from the medium.

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Third, prior to injection, the gas is compressed in order to overcome the hydraulic pressure in

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the reactor. As the bubbles rise through the reactor they expand releasing the compression

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energy. All these elements are taken account of to calculate the heat flux. 9 ACS Paragon Plus Environment


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RESULTS AND DISCUSSION

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Temperature Profiles as Function of Geographic Location. In a primary step, the general

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temperature profiles are analyzed and characterized (Fig. 1). For this purpose, we selected

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three US locations within three different climate zones. Of the chosen locations, Boston in

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Massachusetts corresponds to a cold climate according to the Köpper-Geiger climate

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classification.39 By contrast, Sacramento in California and Hilo in Hawaii are situated more

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south and therefore have a temperate climate, with dry summers (Mediterranean) and a

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tropical climate respectively. Temperature profiles of additional locations, varying panel

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distances and east-west panel orientation are described in the supporting information (Fig. S9

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– S11). For the interpretation of the presented temperature profiles it is important to keep in

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mind that the selected panel distance of 0.5 m already results in significant shading of the

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panels.

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Figure 1. Temporal temperature profile for photobioreactors located in (A) Boston, MA, (B)

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Sacromento, CA and (C) Hilo, HI. Black and grey lines correspond to the reactor and air

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temperature respectively. (panel distance: 0.5 m, panel thickness: 0.05 m, orientation: north-

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south)

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In all instances the reactor temperature (black line) follows the daily and diurnal fluctuations

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of the air temperature (grey line). However, the average temperature of the reactors is slightly

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warmer and day-night-cycles are more pronounced. In summer the reactor temperature may

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exceed 40 °C even for cold climates such as Boston, posing a potential threat for cell

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cultures.15,16 Additionally, reactor and air temperature in Boston drops to 0 °C and below for 11 ACS Paragon Plus Environment


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nearly one quarter of the year. Under these circumstances the cultivation time is rather

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limited. Both Sacramento and Hilo show less extreme reactor temperature profiles. In

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Sacramento, the reactor temperature drops below 0 °C only on few days of the year while it

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occasionally exceeds 40 °C. In Hilo on Hawaii, the reactor and air temperature stays

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constantly at an elevated level, which is typical for a tropical climate. However, the reactor

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temperature also exceeds 40 °C at some days for the chosen reactor geometry.

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As demonstrated above, Sacramento with its Mediterranean climate is well suited for

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cultivating algae. Moreover, the profile shows a seasonal temperature cycle, typical for all

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non-tropical regions. Thus, Sacramento is selected as exemplary site for further parameter

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studies (Fig. 2 to 4).

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Analysis of Affecting Heat Fluxes. To optimize thermal management, it is essential to

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understand the impact of the various heat fluxes on the total heat balance of the reactor. We

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thus analyzed the time-related profiles of the most important heat fluxes during three

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exemplary days in late spring (Fig. 2A).

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Figure 2. (A) Temporal course of the most important heat fluxes affecting the reactor

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temperature. (B) Yearly average of the positive value of the heat fluxes. (for both subfigures:

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location: Sacramento, panel distance: 0.5 m, panel thickness 0.05 m, orientation: north-south)

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As expected most heat fluxes follow the typical day-night-cycle. Additionally, heat fluxes

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such as direct (“DNI”) and diffuse irradiation (“DHI”) strongly depend on daily weather

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conditions. For days with essentially no clouds, heat resulting from direct sunlight is very

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high (day 114). In contrast, for a 100 %-cloud coverage (day 116), direct sunlight is

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significantly reduced, while at the same time diffuse radiation increases, as more light is

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scattered by the water molecules in the atmosphere. Diffuse light is partially compensating for 13 ACS Paragon Plus Environment


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the losses of direct irradiation, but the overall heat flux still decreases with increasing cloud

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coverage. When clouds occasionally pass the sun (day 115), the temporal profiles of direct

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radiation displays several peaks in contrast to the smooth profile of day 114. The individual

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peaks represent phases of partially blue sky, when direct light is momentarily not blocked by

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clouds.

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To quantify the total impact of the heat fluxes the yearly average of the positive value is

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calculated and compared (Fig. 2B). On a yearly basis, the reactor heat radiation (“Reac. IR”)

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is the most important of all heat fluxes, followed by the ground heat radiation (“Ground IR”)

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and the atmospheric heat radiation (“Atmos. IR”). Heat from the visible spectrum of light,

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DNI and DHI, contributes only to around 6 % to the total heat flux. However, they represent

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the only light fraction that can be converted via photosynthesis into biomass. All further heat

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fluxes, mostly reflections of the ground and the reactor panels, contribute around 5 % to the

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total heat flux and are not displayed separately but treated as combined heat flux in the figure

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(“Other”). In this context, it is important to note, that even though individual reflection-related

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heat fluxes only have minor impact on the heat balance, the sum of all these heat fluxes is

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comparable to the irradiation of sunlight. Thus, reflections have to be taken into account for

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simulations of the temperature in closed photobioreactors.

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Captured Sunlight as Function of Reactor Geometry. A photobioreactor is a biomass

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production system. Consequently, it is important to evaluate its ability to produce biomass in

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the context of temperature management. As biomass production is driven by radiation in the

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visible spectrum of light, the energy of sunlight captured by the reactor panels is used as a

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figure of merit to analyze the performance of photobioreactor systems. (Fig. 3)

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Two performance indicators are examined. First, captured sunlight is related to the ground

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area occupied by the reactor panels, being a measure for the areal productivity of a given

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panel array (lines with empty markers, left y-axis). Second, captured sunlight is related to the 14 ACS Paragon Plus Environment

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reactor volume (lines with filled markers, right y-axis). Within certain limits, more light per

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volume translates into higher biomass productivity and therefore into lower operational and

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capital costs. Captured sunlight with respect to the reactor volume thus can be described as a

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measure for the efficiency of a photobioreactor system.

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Figure 3. Quantity of captured sunlight with respect to the ground area and the reactor

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volume displayed as function of the panel distance and panel thickness. Lines with empty

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markers and filled markers correspond to the left and right y-axis, respectively. Square, circle,

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diamond and triangle markers indicate panel thicknesses of 0.025 m, 0.05 m, 0.1 m and

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0.15 m. (location: Sacramento, CA, orientation: north-south)

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According to Figure 3, the captured sunlight per ground area increases with decreasing panel

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distance until it peaks at a distance between of 0.2 m and 0.4 m. This peak is a result of a

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simplification made for the calculation in the model. Typically the top surface can be

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considered small in comparison to the sides of the reactor. Additionally the top may be

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covered by a frame holding the panel or instrumentations preventing the light from entering

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the reactor. Therefore, the top area is neglected in the current model for heat exchange 15 ACS Paragon Plus Environment


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including irradiation. However, for the case of a transparent top surface, i.e. light can enter

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the reactor through the top, captured sunlight related to the ground area would constantly

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increase even for small panel distances and be basically independent of the panel thickness

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(not shown here).

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The theoretical maximum value for the areal light capture is represented by the global

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horizontal irradiation (GHI). For the given location, Sacramento, the average GHI is

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6491 MJ m-2 a-1. Though, even for small panel distances this value cannot be reached, as a

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fraction of the incident light always is reflected back to the atmosphere. For the given

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configurations around two thirds of the GHI can be captured by the reactor panels.

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When captured sunlight is not related to the ground area but to the reactor volume small panel

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distances are not very favorable, as only little light is captured by the individual panel. By

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increasing the panel distance, more and more light is captured per culture volume up to a

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distance of around 2 m. From this point onwards the captured sunlight per reactor volume

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stays more or less constant.

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As small panel distances lead to good areal productivities and large panel distances result in

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high photobioreactor efficiencies trade-offs are necessary to optimize the overall performance

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of an algae cultivation plant. As already mentioned, panel distances above 2 m are no

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reasonable option as the light captured by the reactor increases only very moderately while

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the areal productivity decreases at the same time. Conversely, very small panel distances

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below 0.3 m would require a great number of reactors to capture the sunlight resulting in high

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investment costs. Thus, panel distances between 0.3 m and 2 m appear the most interesting

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range in terms of biomass productivity. Most notably, small panel thicknesses exert a positive

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effect on captured sunlight related to the reactor volume, while having neutral to positive

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effect (depending whether the top surface area is neglected or not) when related to the ground

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area. Thus, from a performance point of view, thin panels should be preferred in production

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plant design. 16 ACS Paragon Plus Environment

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Limitations in Cultivation Time as Result of Extreme Reactor Temperatures. The

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thermal behavior of the reactor as a function of the panel thickness and panel distance is

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examined in Figure 4. For this purpose the temperature range for technically and

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economically reasonable algae cultivation is set to 0 °C – 40 °C. The temperature model is

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applied to compute the number of days in a year when reactor temperature exceeds (Fig. 4A)

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or drops below (Fig. 4B) those limits. The remaining days correspond to the total cultivation

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time.

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Figure 4. (A) Number of days too hot (Treactor > 40 °C) and (B) days too cold (Treactor < 0 °C)

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for algae cultivation displayed as function of the panel distance and panel thickness. Square,

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circle, diamond and triangle markers correspond to panel thicknesses of 0.025 m, 0.05 m,

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0.1 m and 0.15 m, respectively. (location: Sacramento, CA, orientation: north-south)

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According to our results, both panel distance and thickness of the panels strongly influence

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the thermal behavior of the reactor. For small distances and thicknesses the number of

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extreme temperature events in both directions of the temperature scale is very small. Thus

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nearly year-round cultivation is possible at the exemplary site of Sacramento. However, with

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increasing panel distances and decreasing panel thicknesses the number of days with

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temperatures outside the tolerable range significantly increases. Interestingly, this not only

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true for hot periods, as during cold phases tighter packed panels ‘loose’ less heat to the

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atmosphere than further distanced panels.

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Very thin panels are especially prone to extreme reactor temperatures. Therefore, cultivation

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time may be reduced to less than half of the year under certain conditions. In order to still

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make use of thin panels in outdoor cultivation, it is therefore advisable to choose a small

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panel distance in order to reduce the number of days with extreme temperatures. Thicker

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panels are less sensitive to extreme temperature events as they contain a larger liquid volume

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and react slower on the influence of the various heat fluxes. Hence, from an exclusive

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temperature management point of view, thick reactor panels should be preferred to thin

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panels.

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However, the reactor performance, expressed by the amount of captured sunlight, improves

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with decreasing panel thickness (Fig. 3). Considering both, temperature management and

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reactor performance, it is thus advisable to choose a medium panel thickness of 0.05 m to

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0.1 m. In order to optimize areal productivity and reduce extreme temperature events a panel

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distance of 0.5 m to 1 m appears reasonable.

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Suitability of Various Geographic Locations for Algae Cultivation. Among other criteria,

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the suitability of a location for algae cultivation depends on the quantity of sunlight provided

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at the respective site. Moreover, temporal reactor temperatures determine the total cultivation

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time. Taking both aspects into account for various US-locations, we calculated the quantity of 18 ACS Paragon Plus Environment

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captured sunlight at days of tolerable reactor temperatures (0 °C – 40 °C) (Fig. 5A, light grey

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bar). The considered spots, from north to south are: Forks (WA), Boston (MA), Sacramento

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(CA), Phoenix (AZ), New Orleans (LA) and Hilo (HI). Further, for comparison, the GHI

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(black bar) and the captured sunlight without temperature-related limitation in cultivation

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time are determined (medium grey bar). Based on our previous results a panel distance of

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0.5 m and a panel thickness of 0.05 m are chosen for the analysis.

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396 397 398

Figure 5. (A) Captured sunlight received at days of tolerable temperatures (0 °C ≤ Treactor ≤

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40 °C) in relation to captured sunlight for all reactor temperatures and in relation to the global

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horizontal irradiation. (B) Heating and cooling demand for various temperature regimes and

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locations. (for both subfigures: panel distance 0.5 m, panel thickness 0.05 m, orientation:

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north-south)

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As expected, GHI increases from the most northern location Forks over Boston and

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Sacramento to Phoenix. As a consequence of typically high cloud coverage in subtropical and

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tropical regions, the GHIs in New Orleans and Hilo (yearly average around 6000 MJ m-2 a-1)

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do not reach the value of Phoenix (7500 MJ m-2 a-1).

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According to the GHI, Phoenix in Arizona has the highest potential for algae production.

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However, the ‘true’ production potential is much lower (light grey bar). As the temperature of

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the culture medium in Phoenix often exceeds 40 °C, the cultivation period is limited to a

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relatively small fraction of the year. This indicates that deserts are not a favorable site for

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algae production in photobioreactors. According to our study the best places for algae

413

cultivation can be found in Mediterranean (Sacramento) and tropical climates (Hilo).

414 415

Energy Requirements for Active Temperature Control. Apart from passively controlling

416

the cultivation temperature by thermally optimizing the reactor design, temperature can be

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actively controlled through a cooling and heating system. We therefore calculated the thermal

418

energy that has to be removed (negative values) or applied (positive value) in order to keep

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the reactor temperature within certain intervals (Fig. 5B). For interpretation of the results, this

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thermal energy demand is related to the energy content stored in form of algae biomass:

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Assuming an areal productivity of 20 g m-2 d-1 and a heating value of 22 MJ kg-1 for algae

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biomass40, the amount of chemical energy bound in algae biomass is 161 MJ m-2 a-1. For cold

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climates this value is often in the same order of magnitude as the thermal energy required to

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heat the reactors, e.g. the thermal energy required to keep the temperature above 0 °C in

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Boston is around 400 MJ m-2 a-1. Thus heating is only a reasonable option if algae are not

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cultivated for energetic use or if waste heat from other sectors could be adopted.

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In order to remove thermal energy from the reactors, a cooling medium is required. Assuming

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that 500 MJ m-2 a-1 of thermal energy need to be removed, around 35 t m-2 a-1 of water are

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required when the temperature difference of incoming to outgoing cooling water is 15 °C. 20 ACS Paragon Plus Environment

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Further assuming that the water source is situated 10 m below plant level, around

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3.5 MJ m-2 a-1 of mechanical energy are required for pumping. When comparing this value to

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the 161 MJ m-2 a-1 provided by the algae biomass cooling is in principle an acceptable option.

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However, it has to be kept in mind that the energy to provide cooling water is usually higher

434

as friction losses in the pipes and the efficiency of the pump have to be considered. Moreover,

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the height difference between the water source and the algae plant can be larger than 10 m,

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resulting in a higher energy demand.

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Both, heating and cooling of the algae reactors requires the installation of heat exchangers,

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pumps, pipes, etc. Thus, even if cooling and heating are acceptable solutions from an

439

energetic perspective, active temperature control may still not be economically viable due to

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high investment costs.

441 442

Implications for Commercial Algae Cultivation in Photobiobreactors. It has been

443

demonstrated that temperature simulation is important to adequately assess the potential of

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algae cultivation at specific geographical locations. Additionally, temperature simulation can

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be used to optimize reactor dimensioning with respect to both, light input and cultivation

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temperature. Therefore, temperature simulation represents a significant asset to the process of

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an integrated reactor and plant design. In this context, mutual shading of the panels has a

448

decisive effect on reactor temperature and should not be neglected.

449

Algae cultivated in outdoor photobioreactors are exposed to strong temperature variations.

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According to our simulations, at most of the examined locations reactor temperature exceeded

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40 °C at least once during summer. In winter, however, very cold reactor temperatures around

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0 °C are common for nearly all climates with the exception of tropical regions. Consequently,

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it is essential for commercial cultivation that algae strains can withstand such unfavorable

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temperatures, in particular the occurrence of temperature peaks exceeding the 40 °C

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threshold. High productivity over a broad temperature range might prove economically 21 ACS Paragon Plus Environment


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beneficial and should therefore be taken into account for strain selection. As an alternative to

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a single algae strain for year-round cultivation two strains, one adapted to cold and one to

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warm cultivation temperatures, can be utilized in different seasons.13,41,42

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Lastly, our study indicates that deserts represent very challenging areas for algae cultivation

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in closed photobioreactors. Although deserts usually provide high levels of irradiation and

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large areas of available non-arable land and are therefore suggested as suitable for algae

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cultivation, reactor temperatures in these regions may climb to 50 °C and above. As water for

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cooling reactors is usually rare in these areas, other technical modifications would be

464

necessary to reduce cultivation temperature. One option is the usage of nets spanned over

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panel rows that provide shade during the hottest times of the year. The impact of such an

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approach on reactor temperatures however is not clear and has to be addressed by future

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research. Furthermore, technical measures for cooling are generally associated with costs.

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Very few algae, mostly cyanobacteria, are capable of resisting cultivation temperatures of

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50 °C.43 By using such thermophile organisms algae cultivation in uncooled photobioreactors

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is theoretically possible even in hot environments like deserts. However, currently little

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practical experience exists for large-scale cultivation of thermophilic algae.

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In the context of the demonstrated importance of temperature simulation additional research

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should be focused on extending the simulation tool to cover promising reactor types other

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than flat panel reactors. Most important, however, is the implementation of a temperature-

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sensitive growth model for microalgae to compute realistic productivity values for outdoor

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algae cultivation plants and site-specific growth conditions. Such an implementation is subject

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to our ongoing work.

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ACKNOWLEDGEMENTS

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

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Education and Research (Project: Advanced Biomass Value, 03SF0446C) and the support 22 ACS Paragon Plus Environment

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

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Andreas Sizmann and Oliver Boegler for many fruitful discussions.

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ASSOCIATED CONTENT

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S1 Description of the temperature model, S2 Supplementary temperature simulations and

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related content. This information is available free of charge via the Internet at

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http://pubs.acs.org/.

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REFERENCES

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