Simulation-based study of the energy requirements linked to the temperature control of micro-algae culture in outdoor photobioreactors.

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1 Simulation-based study of te energy requirements linked to te temperature control of micro-algae culture in outdoor potobioreactors. Lorenzo Cappai 1*, Marie-Amélie de Ville d Avray 1, Ounayda Mdere 1, Jua Linnekoski 2, Eduardo Rodríguez Verdú 3, Eloy Cápuli Fernández 3 Affiliations: 1 CASPEO, 3 avenue Claude Guillemin, BP 36009, Orléans CEDEX 2, France 2 VTT Tecnical Researc Centre of Finland, Vuorimieentie 3 (Espoo), P.O. Box 1000, FI VTT, Finland 3 Bio Fuel Systems, Calle Sevilla, 6-8, San Vicente del Raspeig, Alicante, Spain Keywords: Potobioreactor, Solar energy, Temperature control, Termal balance, Simulation, Energy requirements ABSTRACT Outdoor microalgae potobioreactors are exposed to continuously variable weater conditions, causing permanent fluctuations of culture temperature tat must be limited witin a strain-dependent range. Te optimization of potobioreactor performance requires to be able to predict te culture temperature evolution and related power requirements as a function of weater conditions as well as potobioreactor design. Based on tis perspective, a termal model for vertical tubular potobioreactors was proposed and validated using experimental data from industrial-scale potobioreactors. Te model was ten used to predict te annual amount of energy required to maintain te culture temperature witin a desired range, for different reactor configurations and for several locations in te world. Te use of weater databases is of major importance to coose te best location to build microalgae production facilities and to optimize influent geometrical and operating parameters, wic can play wanted or unwanted roles depending on te meteorological conditions of te site. 1

2 1. Introduction Autotropic microalgae, wic use potons as energy source to fix carbon dioxide, are one of te most attractive new sources for cemicals, food, biofuels and ig-value bioactives ([1]; [2]; [3]). Tanks to teir ig potosyntetic yield compared to terrestrial plants, microalgae appear to be a major source of renewable biodiesel tat is capable of meeting te global demand for transport fuels [4]; owever, altoug microalgal biodiesel is tecnically feasible, its cost of production needs to be reduced by exploiting te biorefinery concept and acieving progress in PBR1 engineering. Culture systems to produce microalgal mass ave come a long way [5]. Currently, te most widespread large-scale microalgae production systems are open ponds and closed PBR tecnologies [6]. Open ponds are ceaper, but less efficient tan closed PBRs, wic ensure iger biomass productivity, better mixing, ligt and carbon dioxide utilization, less contamination, and require less land area ([7]; [8]; [9]). In particular, column PBRs offer te most efficient mixing, te igest volumetric mass transfer rates and te best controllable algae growt conditions [10]. However, te control of process parameters at an affordable cost is still a callenge. Te space and ligt requirements of massive biomass production imply tat microalgae farms will be outdoor and exposed to continuous fluctuations of climate variables suc as solar radiation, air temperature or wind speed. And, as ligt availability and culture temperature ave a strong influence on te rate of potosyntesis [11], it is crucial not to sift too far away from te optimal temperature of te produced algae species, wile ensuring sufficient available solar radiation. Consequently, PBR design must balance contradictory requirements: teir ratio of surface area to culture volume is generally maximized to ensure ligt availability, wic makes te system very sensitive to its environment regarding eat transfer. As a result, sunligt may overwarm te culture medium, even in vertical tubular PBRs, wic tend to eat less tan orizontal ones, wile at nigt te temperature can decrease below acceptable levels [12]. In most locations, temperature control is ten necessary to maintain te culture witin a favourable temperature range, wic induces ig infrastructure and operating costs [13]. Tis aspect cannot be neglected wen evaluating te economic feasibility of large-scale algae production systems. For a given location, finding a layout tat allows an almost passive termal regulation or at least limits te energy requirements could ence break a main limitation of tis tecnology. Tis implies to analyse and model te termal excange between te PBR and its environment. In tis perspective, Gutiérrez et al. [14] used a lumped parameter model to sow tat conventional energy usage could be reduced by optimizing te geometry and te sading device of an outdoor tank PBR. Bécet et al. [15] were te first to apply tis kind of approac to a column PBR, in order to predict te evolution of culture temperature as a function of location, reactor geometry and environmental variables. Te 1 PBR: potobioreactor 2

3 resulting model enables to predict te culture medium temperature, its canges and te energy required to maintain it witin acceptable ranges, and so to compare possible layouts. Pereira et al. [16] adapted tis model to flat plate PBRs in order to investigate te effect of various design parameters on brot temperature. Goetz et al. [17] proposed a dynamic termal model for intensified closed flat panel PBRs. However, none of te existing models can be directly applied for te optimisation of industrial-scale tubular potobioreactor configurations wit complex tree-dimensional geometry, in wic sading effects can ave significant impact on solar eat gain and tus on te evolution of culture temperature trougout te day. In tis perspective, te present work aims to propose a matematical modelling and simulation metodology to simulate eat transfers in a field of industrial-scale tubular PBRs, taking into account te sading effects generated by complex tree-dimensional PBR geometries, and to validate it experimentally. 2. Experimental Te present work is based on te study of a real microalgae production facility based in Alicante (Spain). Te system to be modelled, namely te potobioreactors, is described in Section 2.1. Te termal model and te metodology used for its validation are presented in Sections 2.2 and 2.3, respectively. Finally, te simulation tests performed wit te validated model are presented in Section Potobioreactors Te PBR used for tis study is described in Patent EP A1 [18]. Te PBR is composed of an arrangement of vertical annular columns, and eac column is composed of an outer tube and an inner tube (Fig. 1). Fig. 1. Vertical tubular PBR and cross sections of a single column (BFS, Alicante, Spain). 3

4 A tripase culture medium, composed of sea water, air bubbles and solid particles, flows in te annular space between te outer and te inner tube. Te inner tube is opened to te atmospere and tus in contact wit te surrounding air. Te culture from all te columns is mixed and recirculated, making te culture temperature uniform among te different columns. Te measuring point for evaluating te average culture temperature in te PBR is located just after te mixing operation. Due to te vertical structure of te PBR, te columns sade one anoter. As a result of tis, only a fraction of te total external surface of te PBR is exposed to direct sun radiation. Te parts and proportion of PBR surface exposed to direct solar radiation vary wit sun position, wic depends on geograpical location, day of te year and our of te day Termal model Te model accounts for te termal excanges between te microalgae culture contained in te PBR and its environment. It predicts te temporal evolution of culture temperature Energy balance Te model is based on te following assumptions: (1) Te culture is considered perfectly mixed and its temperature is tus assumed uniform in all columns; indeed, on-site measurements on a sunny day sowed tat temperature is uniform inside eac single column due to te ig turbulence, and tat te coolest column is generally 1.5 to 2 C freser tan te temperature in te measuring point, wile te ottest one is 1.5 to 2 C warmer. It is important to note tat on cloudy days tese temperature differences will be lower and tat te measured temperature after mixing will always be in between te ottest and fresest values. As te temperature gradient between columns is significantly lower tan te amplitude of culture temperature variation during 24 ours, and tat te scope of tis study is to evaluate te evolution of te average culture temperature, te assumption of a uniform culture temperature trougout te wole PBR volume is acceptable. (2) Te termal radiations emitted by te PBR, te air and te ground are neglected. Termal radiation refers to te energy emitted by objects due to teir temperature and te corresponding radiative transfer can be calculated according to te Stefan-Boltzmann law. However, according to Wien s displacement law, and given teir expected range of temperature values, te PBR, air and ground emit termal radiation in te far infrared, namely above 5000 nm. And yet, te constitutive material of PBR outer tube is PMMA (polymetyl metacrylate) wic is transparent at visible and near infrared wavelengts, but opaque in te infrared region beyond 2200 nm. As te majority of solar radiation lies witin te wavelengt range of nm, solar radiation is almost totally transmitted troug PMMA and absorbed by te culture, tus contributing to culture warming. However, te termal radiation 4

5 emitted by te culture is not transmitted by PMMA: tis penomenon is referred to as greenouse effects and contributes to culture warming. Similarly, termal radiations emitted by te surrounding air and ground are almost not transmitted to te culture by PMMA. (3) Te variations of entalpy associated to air and CO 2 inlet flows and water evaporation were evaluated and appeared negligible in comparison wit oter contributions (1% of te total energy excanged between te PBR and te environment). Tis is due to te fact tat te gas flows are very low compared to te total amount of culture, and te system is closed, limiting evaporation to te excange wit tese gases. Tese terms are tus neglected in te eat balance. Terefore, te termal model accounts for te solar radiation and for te eat transfer between te culture and te surrounding air by convection and conduction. Consequently, te temporal evolution of culture temperature can be modelled by te following ordinary differential equation: V l cult C pl dt dt cult Q rad _ sol inner_ tube S inner_ tube ( Tair Tcult) outer_ tubesouter_ tube ( T air T cult ) (1) were V cult (m 3 ) is te total culture volume contained in a PBR, T cult (K) is te culture temperature, ρ l (kg.m -3 ) is te culture density, C pl (J.kg -1.K -1 ) is te culture specific eat, Q rad_sol (W) is te solar radiation flux received by te culture, inner_tube (W.m -2.K -1 ) is te overall eat transfer coefficient between te culture and te air contained in te inner tube, S inner_tube (m 2 ) is te total cylindrical area of inner tubes of te PBR, T air (K) is te outside air temperature, outer_tube (W.m -2.K -1 ) is te overall eat transfer coefficient between te culture and te air surrounding te outer tube, and S outer_tube (m 2 ) is te total cylindrical area of outer tubes of te PBR Solar radiation flux Solar radiation impinging on te field of PBRs includes tree terms [19]: (1) Te direct, or beam solar radiation, wic is te solar radiation received from te sun witout aving been scattered by te atmospere; (2) Te diffuse solar radiation, received from te sun after its direction as been canged due to scattering by te atmospere. (3) Te reflected radiation, coming from surrounding objects and depending mainly on ground albedo [20]. Te sum of direct and diffuse solar radiations is referred to as total solar radiation. Depending on sun position, te amount of total solar radiation received by te culture can be significantly reduced, eiter by mutual sading between PBR columns, or by cast sadows created by surrounding buildings or objects. Terefore, it is essential to take into account te effect of sadows in te dynamic eat balance. In order to generalize te metod to any PBR geometry and surrounding environment, an approac based on 3D modelling of te PBR geometry was adopted to calculate te solar radiation. A single 5

6 PBR (Fig. 2 (a)) and a field of nine PBRs (Fig. 2 (b)) were drawn using Rino/Grassopper3D modelling tool. Ten, te Ladybug Grassopper3D plugin [21] was used to estimate te total solar radiation impinging on te single PBR, and on te central PBR in te middle of te field, for eac our of te year. One advantage of Ladybug is tat it can import ourly values of climate data from files in Energy Plus Weater format (EPW) and use tem to calculate solar radiation impinging on a 3D geometry, taking into account te sading effects. In tis way, any PBR configuration can be tested over an entire year and for different locations on Eart. For tis study, weater data downloaded from te US Department of Energy website [22] were used. Fig. 2. 3D modelling of an isolated PBR (a) and of a field of nine PBRs (b) and corresponding average radiations (direct and diffuse, in kw.m-2) impinging on one PBR between 3 and 4 pm, on January 1st in Alicante (Spain) for an isolated PBR (c) and a surrounded one (d). Examples of solar radiation calculations performed wit Ladybug are sown on Fig. 2 (c) and (d). Te different colours represent te different intensities of total solar radiation impinging on te structure, and enable to appreend te effect of sading. In comparison wit te case of an isolated PBR (Fig. 2 (c)), te intensity of solar radiation impinging on te structure is significantly reduced wen te PBR is in te middle of a field of nine PBRs (Fig. 2 (d)). For a given our of te year, te solar radiation flux of te culture dynamic eat balance is calculated as follows: Q S I I rad _ sol PBR PBR ground (2) were ε is te emissivity of te culture, τ is te transmittance of te PBR wall, S PBR (m 2 ) is te external surface of te PBR, I PBR (W.m -2 ) is te ourly mean value of total solar radiation impinging 6

7 on PBR surface, ρ is te ground albedo and I ground (W.m -2 ) is te ourly mean value of solar radiation impinging on te ground. I PBR is calculated wit Ladybug from PBR 3D geometry and I ground is extracted from a data file downloaded from te US Department of Energy website. It as been reported in te literature tat te effect of dust deposits on PBR walls can significantly reduce teir transmittance [23]. To take tis effect into account in te eat balance, a percentage of reduction can be applied to te value of te transmittance of PBR wall in Eq Convective and conductive eat transfer Heat is transferred by convection and conduction troug te walls of te outer and inner tube of eac vertical column of te PBR. Te overall eat transfer coefficient between te culture and te air surrounding te outer tube is obtained by considering tree termal resistances in series: outer _ tube 1 TPB 1 wall 1 ext 1 (3) wit TPB (W.m -2.K -1 ) te convective eat transfer coefficient between te culture and te outer tube, wall (W.m -2.K -1 ) te conductive eat transfer coefficient troug te outer tube wall, and ext (W.m - 2.K -1 ) te convective eat transfer coefficient between te outer tube and te external air. TPB depends on te ydrodynamics of te tripase air-culture-solid mix and is modelled by te following empirical correlation, proposed by Su et al. [24] according to Kim and Yang [25]: TPB kllC pl [( Vl V g )( ss ll gg ) Vl l ] g ll 1/ 2 1/ 2 (4) were k l (J.m -1.s -1.K -1 ) is te liquid termal conductivity, C pl (J.kg -1.K -1 ) te liquid eat capacity, V l and V g (m.s -1 ) te liquid and gas superficial velocities, ρ s, ρ l and ρ g (kg.m -3 ) te solid, liquid and gas densities, g (m.s -2 ) te gravitational acceleration, ε s, ε l and ε g (-) te solid, liquid and gas volumetric fractions and μ l (kg.m -1.s -1 ) te liquid viscosity. wall is given by: wall k wall R Rln 2 R 1 (5) 7

8 wit k wall (J.m -1.s -1.K -1 ) te wall termal conductivity, R (m) te mean radius and R 1 and R 2 (m), te internal and external radii respectively. Te expression of ext depends on te situation. Wen tere is wind, only forced convection is taken into account and ext, wic depends on wind speed, is modelled by te following empirical correlation proposed by Mitcell [26]: ext v 8.6 D 0.6 wind 0.4 (6) were v wind (m.s -1 ) is te wind speed and D (m) te outer tube diameter. Wen tere is no wind, only free convection is taken into account. Te corresponding eat transfer coefficient is calculated using te correlation recommended by McAdams [27] for vertical cylinders: ext k 0.13 air Ra H 1/ 3 H _ air (7) were k air (J.m -1.s -1.K -1 ) is te air termal conductivity, H (m) te eigt of cylinder, and Ra H_air (-) te air Rayleig number. Te overall eat transfer coefficient between te culture and te air inside te inner tube is obtained by considering tree termal resistances in series: inner_ tube 1 TPB 1 wall 1 int 1 (8) wit TPB (W.m -2.K -1 ) te convective eat transfer coefficient between te culture and te inner tube, wall (W.m -2.K -1 ) te conductive eat transfer coefficient troug te inner tube wall, and int (W.m - 2.K -1 ) te convective eat transfer coefficient between te inner tube wall and te fluid contained in it. Te int eat transfer coefficient is modelled by te following empirical correlation for gas free convection in vertical enclosures [28]: int k air Ra D 1/3 D _ air H D 1/9 (9) 8

9 were k air (J.m -1.s -1.K -1 ) is te air termal conductivity, H (m) te eigt of cylinder, D (m) te tube diameter and Ra D_air (-) te air Rayleig number Termal model implementation Te termal model was coded using Visual Basic.NET language in te Grassopper3D grapical algoritm editor, in order to perform te calculation of ourly values of solar radiation and te resolution of te ordinary differential equation (1) in a single program. Te values of solar radiation term (Q rad_sol), air temperature (T air) and wind speed (v wind) are assumed to be constant during te one-our intervals and fed to Eq. (1) wic is solved numerically using a time step of one minute. In tis way, te calculation of culture temperature evolution for a wole year, namely 8760 ours, can be acieved in a single run Model validation metodology Te model validation was performed using industrial PBRs suc as described in section 2.1. Te following experimental data were collected: (1) average culture temperatures measured in te PBR measuring point every our; (2) air temperatures measured on site every two ours; (3) average wind speed measured in te nearest weater station every our. All tese data were collected during several monts - from November 2011 until April Te simulated culture temperatures obtained wit te termal model presented in section 2.2 ave been compared wit te experimental culture temperatures Power requirement simulations Te simulation results obtained wit te PBR termal model are used to calculate te energy necessary to maintain te culture temperature witin a desired range over a given time period. In tis perspective, a maximal and a minimal value of culture temperature are set for a given algae strain. Te energy requirements are calculated from te simulated culture temperature profiles: if, during a time step, te culture temperature exceeds te maximal allowed temperature, ten te necessary cooling power is equal to te net positive global energy tat inputs into te system, expressed as: Q cooling Q rad_ sol inner_ tube S inner_ tube ( Tair Tcult ) outer _ tubesouter_ tube ( T air T cult ) (10) were T cult is taken equal to te maximal culture temperature. 9

10 Simulated culture temperature ( C) Similarly, if te culture temperature drops below te minimal temperature, ten te eating power is equal to te net negative global energy tat exits te system, calculated wit Eq. (10) in wic T cult is taken equal to te minimal temperature. In tis study, annual power requirements are calculated for a 48-columns PBR suc as described in section 2.1. To study te beaviour of te structure in a full scale industrial application in wic PBRs sade one anoter and assess te impact of sadow effects on te eat balance, two possible layouts are examined: (1) a single PBR standing wit no surrounding objects sading it; (2) a PBR in te middle of a square wit eigt PBRs surrounding it as illustrated on Fig. 2 (a) and (b). Moreover, te effect of te tickness of te outer tube wall is studied by modifying its value between 3 mm and 7 mm. Annual power requirements are calculated for a culture able to produce in a range of temperatures between 10 C (T MIN) and 25 C (T MAX). Several geograpical locations caracterized by different Köppen-Geiger climate classes [29] were selected to study te beaviour of te system: (1) ot desert climate (Poenix, USA); (2) Mediterranean climate (Pert, Australia and Montpellier, France); (3) oceanic climate (Paris, France) and its subtropical igland variety (Quito, Ecuador); (4) semi-arid climate (Alicante, Spain); (5) tropical rainforest climate (Belem, Brazil) and tropical savanna one (Belo Horizonte, Brazil). 3. Results and discussion 3.1. Model validation results and temperature prediction accuracy Fig. 3 sows te simulated culture temperatures as a function of te measured ones. More tan 90% of values of te culture temperature are predicted wit less tan 2 C of difference Experimental points y=x Experimental culture temperature ( C) Fig. 3. Simulated versus experimental culture temperatures ( C) between November 2011 and April 2012 (Alicante, Spain). 10

11 Fig. 4 sows te integration of te termal model during seven consecutive days. Altoug te model neglects te infrared termal radiation emitted by te culture and surroundings, te comparison of simulation results wit experimental points is igly satisfactory during te day, confirming te assumption tat te contribution of termal radiation is negligible wit respect to te contribution of solar radiation. Tis assumption does not affect te capacity of te model to predict te peak temperatures during te day, but could account for te sligtly increased difference between simulated and experimental values during te nigt. Fig. 4. Simulated (line) and experimental (crosses) culture temperatures ( C) during seven consecutive days in February (Alicante, Spain). In view of tese results, te termal PBR model can be considered validated Heat balance analysis Te analysis of termal resistances of equation (3) igligts tat te eat excange between te external air and te culture depends primarily on wind speed, and secondly on te tickness and conductivity of te outer tube. Wen te wind speed is low (below 2 m.s -1 ), its related termal resistance is by far te biggest and limiting one in te series of termal resistances for tis PBR system. In oter words, at low wind speeds, reducing te termal resistances related to wall conduction or convective transfer troug culture mixing as a negligible effect on te eat excange rate between te culture and te surrounding air. However, wen te wind speed exceeds 2 m.s -1, te termal resistance associated to wall conduction starts to ave an appreciable effect on te evolution of culture temperature. 11

12 Depending on te meteorological situation, te termal insulation of PBR walls can ave wanted or unwanted effects. Tis is summarized in Fig. 5. In case a) of Fig. 5, culture temperature is at its upper limit and an improvement in te eat excange wit surrounding air can only worsen te situation. In suc a situation, a strong wind would be deleterious and wall tickening could elp to reduce te cooling power required to control te culture temperature. In case c), te culture temperature is also at its upper limit, but enancing te eat excange wit surrounding air would instead improve te performances of te system, leading to directly opposite conclusions. We can ence conclude tat te optimisation of te system must take into account te climate data and ow often eac one of te exposed situations recurs in te studied location. Fig. 5. Summary of possible meteorological situations and effect of wind and wall conduction resistances on power consumption for culture temperature control Simulated power requirements Te model was fed wit climate data from files downloaded from te US Department of Energy to perform simulations. Te annual eating and cooling power requirements of an isolated PBR for different locations and wall ticknesses are reported on Fig. 6 a) and b), respectively. As te final objective is to ave an industrial field of PBR, te effect of mutual sading between PBRs as to be investigated. Te differences in total power consumption between a PBR in an industrial field and an isolated PBR are reported on Fig. 6 c), tus sowing te impact of sading effects on PBR energy requirements. Te values represent te termal energy to be subtracted or added to te system. In case eat pumps are used, te electrical requirement can be estimated equal to one tird of te ones reported in Fig

13 Fig.6. Simulation of annual eating (a) and cooling (b) power requirements of a single PBR for various geograpical locations; analysis of te sading effects in industrial field configuration (c) on te total power consumption (negative values indicate less power consumption) Impact of te site As expected, te coice of te production site is of paramount importance. In Quito, energy requirements are almost null, due to te very stable day and nigt temperature canges and average minimal and maximal temperatures between 10 and 20 C all year long, wic are in line wit te minimal and maximal culture temperatures considered in te simulations. Te igest energy requirements are observed in Poenix; indeed, tis site presents an annual average of 107 days wit air temperatures reacing at least 38 C. For te studied system, we could ence direct our attention towards sites classified as subtropical igland variety of te oceanic climate. Tis is a type of climate caracteristic of te iglands inside te tropics in Mexico, Peru, Bolivia, Madagascar, Zambia, Zimbabwe, but it is also found in central Argentina and Sout Africa, outside te tropics. Of course very different climates can fall inside tis classification, as we can appreciate from te 13

14 very different results of simulations in Pert and Montpellier, wic bot are classified as Mediterranean climate. Moreover, energy requirements are only one criterion for identifying potential sites for microalgae production, even if it is very important. Oter criteria tat could be limiting in tese areas could be te slope of te ground, te accessibility of te site, te proximity to stationary sources of CO 2 emissions and not very far from te coast, witout considering economic and political situation of te osting country Impact of outer tube tickness In te studied sites, an increase in te outer tube tickness induces a reduction of global energy requirements. Depending on te location, te outer tube tickness can ave a strong influence on te termal balance of te PBR. Te locations were tis variable as te biggest absolute energetic impact are in te descending order: (1) Poenix, were we can save up to kw per year per PBR by increasing te outer tube tickness from 3 to 7 mm, (2) Paris, were a bigger termal insulation can save up to kw per year per PBR, followed by (3) Belem, (4) Alicante, (5) Montpellier, (6) Pert, (7) Belo Horizonte and (8) Quito. It is wort noting tat te outer tube tickness as a very low impact in locations were te average wind speed is low, and ence te limiting resistance of te system (Quito and Belo Horizonte). Neverteless, te average wind speed is not te best and only variable to look at, since te wind can vary considerably depending on te season and moment of te day, and its effect can be eiter positive or negative depending on its association to air and culture temperatures. Tis is wy, in a site wit low average wind speed, were occasionally a stronger wind can be linked to ig temperature differences between air and culture, as it is te case in Poenix, we can observe a strong impact on te energy requirements of te outer tube tickness. Using detailed climate data and not averaged over large periods of time is terefore very important to assess te optimum value of some geometrical parameters. Indeed, meteorological averages could lead to misleading conclusions because tey can ide specific trends, like a frequent concomitant presence of ot air temperature and strong winds in te middle of te day during a particular season, wic would strongly affect te eat balance of te PBR Impact of mutual sading between different PBRs More sading results in a decrease in total energy consumption (15% on average), except in Paris were total energy consumption is sligtly iger in te PBR field configuration tan in te isolated PBR. Indeed, wen a PBR is surrounded, and ence saded by te oter ones, te energy required to eat te culture tends to increase, wile te one needed to cool it tends to decrease. Amongst te studied sites, Paris is te only place were annual eating requirement is muc iger tan cooling demand, wic explains te deleterious effect of sading on power consumption in tis location. 14

15 Wind velocity may be impacted in a field of PBRs and affect te termal balance, tis potential effect as been neglected in te present study. However, tis sould be investigated wen performing a feasibility study concerning te implantation in a specific site. 4. Conclusion In te continuity wit modelling approaces described in te literature, tis study presents a matematical model predicting culture temperature in a vertical concentric tubular potobioreactor wit complex geometry. Te model considers te eat transfer penomena involved in te eat excange between te system and te surrounding environment. Its implementation in a simulation tool based on 3D-modelling enables to take into account te effects of sading and real meteorological conditions in te dynamic energy balance. Te model was validated on industrialscale potobioreactors wit a large number of ourly experimental data. Te model allows to calculate te annual energy requirements and ow to reduce tem by coosing te most appropriate values of key parameters, taking into account te geograpical location and te strain-dependent temperature range. Results confirm te interest of a modelling approac to get a better assessment of te plant profitability and of te environmental impact, tat can largely depend on te energy consumption related to temperature control. Acknowledgments Tis work was acieved in te frame of te BISIGODOS project, wic as received funding from te European Union s 7t Framework Programme under Grant Agreement No Te funding from te European Commission is gratefully acknowledged. 15

16 References 1. Spolaore, P., Joannis-Cassan, C., Duran, E., Isambert, A. (2006). Commercial applications of microalgae. Journal of Bioscience and Bioengineering, 101(2), Rasala, B. A., Muto, M., Lee, P. A., Jager, M., Cardoso, R. M., Benke, A., Kirk, P., Hokanson, C. A., Crea, R., Mendez, M., Mayfield, S. P. (2010). Production of terapeutic proteins in algae, analysis of expression of seven uman proteins in te cloroplast of Clamydomonas reinardtii. Plant Biotecnology Journal, 8(6), Tredici, M.R. (2010). Potobiology of microalgae mass cultures: Understanding te tools for te next green revolution. Biofuels, 1(1), Cisti, Y. (2007). Biodiesel from microalgae, Biotecnology Advances, 25, Seean, J., Dunaay, T., Benemann, J., Roessler, P. (1998). A look back at te U.S. department of energy s aquatic species program biodiesel from algae. Tecnical report, U.S. Department of Energy. 6. Brennan, L., Owende, P. (2010). Biofuels from microalgae a review of tecnologies for production, processing, and extractions of biofuels and coproducts. Renewable and Sustainable Energy Reviews, 14, Terry, K.L., Raymond, L.P. (1985). System design for te autotropic production of microalgae. Enzyme and Microbial Tecnology, 7(10), Tredici, M. R., Zittelli, G. C. (1998). Efficiency of sunligt utilization: tubular versus flat PBRs. Biotecnology and Bioengineering, 20;57(2), Carvalo, A. P., Meireles, L. A., Malcata, F. X. (2006). Microalgal Reactors: A Review of Enclosed System Designs and Performances. Biotecnol. Prog., 22(6), Eriksen, N. (2008). Te tecnology of microalgal culturing. Biotecnology Letters, 30(9), Goldman, J.C. (1979). Temperature effects on steady-state growt, posporus uptake, and te cemical composition of a marine pytoplankter. Microb. Ecol., 5, Wang, B., Lan, C. Q., Horsman, M. (2012) Closed PBRs for production of microalgal biomasses. Biotecnology Advances, 30(4), Morita, M., Watanabe, Y., Saiki, H. (2001). Evaluation of PBR eat balance for predicting canges in culture medium temperature due to ligt irradiation. Biotecnology and Bioengineering, 74(6), Gutiérrez, J., Porta-Gándara, M. A., Fernández, J. L. (2008). Passive temperature solar control of an outdoor PBR. Renewable Energy, 33(8), Bécet, Q., Silton, A., Fringer, O. B., Muñoz, R., Guieysse, B. (2010). Mecanistic modeling of brot temperature in outdoor PBRs. Environmental Science and Tecnology, 44 (6), Pereira, D. A., Rodrigues, V. O., Gomez, S. V., Sales, E. A., Jorquera, O. (2013). Parametric sensitivity analysis for temperature control in outdoor PBRs. Bioresource Tecnology, 144, Goetz, V., Le Borgne, F., Pruvost, J., Plantard, G., Legrand, J. (2011). A generic temperature model for solar potobioreactors, Cemical Engineering Journal, 175,

17 18. Stroïazzo-Mougin, B. A. J., Rodriguez Verdu, E., Capuli Fernandez, E. (2009). Continuous system for te generation of ig nutritional value and energy resources, European patent No EP A Duffie, J. A., Beckman, W. A. (1980). Solar Engineering of Termal Processes. Wiley, New York. 20. Ineicen, P., Guisan, O., Perez, R. (1990). Ground-reflected radiation and albedo. Solar Energy, 44 (4), Roudsari, M. S., Pak, M., Smit, A. (2013). Ladybug: a parametric environmental plugin for Grassopper to elp designers create and environmentally-conscious design. Proceedings of 13t Conference of International Building Performance Simulation Association, Cambéry, France, August US Department of Energy website: ttp://apps1.eere.energy.gov/buildings/energyplus/weaterdata_about.cfm 23. Elminir, H. K., Gitas, A. E., Hamid, R. H., El-Hussainy, F., Beeary, M. M., Abdel-Moneim, K. M. (2006). Effect of dust on te transparent cover of solar collectors. Energy Conversion and Management, 47(18-19), Su, I. S., Jin, G. T., Kim, S. D. (1985) Heat transfer coefficients in tree pase fluidized beds. Int. J. Multipase Flow, 11, Kim, S. D., Kang, Y. (1997). Heat and mass transfer in tree-pase fluidizedbed reactors - an overview. Cemical Engineering Science, 52(21-22), Mitcell, J. W. (1976). Heat transfer from speres and oter animal forms. Biopysical J., 16, McAdams, W. H. (1954). Heat transmission, 3 rd Edition, McGrawHill, New York. 28. Cengel, Y. A. (1997). Introduction to Termodynamics and Heat Transfer. McGraw-Hill. 29. Kottek, M., Grieser, J., Beck, C., Rudolf, B., Rubel, F. (2006). World Map of te Köppen-Geiger climate classification updated, Meteorologisce Zeitscrift, 15(3),

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