Modelling of Microalgae Culture Systems with Applications to Control and Optimization

  • Olivier Bernard
  • Francis Mairet
  • Benoît Chachuat
Chapter
Part of the Advances in Biochemical Engineering/Biotechnology book series (ABE, volume 153)

Abstract

Mathematical modeling is becoming ever more important to assess the potential, guide the design, and enable the efficient operation and control of industrial-scale microalgae culture systems (MCS). The development of overall, inherently multiphysics, models involves coupling separate submodels of (i) the intrinsic biological properties, including growth, decay, and biosynthesis as well as the effect of light and temperature on these processes, and (ii) the physical properties, such as the hydrodynamics, light attenuation, and temperature in the culture medium. When considering high-density microalgae culture, in particular, the coupling between biology and physics becomes critical. This chapter reviews existing models, with a particular focus on the Droop model, which is a precursor model, and it highlights the structure common to many microalgae growth models. It summarizes the main developments and difficulties towards multiphysics models of MCS as well as applications of these models for monitoring, control, and optimization purposes.

Graphical Abstract

Keywords

Microalgae Photobioreactors Raceways Modeling Optimization Biofuel CO2 mitigation 

References

  1. 1.
    Akhmetzhanov A, Grognard F, Masci P, Bernard O (2010) Optimization of a photobioreactor biomass production using natural light. In: Proceedings of the 49th CDC conference, AtlantaGoogle Scholar
  2. 2.
    Anning T, MacIntyre HL, Pratt SM, Sammes PJ, Gibb S, Geider RJ (2000) Photoacclimation in the marine diatom skeletonema costatum. Limnol Oceanogr 45(8):1807–1817CrossRefGoogle Scholar
  3. 3.
    Baly ECC (1935) The kinetics of photosynthesis. Proc Royal Soc Lond Ser B B117:218–239CrossRefGoogle Scholar
  4. 4.
    Becerra-Celis G, Hafidi G, Tebbani S, Dumur D, Isambert A (2008) Nonlinear predictive control for continuous microalgae cultivation process in a photobioreactor. In: Proceedings of the 10th international conference on control, automation, robotics and vision, Hannoi, pp 1373–1378, 17–20 Dec 2008Google Scholar
  5. 5.
    Béchet Q, Shilton A, Fringer OB, Muñoz R, Guieysse B (2010) Mechanistic modeling of broth temperature in outdoor photobioreactors. Environ Sci Technol 44(6):2197–2203CrossRefGoogle Scholar
  6. 6.
    Béchet Q, Shilton A, Park JB, Craggs RJ, Guieysse B (2011) Universal temperature model for shallow algal ponds provides improved accuracy. Environ Sci Technol 45(8):3702–3709CrossRefGoogle Scholar
  7. 7.
    Ben-Yaakov S, Guterman H, Vonshak A, Richmond A (1985) An automatic method for on-line estimation of the photosynthetic rate in open algal ponds. Biotechnol Bioeng 27(8):1136–1145CrossRefGoogle Scholar
  8. 8.
    Benemann JR, Tillett DM (1987) Effects of fluctuating environments on the selection of high yielding microalgae. Technical report, Georgia Institute of Technology, AtlantaGoogle Scholar
  9. 9.
    Berenguel M, Rodriguez F, Acien F, Garcia J (2004) Model predictive control of pH in tubular photobioreactors. J Process Control 14(4):377–387CrossRefGoogle Scholar
  10. 10.
    Bernard O (2011) Hurdles and challenges for modelling and control of microalgae for CO2 mitigation and biofuel production. J Process Control 21(10):1378–1389CrossRefGoogle Scholar
  11. 11.
    Bernard O, Boulanger A-C, Bristeau M-O, Sainte-Marie J (2013) A 2D model for hydrodynamics and biology coupling applied to algae growth simulations. ESAIM Math Model Numer Anal 47:1387–1412CrossRefGoogle Scholar
  12. 12.
    Bernard O, Gouzé J-L (1995) Transient behavior of biological loop models, with application to the Droop model. Math Biosci 127(1):19–43CrossRefGoogle Scholar
  13. 13.
    Bernard O, Gouzé J-L (1999) Nonlinear qualitative signal processing for biological systems: application to the algal growth in bioreactors. Math Biosci 157:357–372CrossRefGoogle Scholar
  14. 14.
    Bernard O, Gouzé J-L (2002) Global qualitative behavior of a class of nonlinear biological systems: application to the qualitative validation of phytoplankton growth models. Artif Intell 136:29–59CrossRefGoogle Scholar
  15. 15.
    Bernard O, Rémond B (2012) Validation of a simple model accounting for light and temperature effect on microalgal growth. Bioresour Technol 123:520–527CrossRefGoogle Scholar
  16. 16.
    Bernard O, Sallet G, Sciandra A (1998) Nonlinear observers for a class of biotechnological systems. Application to validation of a phytoplanktonic growth model. IEEE Trans Autom Control 43:1056–1065CrossRefGoogle Scholar
  17. 17.
    Bougaran G, Bernard O, Sciandra A (2010) Modelling continuous cultures of microalgae colimited with nitrogen and phosphorus. J Theor Biol 265(3):443–454CrossRefGoogle Scholar
  18. 18.
    Buehner MR, Young PM, Willson B, Rausen D, Schoonover R, Babbitt G, Bunch S (2009) Microalgae growth modeling and control for a vertical flat panel photobioreactor. In: Proceedings of the 2009 American control conference, pp 2301–2306Google Scholar
  19. 19.
    Burmaster D (1979) The unsteady continuous culture of phosphate-limited monochrysis lutheri Droop: experimental and theoretical analysis. J Exp Mar Biol Ecol 39(2):167–186CrossRefGoogle Scholar
  20. 20.
    Camacho Rubio F, Garcia Camacho F, Fernandez Sevilla JM, Chisti Y, Molina Grima E (2003) A mechanistic model of photosynthesis in microalgae. Biotechnol Bioeng 81(4):459–473CrossRefGoogle Scholar
  21. 21.
    Celikovsky S, Papacek S, Cervantes-Herrera A, Ruiz-Leon J (2010) Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis. IEEE Trans Autom Control 55(3):767–772CrossRefGoogle Scholar
  22. 22.
    Chisti Y (2007) Biodiesel from microalgae. Biotechnol Adv 25:294–306CrossRefGoogle Scholar
  23. 23.
    Cogne G, Gros J-B, Dussap C-G (2003) Identification of a metabolic network structure representative of Arthrospira (spirulina) platensis metabolism. Biotechnol Bioeng 84(6):667–676CrossRefGoogle Scholar
  24. 24.
    Cogne G, Rügen M, Bockmayr A, Titica M, Dussap C-G, Cornet J-F, Legrand J (2011) A model-based method for investigating bioenergetic processes in autotrophically growing eukaryotic microalgae: application to the green algae Chlamydomonas reinhardtii. Biotechnol Prog 27(3):631–640CrossRefGoogle Scholar
  25. 25.
    Combe C, Hartmann P, Rabouille S, Talec A, Sciandra A, Bernard O (Submitted). Long-term adaptive response to high-frequency light signals in the unicellular photosynthetic eukaryote Dunaliella salina. Biotechnol BioengGoogle Scholar
  26. 26.
    Cornet J-F, Dussap C-G (2009) A simple and reliable formula for assessment of maximum volumetric productivities in photobioreactors. Biotechnol Prog 25(2):424–435CrossRefGoogle Scholar
  27. 27.
    Cornet JF, Dussap CG, Cluzel P, Dubertret G (1992) A structured model for simulation of cultures of the cyanobacterium spirulina platensis in photobioreactors: II. Identification of kinetic parameters under light and mineral limitations. Biotechnol Bioeng 40(7):826–834CrossRefGoogle Scholar
  28. 28.
    Csogor Z, Herrenbauer M, Schmidt K, Posten C (2001) Light distribution in a novel photobioreactor—modelling for optimization. J Appl Phycol 13:325–333CrossRefGoogle Scholar
  29. 29.
    Dillschneider R, Posten C (2013) A linear programming approach for modeling and simulation of growth and lipid accumulation of phaeodactylum tricornutum. Energies 6(10):5333–5356CrossRefGoogle Scholar
  30. 30.
    Droop MR (1968) Vitamin B12 and marine ecology. IV. The kinetics of uptake growth and inhibition in Monochrysis lutheri. J Mar Biol Assoc UK 48(3):689–733CrossRefGoogle Scholar
  31. 31.
    Droop MR (1983) 25 years of algal growth kinetics, a personal view. Bot Mar 16:99–112Google Scholar
  32. 32.
    Dugdale RC (1967) Nutrient limitation in the sea: dynamics, identification and significance. Limnol Oceanogr 12:685–695CrossRefGoogle Scholar
  33. 33.
    Eilers PHC, Peeters JCH (1988) A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton. Ecol Model 42(3–4):199–215CrossRefGoogle Scholar
  34. 34.
    Eilers PHC, Peeters JCH (1993) Dynamic behaviour of a model for photosynthesis and photoinhibition. Ecol Model 69(1–2):113–133CrossRefGoogle Scholar
  35. 35.
    Esposito S, Botte V, Iudicone D, d’Alcala MR (2009) Numerical analysis of cumulative impact of phytoplankton photoresponses to light variation on carbon assimilation. J Theor Biol 261(3):361–371CrossRefGoogle Scholar
  36. 36.
    Faugeras B, Bernard O, Sciandra A, Levy M (2004) A mechanistic modelling and data assimilation approach to estimate the carbon/chlorophyll and carbon/nitrogen ratios in a coupled hydrodynamical-biological model. Nonlinear Process Geophys 11:515–533CrossRefGoogle Scholar
  37. 37.
    Fernandez FG, Camacho FG, Perez JA, Sevilla JM, Grima EM (1997) A model for light distribution and average solar irradiance inside outdoor tubular photobioreactors for the microalgal mass culture. Biotechnol Bioeng 55(5):701–714CrossRefGoogle Scholar
  38. 38.
    Flynn K (1991) A mechanistic model for describing dynamic multi-nutrient, light, temperature interactions in phytoplankton. J Plankton Res 23:977–997CrossRefGoogle Scholar
  39. 39.
    Franco-Lara E, Havel J, Peterat F, Weuster‐Botz D (2006) Model-supported optimization of phototrophic growth in a stirred-tank photobioreactor. Biotechnol Bioeng 95:1177–1187CrossRefGoogle Scholar
  40. 40.
    Garcia Camacho F, Sanchez Miron A, Molina Grima E, Camacho Rubio F, Merchuck JC (2012) A mechanistic model of photosynthesis in microalgae including photoacclimation dynamics. J Theor Biol 304:1–15CrossRefGoogle Scholar
  41. 41.
    Garcia Sanchez JL, Berenguel M, Rodriguez F, Fernandez Sevilla JM, Brindley Alias C, Acien Fernandez F (2003) Minimization of carbon losses in pilot-scale outdoor photobioreactors by model-based predictive control. Biotechnol Bioeng 84(5):533–543CrossRefGoogle Scholar
  42. 42.
    Geider R, MacIntyre H, Kana T (1998) A dynamic regulatory model of phytoplanktonic acclimation to light, nutrients, and temperature. Limnol Oceanogr 43:679–694CrossRefGoogle Scholar
  43. 43.
    Geider RJ (1987) Light and temperature dependence of the carbon to chlorophyll a ratio in microalgae and cyanobacteria: implications for physiology and growth of phytoplankton. New Phytol 106(1):1–34Google Scholar
  44. 44.
    Goffaux G, Vande Wouwer A, Bernard O (2009) Continuous-discrete interval observers applied to the monitoring of cultures of microalgae. J Process Control 19:1182–1190CrossRefGoogle Scholar
  45. 45.
    Grobbelaar JU, Soeder CJ, Stengel E (1990) Modeling algal productivity in large outdoor cultures and waste treatment systems. Biomass 21:297–314CrossRefGoogle Scholar
  46. 46.
    Grognard F, Akhmetzhanov AR, Bernard O (2014) Optimal strategies for biomass productivity maximization in a photobioreactor using natural light. Automatica 50:359–368CrossRefGoogle Scholar
  47. 47.
    Guest JS, van Loosdrecht MCM, Skerlos SJ, Love NG (2013) Lumped pathway metabolic model of organic carbon accumulation and mobilization by the alga Chlamydomonas reinhardtii. Environ Sci Technol 47(7):3258–3267Google Scholar
  48. 48.
    Guterman H, Ben-Yaakov S, Vonshak A (1989) Automatic on-line growth estimation method for outdoor algal biomass production. Biotechnol Bioeng 34(2):143–152CrossRefGoogle Scholar
  49. 49.
    Guterman H, Vonshak A, Ben-Yaakov S (1990) A macromodel for outdoor algal mass production. Biotechnol Bioeng 35(8):809–819CrossRefGoogle Scholar
  50. 50.
    Han B-P (2002) A mechanistic model of algal photoinhibition induced by photodamage to photosystem-II. J Theor Biol 214(4):519–527CrossRefGoogle Scholar
  51. 51.
    Hartmann P, Béchet Q, Bernard O (2014) The effect of time scales in photosynthesis on microalgae productivity. Bioprocess Biosyst Eng 37(1):17–25Google Scholar
  52. 52.
    Hartmann P, Combe C, Rabouille S, Sciandra A, Bernard O (2014). Impact of hydrodynamics on single cell algal photosynthesis in raceways: characterization of the hydrodynamic system and light paterns. In: Proceedings of the 19th IFAC world congress, Cape TownGoogle Scholar
  53. 53.
    Hu D, Liu H, Yang C, Hu E (2008) The design and optimization for light-algae bioreactor controller based on artificial neural network-model predictive control. Acta Astronaut 63:1067–1075CrossRefGoogle Scholar
  54. 54.
    Hu Q, Sommerfeld M, Jarvis E, Ghirardi M, Posewitz M, Seibert M, Darzins A (2008) Microalgal triacylglycerols as feedstocks for biofuel production: perspectives and advances. Plant J 54(4):621–639CrossRefGoogle Scholar
  55. 55.
    Huisman J, Matthijs HCP, Visser PM, Balke H, Sigon CAM, Passarge J, Weissing FJ, Mur LR (2002) Principles of the light-limited chemostat: theory and ecological applications. Antonie Van Leeuwenhoek 81(1–4):117–133CrossRefGoogle Scholar
  56. 56.
    Huisman J, Weissing FJ (1994) Light-limited growth and competition for light in well-mixed aquatic environments: an elementary model. Ecology 75:507–520CrossRefGoogle Scholar
  57. 57.
    Kliphuis AM, Klok AJ, Martens DE, Lamers PP, Janssen M, Wijffels RH (2012) Metabolic modeling of Chlamydomonas reinhardtii: energy requirements for photoautotrophic growth and maintenance. J Appl Phycol 24(2):253–266CrossRefGoogle Scholar
  58. 58.
    Knoop H, Gründel M, Zilliges Y, Lehmann R, Hoffmann S, Lockau W, Steuer R (2013) Flux balance analysis of cyanobacterial metabolism: the metabolic network of Synechocystis sp. PCC 6803. PLoS Comput Biol 9(6):e1003081CrossRefGoogle Scholar
  59. 59.
    Kok B (1956) On the inhibition of photosynthesis by intense light. Biochim Biophys Acta 21(2):234–244CrossRefGoogle Scholar
  60. 60.
    Kroon B, Ketelaars H, Fallowfield H, Mur L (1989) Modelling microalgal productivity in a high rate algal pond based on wavelength dependent optical properties. J Appl Phycol 1:247–256CrossRefGoogle Scholar
  61. 61.
    Lacour T, Sciandra A, Talec A, Mayzaud P, Bernard O (2012) Diel variations of carbohydrates and neutral lipids in N-sufficient and N-limited cyclostat cultures of isochrysis sp. J Phycol 48:966–975CrossRefGoogle Scholar
  62. 62.
    Lange K, Oyarzun FJ (1992) The attractiveness of the Droop equations. Math Biosci 111:261–278CrossRefGoogle Scholar
  63. 63.
    Lardon L, Hélias A, Sialve B, Steyer J-P, Bernard O (2009) Life-cycle assessment of biodiesel production from microalgae. Environ Sci Technol 43:6475–6481CrossRefGoogle Scholar
  64. 64.
    Luo H-P, Al-Dahhan MH (2004) Analyzing and modeling of photobioreactors by combining first principles of physiology and hydrodynamics. Biotechnol Bioeng 85(4):382–393CrossRefGoogle Scholar
  65. 65.
    MacIntyre HL, Kana TM, Anning T, Geider RJ (2002) Photoacclimation of photosynthesis irradiance response curves and photosynthetic pigments in microalgae and cyanobacteria. J Phycol 38(1):17–38CrossRefGoogle Scholar
  66. 66.
    Mailleret L, Gouzé J-L, Bernard O (2005) Nonlinear control for algae growth models in the chemostat. Bioprocess Biosyst Eng 27:319–328CrossRefGoogle Scholar
  67. 67.
    Mairet F, Bernard O, Masci P, Lacour T, Sciandra A (2011) Modelling neutral lipid production by the microalga Isochrysis affinis galbana under nitrogen limitation. Biores Technol 102:142–149CrossRefGoogle Scholar
  68. 68.
    Mairet F, Moisan M, Bernard O (2014) Estimation of neutral lipid and carbohydrate quotas in microalgae using adaptive interval observers. Bioprocess Biosyst Eng 37(1):51–61Google Scholar
  69. 69.
    Mairet F, Muñoz-Tamayo R, Bernard, O (2013b) Adaptive control to optimize microalgae production. In: Proceedings of the 12th international symposium on computer applications in biotechnology, MumbaiGoogle Scholar
  70. 70.
    Marshall HL, Geider RJ, Flynn KJ (2000) A mechanistic model of photoinhibition. New Phytol 145:347–359CrossRefGoogle Scholar
  71. 71.
    Marshall J, Sala K (2011) A stochastic lagrangian approach for simulating the effect of turbulent mixing on algae growth rate in a photobioreactor. Chem Eng Sci 66(3):384–392CrossRefGoogle Scholar
  72. 72.
    Masci P, Grognard F, Bernard O (2008) Continuous selection of the fastest growing species in the chemostat. In: Proceedings of the 17th IFAC world congress, SeoulGoogle Scholar
  73. 73.
    Metting F (1996) Biodiversity and application of microalgae. J Ind Microbiol Biotechnol 17:477–489CrossRefGoogle Scholar
  74. 74.
    Milledge JJ (2011) Commercial application of microalgae other than as biofuels: a brief review. Rev Environ Sci BioTechnol 10(1):31–41CrossRefGoogle Scholar
  75. 75.
    Nikolaou A, Bernardi A, Meneghesso A, Bezzo F, Morosinotto T, Chachuat B (2015) A model of chlorophyll fluorescence in microalgae integrating photoproduction, photoinhibition and photoregulation. J Biotechnol 194:91–99Google Scholar
  76. 76.
    Norberg J (2004) Biodiversity and ecosystem functioning: a complex adaptive systems approach. Limnol Oceanogr 49(4):1269–1277CrossRefGoogle Scholar
  77. 77.
    Packer A, Li Y, Andersen T, Hu Q, Kuang Y, Sommerfeld M (2011) Growth and neutral lipid synthesis in green microalgae: a mathematical model. Bioresour Technol 102(1):111–117CrossRefGoogle Scholar
  78. 78.
    Pahlow M (2005) Linking chlorophyll-nutrient dynamics to the redfield N:C ratio with a model of optimal phytoplankton growth. Mar Ecol-Progress Ser 287:33–43CrossRefGoogle Scholar
  79. 79.
    Peeters JCH, Eilers P (1978) The relationship between light intensity and photosynthesis: a simple mathematical model. Hydrobiol Bull 12:134–136CrossRefGoogle Scholar
  80. 80.
    Perner-Nochta I, Posten C (2007) Simulations of light intensity variation in photobioreactors. J Biotechnol 131:276–285CrossRefGoogle Scholar
  81. 81.
    Platt T, Gallegos CL, Harrison WG (1980) Photoinhibition of photosynthesis in natural assemblages of marine phytoplankton. J Mar Res 38:687–701Google Scholar
  82. 82.
    Post AF, Dubinsky Z, Wyman K, Falkowski PG (1985) Physiological responses of a marine planktonic diatom to transitions in growth irradiance. Mar Ecol Progress Ser 25:141–149CrossRefGoogle Scholar
  83. 83.
    Posten C (2009) Design principles of photo-bioreactors for cultivation of microalgae. Eng Life Sci 9:165–177CrossRefGoogle Scholar
  84. 84.
    Pottier L, Pruvost J, Deremetz J, Cornet J-F, Legrand J, Dussap C (2005) A fully predictive model for one-dimensional light attenuation by Chlamydomonas reinhardtii in a torus photobioreactor. Biotechnol Bioeng 91:569–582CrossRefGoogle Scholar
  85. 85.
    Pruvost J, Pottier L, Legrand J (2006) Numerical investigation of hydrodynamic and mixing conditions in a torus photobioreactor. Chem Eng Sci 61:4476–4489CrossRefGoogle Scholar
  86. 86.
    Pulz O, Gross W (2004) Valuable products from biotechnology of microalgae. Appl Microbiol Biotechnol 65(6):635–648CrossRefGoogle Scholar
  87. 87.
    Ras M, Steyer J-P, Bernard O (2013) Temperature effect on microalgae: a crucial factor for outdoor production. Rev Environ Sci Bio/Technol 12:153–164CrossRefGoogle Scholar
  88. 88.
    Rehak B, Celikovsky S, Papacek S (2008) Model for photosynthesis and photoinhibition: parameter identification based on the harmonic irradiation O2 response measurement. IEEE Trans Autom Control 53:101–108CrossRefGoogle Scholar
  89. 89.
    Riley GA (1946) Factors controlling phytoplankton populations on georges bank. J Mar Res 6:54–73Google Scholar
  90. 90.
    Rodolfi L, Zittelli GC, Bassi N, Padovani G, Biondi N, Bonini G, Tredici MR (2009) Microalgae for oil: strain selection, induction of lipid synthesis and outdoor mass cultivation in a low-cost photobioreactor. Biotechnol Bioeng 102(1):100–112CrossRefGoogle Scholar
  91. 91.
    Rosello Sastre R, Coesgoer Z, Perner-Nochta I, Fleck-Schneider P, Posten C (2007) Scale-down of microalgae cultivations in tubular photo-bioreactors - a conceptual approach. J Biotechnol 132:127–133CrossRefGoogle Scholar
  92. 92.
    Ross O, Geider R (2009) New cell-based model of photosynthesis and photo-acclimation: accumulation and mobilisation of energy reserves in phytoplankton. Mar Ecol Progress Ser 383:53–71CrossRefGoogle Scholar
  93. 93.
    Rosso L, Lobry J, Flandrois J (1993) An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. J Theor Biol 162(4):447–463CrossRefGoogle Scholar
  94. 94.
    Sandnes JM, Ringstad T, Wenner D, Heyerdahl PH, Källqvist T, Gislerod HR (2006) Real-time monitoring and automatic density control of large-scale microalgal cultures using near infrared (NIR) optical density sensors. J Biotechnol 122(2):209–215CrossRefGoogle Scholar
  95. 95.
    Sciandra A (1991) Coupling and uncoupling between nitrate uptake and growth rate in Prorocentrum minimum (dinophyceae) under different frequencies of pulsed nitrate supply. Mar Ecol Progress Ser 72:261–269CrossRefGoogle Scholar
  96. 96.
    Sciandra A, Gostan J, Collos Y, Descolas-Gros C, Leboulanger C, Martin-Jézéquel V, Denis M, Lefèvre D, Copin C, Avril B (1997) Growth compensating phenomena in continuous cultures of dunaliella tertiolecta limited simultaneously by light and nitrate. Limnol Oceanogr 46:1325–1339CrossRefGoogle Scholar
  97. 97.
    Sciandra A, Ramani P (1994) The limitations of continuous cultures with low rates of medium renewal per cell. J Exp Mar Biol Ecol 178:1–15CrossRefGoogle Scholar
  98. 98.
    Shastri AA, Morgan JA (2005) Flux balance analysis of photoautotrophic metabolism. Biotechnol Progress 21(6):1617–1626CrossRefGoogle Scholar
  99. 99.
    Sheehan J, Dunahay T, Benemann J, Roessler P (1998) A look back at the U.S. Department of Energy’s aquatic species program—Biodiesel from algae. Technical report, U.S. Department of EnergyGoogle Scholar
  100. 100.
    Spolaore P, Joannis-Cassan C, Duran E, Isambert A (2006) Commercial applications of microalgae. J Biosci Bioeng 101(2):87–96CrossRefGoogle Scholar
  101. 101.
    Steele JH (1962) Environmental control of photosynthesis in the sea. Limnol Oceanogr 7:137–150CrossRefGoogle Scholar
  102. 102.
    Stramski D, Sciandra A, Claustre H (2002) Effects of temperature, nitrogen, and light limitation on the optical properties of the marine diatom thalassiosira pseudonana. Limnol Oceanogr 47:392–403CrossRefGoogle Scholar
  103. 103.
    Su WW, Li J, Xu N-S (2003) State and parameter estimation of microalgal photobioreactor cultures based on local irradiance measurement. J Biotechnol 105(1–2):165–178CrossRefGoogle Scholar
  104. 104.
    Suh I, Lee S (2003) A light distribution model for an internally radiating photobioreactor. Biotechnol Bioeng 82:180–189CrossRefGoogle Scholar
  105. 105.
    Sukenik A, Falkowski PG, Bennett J (1987) Potential enhancement of photosynthetic energy conversion in algal mass culture. Biotechnol Bioeng 30(8):970–977CrossRefGoogle Scholar
  106. 106.
    Sukenik A, Levy RS, Levy Y, Falkowski PG, Dubinsky Z (1991) Optimizing algal biomass production in an outdoor pond: a simulation model. J Appl Phycol 3:191–201CrossRefGoogle Scholar
  107. 107.
    Takache H, Christophe G, Cornet J.-F, Pruvost J (2009) Experimental and theoretical assessment of maximum productivities for the microalgae chlamydomonas reinhardtii in two different geometries of photobioreactors. Biotechnol Progress 26:431–440Google Scholar
  108. 108.
    Turpin D (1991) Effects of inorganic N availability on algal photosynthesis and carbon metabolism. J Phycol 27:14–20CrossRefGoogle Scholar
  109. 109.
    Vatcheva I, deJong H, Bernard O, Mars N (2006) Experiment selection for the discrimination of semi-quantitative models of dynamical systems. Artif Intell 170:472–506CrossRefGoogle Scholar
  110. 110.
    Vollenweider RA (1966) Calculation models of photosynthesis-depth curves and some implications regarding day rate estimates in primary production measurements. In: Goldman CR (ed) Primary productivity in aquatic environments. University of California Press, California, pp 425–457Google Scholar
  111. 111.
    Wijffels RH, Barbosa MJ (2010) An outlook on microalgal biofuels. Science 329(5993):796–799CrossRefGoogle Scholar
  112. 112.
    Wu X, Merchuk JC (2002) Simulation of algae growth in a bench-scale bubble column reactor. Biotechnol Bioeng 80(2):156–168CrossRefGoogle Scholar
  113. 113.
    Yang C, Hua Q, Shimizu K (2000) Energetics and carbon metabolism during growth of microalgal cells under photoautotrophic, mixotrophic and cyclic light-autotrophic/dark-heterotrophic conditions. Biochem Eng J 6(2):87–102CrossRefGoogle Scholar
  114. 114.
    Yoshimoto N, Sat T, Kondo Y (2005) Dynamic discrete model of flashing light effect in photosynthesis of microalgae. J Appl Phycol 17:207–214CrossRefGoogle Scholar
  115. 115.
    Zonneveld C (1997) Modeling effects of photoadaption on the photosynthesis-irradiance curve. J Theor Biol 186(3):381–388CrossRefGoogle Scholar
  116. 116.
    Zonneveld C (1998) A cell-based model for the chlorophyll a to carbon ratio in phytoplankton. Ecol Mod 113:55–70CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Olivier Bernard
    • 1
    • 2
  • Francis Mairet
    • 1
    • 2
  • Benoît Chachuat
    • 3
  1. 1.BIOCORE, INRIASophia-Antipolis CedexFrance
  2. 2.LOV, CNRSSorbonne Universités, UPMC Université Paris 06Villefranche-sur-merFrance
  3. 3.Centre for Process Systems Engineering, Department of Chemical EngineeringImperial College LondonLondonUK

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