A 2D model for hydrodynamics and biology coupling applied to algae growth simulations

Olivier Bernard; Anne-Céline Boulanger; Marie-Odile Bristeau; Jacques Sainte-Marie

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 5, page 1387-1412
  • ISSN: 0764-583X

Abstract

top
Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint–Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.

How to cite

top

Bernard, Olivier, et al. "A 2D model for hydrodynamics and biology coupling applied to algae growth simulations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.5 (2013): 1387-1412. <http://eudml.org/doc/273282>.

@article{Bernard2013,
abstract = {Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint–Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.},
author = {Bernard, Olivier, Boulanger, Anne-Céline, Bristeau, Marie-Odile, Sainte-Marie, Jacques},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {hydrostatic Navier–Stokes equations; Saint–Venant equations; free surface stratified flows; multilayer system; kinetic scheme; droop model; raceway; hydrodynamics and biology coupling; algae growth; hydrostatic Navier-Stokes equations; Saint-Venant equations},
language = {eng},
number = {5},
pages = {1387-1412},
publisher = {EDP-Sciences},
title = {A 2D model for hydrodynamics and biology coupling applied to algae growth simulations},
url = {http://eudml.org/doc/273282},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Bernard, Olivier
AU - Boulanger, Anne-Céline
AU - Bristeau, Marie-Odile
AU - Sainte-Marie, Jacques
TI - A 2D model for hydrodynamics and biology coupling applied to algae growth simulations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 5
SP - 1387
EP - 1412
AB - Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint–Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.
LA - eng
KW - hydrostatic Navier–Stokes equations; Saint–Venant equations; free surface stratified flows; multilayer system; kinetic scheme; droop model; raceway; hydrodynamics and biology coupling; algae growth; hydrostatic Navier-Stokes equations; Saint-Venant equations
UR - http://eudml.org/doc/273282
ER -

References

top
  1. [1] E Audusse, Modelisation hyperbolique et analyse numerique pour les ecoulements en eaux peu profondes. Ph.D. thesis. Université Pierre et Marie Curie - Paris VI (2004). 
  2. [2] E. Audusse and M.-O. Bristeau, Transport of pollutant in shallow water flows: A two time steps kinetic method. ESAIM: M2AN 37 (2003) 389–416. Zbl1137.65392MR1991208
  3. [3] E. Audusse and M.-O. Bristeau, A well-balanced positivity preserving second-order scheme for shallow water flows on unstructured meshes. J. Comput. Phys.206 (2005) 311–333. Zbl1087.76072MR2135839
  4. [4] E. Audusse, M.-O. Bristeau, M. Pelanti and J. Sainte-Marie, Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation. J. Comput. Phys. 230 (2011) 3453–3478. Zbl1316.76055MR2780473
  5. [5] E. Audusse, M.-O. Bristeau, B. Perthame and J. Sainte-Marie, A multilayer saint–venant system with mass exchanges for shallow water flows. Derivation and numerical validation. ESAIM: M2AN 45 (2011) 169–200. Zbl1290.35194MR2781135
  6. [6] E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and Be. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050–2065. Zbl1133.65308MR2086830
  7. [7] S.-D. Ayata, M. Lévy, O. Aumont, A. Sciandra, J. Sainte-Marie, A. Tagliabue and O. Bernard, Phytoplankton growth formulation in marine ecosystem models: should we take into account photo-acclimation and variable stochiometry in oligotrophic areas? To appear in J. Marine Syst. 
  8. [8] M. Baklouti, F. Diaz, C. Pinazo, V. Faure and B. Queguiner, Investigation of mechanistic formulations depicting phytoplankton dynamics for models of marine pelagic ecosystems and description of a new model. Progr. Oceanogr.71 (2006) 1–33. 
  9. [9] A.-J.-C. Barré de Saint-Venant, Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et làintroduction des marées dans leur lit. Comptes Rendus des Séances de l’Académie des Sciences, Paris 73 (1871) 147–154. Zbl03.0482.04JFM03.0482.04
  10. [10] O. Bernard, Hurdles and challenges for modelling and control of microalgae for co2 mitigation and biofuel production. J. Process Control21 (2011) 1378–1389. 
  11. [11] O. Bernard and J.-L. Gouzé, Transient behavior of biological loop models, with application to the Droop model. Math. Biosci.127 (1995) 19–43. Zbl0822.92001MR1323362
  12. [12] O. Bernard and J.-L. Gouzé, Global qualitative behavior of a class of nonlinear biological systems: application to the qualitative validation of phytoplankton growth models. Artif. Intel.136 (2002) 29–59. Zbl0984.68186MR1891584
  13. [13] A.-C. Boulanger and J. Sainte-Marie, Analytical solutions for the free surface hydrostatic euler equations. Submitted to Nonlinearity (2011). Zbl1288.35379
  14. [14] J.-F. Bourgat, P. Le Tallec, F. Mallinger, B. Perthame, Y. Qiu, C. boltzmann and navier-stokes, Research Report RR-2281, Projet MENUSIN. INRIA (1994). 
  15. [15] M.-O. Bristeau and J. Sainte-Marie, Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems. DCDS(B) 10 (2008) 733–759. Zbl1155.35405MR2434908
  16. [16] M.-O. Bristeau, N. Goutal and J. Sainte-Marie, Numerical simulations of a non-hydrostatic shallow water model. Comput. Fluids47 (2011) 51–64. Zbl1271.76035MR2949395
  17. [17] V. Casulli, A semi–implicit finite difference method for non-hydrostatic, free–surface flows. Int. J. Numer. Methods Fluids30 (1999) 425–440. Zbl0944.76050
  18. [18] Y. Chisti, Biodiesel from microalgae. Biotech. Adv.25 (2007) 294–306. 
  19. [19] M.R. Droop, Vitamin B12 and marine ecology. IV. the kinetics of uptake growth and inhibition in Monochrysis lutheri. J. Mar. Biol. Assoc. 48 (1968) 689–733. 
  20. [20] M.R. Droop, 25 years of algal growth kinetics, a personal view. Botanica Marina 16 (1983) 99–112. 
  21. [21] R.C. Dugdale, Nutrient limitation in the sea: dynamics, identification and significance. Limnol. Oceanogr.12 (1967) 685–695. 
  22. [22] S. Esposito, V. Botte, D. Iudicone and M. Ribera d’Alcala, Numerical analysis of cumulative impact of phytoplankton photoresponses to light variation on carbon assimilation. J. Theor. Biol261 (2009) 361–371. MR2974112
  23. [23] R.J. Geider, H.L. MacIntyre and T.M. Kana, A dynamic regulatory model of phytoplanktonic acclimation to light, nutrients, and temperature. Limnol Oceanogr43 (1998) 679–694. 
  24. [24] J.-F. Gerbeau, and B. Perthame, Derivation of viscous saint–venant system for laminar shallow water; numerical validation. Discrete Contin. Dyn. Syst. Ser. B1 (2001) 89–102. Zbl0997.76023MR1821555
  25. [25] J.U. Grobbelaar, C.J. Soeder and E. Stengel, Modeling algal productivity in large outdoor cultures and waste treatment systems. Biomass21 (1990) 297–314. 
  26. [26] H. Guterman, A. Vonshak and S. Ben-Yaakov, A macromodel for outdoor algal mass production. Biotechnol. Bioengineer.35 (1990) 809–819. 
  27. [27] B.P. Han, Photosynthesis-irradiance response at physiological level: a mechanistic model. J. Theoret. Biol.213 (2001) 121–127. 
  28. [28] B.P. Han, A mechanistic model of algal photoinhibition induced by photodamage to photosystem-ii. J. Theoret. Biology214 (2002) 519–527. 
  29. [29] J.-M. Hervouet, Hydrodynamics of Free Surface Flows: Modelling With the Finite Element Method. John Wiley and Sons (2007). Zbl1131.76002
  30. [30] D.L. Huggins, R.H. Piedrahita and T. Rumsey, Analysis of sediment transport modeling using computational fluid dynamics (cfd) for aquaculture raceways. Aquacult. Engrg.31 (2004) 277–293. 
  31. [31] D.L. Huggins, R.H. Piedrahita and T. Rumsey, Use of computational fluid dynamics (cfd) for aquaculture raceway design to increase settling effectiveness. Aquacult. Engrg.33 (2005) 167–180. 
  32. [32] S.C. James and V. Boriah, Modeling algae growth in an open–channel raceway. J Comput. Biol.17 (2010) 895–906. MR2670334
  33. [33] B. Khobalatte and B. Perthame, Maximum principle on the entropy and minimal limitations for kinetic schemes. Research Report RR-1628, Projet MENUSIN. INRIA (1992). Zbl0795.35085
  34. [34] K. Lange and F.J. Oyarzun, The attractiveness of the Droop equations. Math. Biosci.111 (1992) 261–278. Zbl0762.92021MR1181857
  35. [35] H.-P. Luo and M.H. Al-Dahhan, Analyzing and modeling of photobioreactors by combining first principles of physiology and hydrodynamics. Biotechnol. Bioengineer.85 (2004) 382–393. 
  36. [36] F.B. Metting, Biodiversity and application of microalgae. J. Indust. Microbiol. Biotechnol.17 (1996) 477–489. 
  37. [37] J. C. H. Peeters and P. Eilers, The relationship between light intensity and photosynthesis: a simple mathematical model. Hydrobiol. Bull.12 (1978) 134–136. 
  38. [38] I. Perner, C. Posten and J. Broneske, Cfd-aided optimization of a plate photobioreactor for cultivation of microalgae. Chemie Ingenieur Technik74 (2002) 865–869. 
  39. [39] I. Perner-Nochta and C. Posten, Simulations of light intensity variation in photobioreactors. J. Biotechnol.131 (2007) 276–285. 
  40. [40] B. Perthame, Kinetic formulation of conservation laws. Oxford lecture series in mathematics and its applications. Oxford University Press (2002). Zbl1030.35002MR2064166
  41. [41] J. Pruvost, L. Pottier and J. Legrand, Numerical investigation of hydrodynamic and mixing conditions in a torus photobioreactor. Chemical Engineer. Sci.61 (2006) 4476–4489. 
  42. [42] L. Rodolfi, G.C. Zittelli, N. Bassi, G. Padovani, N. Biondi, G. Bonini and M.R. Tredici, Microalgae for Oil: Strain Selection, Induction of Lipid Synthesis and Outdoor Mass Cultivation in a Low-Cost Photobioreactor. Biotechnol. Bioeng.102 (2009) 100–112. 
  43. [43] R. Rosello Sastre, Z. Coesgoer, I. Perner-Nochta, P. Fleck-Schneider and C. Posten, Scale–down of microalgae cultivations in tubular photo-bioreactors – a conceptual approach. J. Biotechnol.132 (2007) 127–133. 
  44. [44] J. Sainte-Marie, Vertically averaged models for the free surface euler system. derivation and kinetic interpretation. Math. Models Methods Appl. Sci. 21 (2011) 459–490. Zbl1223.35253MR2782721
  45. [45] A. Sciandra and P. Ramani, The limitations of continuous cultures with low rates of medium renewal per cell. J. Exp. Mar. Biol. Ecol.178 (1994) 1–15. 
  46. [46] A. Sukenik, P.G. Falkowski and J. Bennett. Potential enhancement of photosynthetic energy conversion in algal mass culture. Biotechnol. Bioengineer.30 (1987) 970–977. 
  47. [47] A. Sukenik, R.S. Levy, Y. Levy, P.G. Falkowski and Z. Dubinsky, Optimizing algal biomass production in an outdoor pond: a simulation model. J. Appl. Phycol.3 (1991) 191–201. 
  48. [48] C. Vejrazka, M. Janssen, M. Streefland and R.H. Wijffels, Photosynthetic efficiency of chlamydomonas reinhardtii in flashing light. Biotechnol. Bioengineer.108 (2011) 2905–2913. 
  49. [49] R.H. Wijffels and M.J. Barbosa, An outlook on microalgal biofuels. Science329 (2010) 796–799. 
  50. [50] P.J.B. Williams and L.M.L. Laurens, Microalgae as biodiesel and biomass feedstocks: Review and analysis of the biochemistry, energetics and economics. Energy Environ. Sci.3 (2010) 554–590. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.