by Olivier Bernard, Jacques Sainte-Marie, Bruno Sialve and Jean-Philippe Steyer
Biofuel production from microalgae represents an acute optimization problem for industry. There is a wide range of parameters that must be taken into account in the development of this technology. Here, mathematical modelling has a vital role to play.
The potential of microalgae as a source of biofuel and as a technological solution for CO2 fixation is the subject of intense academic and industrial research. Large-scale production of microalgae has potential for biofuel applications owing to the high productivity that can be attained in high-rate raceway ponds .
Based in France, “Green Stars” is a large research and development project involving scientists and industry whose aim is to explore the use of micro-algae, particularly in the form of “third generation biofuels”. The program has enormous promise, with this resource potentially offering a tremendous solution for the major economic developments of the coming decade. Some microalgal species have far more efficient growth, by photosynthesis, than terrestrial plants. Moreover, they can accumulate oils or sugars, which can be turned into biodiesel or bioethanol. Twenty to 30 tons of oil per hectare per year are expected to be extracted from micro-algae, compared with six tons from the palm trees and a little more than one ton from rapeseed.
The objective of Green Stars is to lay the foundations for the entire sector, from energy generation to waste recycling and the production of compounds of interest. Green Stars also plans to play a long-term role in this field by training technicians, engineers and researchers.
The role of mathematical modelling and simulations
One of the key challenges in the production of microalgae is to maximize algae growth with respect to the used exogenous energy (paddlewheels, pumps, etc.).
There are a large number of parameters that need to be optimized, including: the characteristics of the biological species, the raceway shape and the stirring provided by the paddlewheel; consequently our strategy is to develop efficient models and numerical tools to reproduce the flow induced by the paddlewheel and the evolution of the biological species within this flow. Here, mathematical models can greatly help us to reduce experimental costs.
Figure 1: A typical raceway for cultivating microalgae. Notice the paddlewheel which mixes the culture suspension. Photo: INRA
Owing to the high heterogeneity of raceways due to gradients of temperature, light intensity and nutrient availability through water height, we cannot use depth-averaged models (Shallow Water type models). We adopt instead more accurate models that have recently been proposed . These models are particularly appropriate for representation of these free surface systems. For hydrodynamics, we use the incompressible hydrostatic Navier-Stokes equations, forced by a paddlewheel-like move. The biological dynamics are represented by an improved and distributed (in space) model that includes light effect on algae growth and carbon storage depending on nitrogen limitation.
We show, through 3D numerical simulations, that our approach is capable of discriminating between situations of rapidly moving water or slow agitation, choosing an optimal water height or proposing initial conditions for the biological variables. Moreover, the simulated velocity fields can provide lagrangian trajectories of the algae. The resulting light pattern to which each cell is submitted when travelling from light (surface) to dark (bottom) can then be derived. It will then be reproduced in lab experiments to study photosynthesis under realistic light patterns.
It is clear, however, that many complex physical phenomena have to be added to our model, such as the effect of sunlight on water temperature/density, evaporation and external forcing (wind). Moreover, some microalgae species do not only swim in the water (advection plus diffusion effects) but also deposit.
 B. Sialve, N. Bernet and O. Bernard: “Anaerobic digestion of microalgae as a necessary step to make microalgal biodiesel sustainable”, Biotechnology Advances, 27:4, p. 409-416, 2009
 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 solution, J. Comp. Phys., 230, p. 3453-3478, 2011.
Olivier Bernard, Inria team Biocore, Sophia-Antipolis, France
Jacques Sainte-Marie, Inria team ANGE, Paris-Rocquencourt, France
Bruno Sialve , INRA Narbonne, France
Jean-Philippe Steyer, INRA Narbonne