Lagrangian Approaches for Modelling and Optimization of Hydrodynamic-Photosynthesis Coupling

Abstract

Microalgae are photosynthetic micro-organisms whose potential has been highlighted in the last decade. Applications can be found from to renewable energy production and wastewater treatment to some high added value commercial products e.g., food, pharmaceutical, cosmetics. Nevertheless, finding optimal growth conditions for full-scale cultivation of microalgae remains challenging in practice. Mathematical models are therefore of great help to better manage this complex, nonlinear dynamical system. The aim of this thesis is to better understand how different factors affect microalgal growth. In a first part, we study the influence of the light attenuation and the optimal condition to maximize the productivity. In this way, we introduce an optical productivity which enables us to determine the optimal condition for general light extinction function. A global optimal optical depth is found which consists in canceling the algal net growth rate at the bottom of the reactors to maximize the optical productivity. It can be used to characterize the optimization of the areal productivity in some specific cases, whereas an asymptotic behaviour has been observed in more general case. We then limit ourselves to a specific reactor - the raceway pond, which is an outdoor circuit basin combining with a paddle wheel. We start by investigating a resource allocation problem issuing from the re-distribution of the light resource to the algae by the paddle wheel. A generic mixing device is considered to assign at each lap the light resource to the algae layers in the raceway. We determine the optimal allocation strategies to maximize the algal growth. In a third part, we show how the shape of the topography affects (or not) the algal growth in raceway ponds. In this way, we consider a hydrodynamical-biological coupled model and introduce an optimization problem associated with the topography to maximize the algal growth. We also combine the optimization of the topographies with the previous allocation strategies to investigate their influence on algal production. Non-trivial topographies are obtained numerically to enhance the algal growth. The mathematical study of these optimization problems leads to new interesting working directions, improves and clarifies the understanding of influence by different factors on algal growth. We conclude with some discussions and perspectives of this work.