Topography optimization for enhancing Microalgal growth in raceway ponds

Abstract

Modeling the evolution process for the growth of microalgae in the raceway pond is a huge challenge, given the complex interaction between hydrodynamics and biological processes occurring across various timescales. The aim of our current study is to investigate theoretically the impact of bottom topography in raceway ponds on microalgae growth. To achieve this goal, we consider a biological model (based on the Han model) coupled with the Saint-Venant systems that model the fluid into the raceway pond. In particular, we focus on the laminar region of the fluid, far from the paddle wheel, and investigate how different topographies may influence the growth rate of microalgae. This consideration enables us to formulate an optimization problem, for which we apply the Pontryagin Maximum Principle (PMP) to identify the optimal topographies that maximize the biomass production over one lap of the raceway pond or multiple laps with a paddle wheel. On the contrary to a widespread belief in the microalgae field, the results show that a flat topography is optimal in a periodic regime. However, non-trivial topographies may be more advantageous in alternative scenarios, such as when considering the effects of mixing devices within the model. This study sheds light on the intricate relationship between bottom topography, fluid dynamics, and microalgae growth in raceway ponds, offering valuable insights into optimizing biomass production.