ADMOS 2023

Algal Cultivation for Bioenergy Production: First Mathematical Modelling Results in Raceways

  • Martinez, Aurea (Universidade de Vigo)
  • Alvarez-Vazquez, Lino Jose (Universidade de Vigo)
  • Rodriguez, Carmen (Universidade de Santiago de Compostela)
  • Vazquez-Mendez, Miguel Ernesto (Universidade de Santiago de Compostela)

Please login to view abstract download link

Wastewater treatment by algae-based technologies is an effective solution that allows, as a by-product, the recovery of materials that can be used, for instance, to produce bioenergy (biodiesel, bioalcohol, etc.) due to the richness of lipides of the algal biomass coming from wastewater treatments. The most used algae cultivation systems are the open-channel raceway ponds (open channels in the shape of an oval equipped with a rotating paddle wheel in order to promote the recirculation of the shallow water inside them) for their low maintenance and energy costs. Raceways allow algal cultivation using wastewater and, once the algae mass has grown enough, it is recovered by any mechanical/chemical harvesting method, and can be employed as source for bioenergy production. One of the main external factors influencing algal productivity is the velocity of the liquid inside the pond, that can be easily controlled by the position and rotational speed of the turning paddle wheel. The optimal design of raceway ponds has been widely studied within the scientific literature, but mainly by the comparison of case studies and the use of statistical techniques. Nevertheless, the application of techniques of optimal control of partial differential equations -as it is our proposal- for the simultaneous optimization of speed and position of the rotating paddlewheel has remained completely unaddressed, as far as we know. In this work we introduce a novel methodology to automate the optimization of location and manage- ment of the paddlewheel in a raceway pond. So, we formulate the problem as an optimal control problem where the state system is given by the coupled nonlinear equations for hydrodynamics and algae/nitrogen/phosphorus concentrations, the control variables are location and rotational speed of the paddlewheel, and the objective function to be maximized represents the global concentration of algae at final time. We present here a detailed, rigorous mathematical formulation of the control problem, we propose a numerical algorithm for its resolution, and we show some preliminary computational results related to the numerical modelling of the problem.