The most used algae cultivation systems are the open-channel raceway ponds for their low maintenance and energy costs. Raceways allow algal cultivation using wastewater, where algae mass 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/or rotational speed of the turning paddle wheel, and by the height of water. In this work we introduce a novel methodology to automate the optimization of the design of raceway ponds based on techniques of optimal control of partial differential equations. So, we formulate the problem as a control problem where the state system is given by the coupled nonlinear equations for hydrodynamics and algae/nitrogen/phosphorus concentrations, 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 optimal 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.

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Published on 24/05/23
Submitted on 24/05/23

Volume Advanced Techniques for Data Assimilation, Inverse Analysis, and Data-based Enrichment of Simulation Models, 2023
DOI: 10.23967/admos.2023.016
Licence: CC BY-NC-SA license

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