Numerical Optimization of a Bioreactor for the Treatment of Eutrophicated Water

Lino J. Alvarez-Vázquez (), Francisco J. Fernández () and Aurea Martínez ()
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Lino J. Alvarez-Vázquez: Universidad de Vigo, Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación
Francisco J. Fernández: Universidad de Santiago de Compostela, Departamento de Matemática Aplicada, Facultad de Matemáticas
Aurea Martínez: Universidad de Vigo, Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 77-85 from Springer

Abstract: Abstract The fundamental idea of a bioreactor consists of holding up eutrophicated water (rich, for instance, in nitrogen) in large tanks where we add a certain quantity of phytoplankton, that we let grow in order to absorb nitrogen and purify water. Its optimal management can be formulated as an optimal control problem with state constraints, where the control can be the quantity of phytoplankton added at each tank or the permanence times, the state variables are the concentrations of the species involved (nutrient, phytoplankton, zooplankton and organic detritus), the objective function to be minimized is the phytoplankton concentration of water leaving the bioreactor, and the state constraints stand for the thresholds imposed on the nitrogen and detritus concentrations in each tank. We recall that this optimal control problem possesses a solution, which can be characterized by a first order optimality condition. After discretizing the control problem, we present a structured algorithm for solving the resulting nonlinear constrained optimization problem. Finally, we also give numerical results for a real-world example.

Keywords: Optimal Control Problem; State Constraint; Numerical Optimization; Eutrophicated Water; Control Constraint (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_7

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