IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-11795-4_7.html
   My bibliography  Save this book chapter

Numerical Optimization of a Bioreactor for the Treatment of Eutrophicated Water

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lino J. Alvarez-Vázquez & Francisco J. Fernández & Aurea Martínez, 2010. "Numerical Optimization of a Bioreactor for the Treatment of Eutrophicated Water," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 77-85, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_7
    DOI: 10.1007/978-3-642-11795-4_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-11795-4_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.