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Optimal Control of Phytoremediation Techniques for Heavy Metals Removal in Shallow Water

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EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization (EngOpt 2018)

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Abstract

In this work we deal with the optimization of different issues related to heavy metals phytoremediation techniques, by combining mathematical modelling, optimal control of partial differential equations and numerical optimization. We introduce a 2D mathematical system of nonlinear partial differential equations modelling the concentrations of heavy metals, algae and nutrients in large waterbodies. We formulate an optimal control problem related to the optimization of the phytoremediation process, and propose a full algorithm for computing the numerical solution of the problem. Finally, we present several numerical results for a realistic problem related to: (i) determining the minimal quantity of algae to be used in the heavy metals remediation process, and (ii) locating the optimal place for such algal mass.

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References

  1. Alvarez-Vázquez, L.J., Fernández, F.J., Martínez, A.: Optimal management of a bioreactor for eutrophicated water treatment: a numerical approach. J. Sci. Comput. 43, 67–91 (2010). https://doi.org/10.1007/s10915-009-9344-7

    Article  MathSciNet  MATH  Google Scholar 

  2. Alvarez-Vázquez, L.J., Fernández, F.J., Muñoz-Sola, R.: Mathematical analysis of a three-dimensional eutrophication model. J. Math. Anal. Appl. 349, 135–155 (2009). https://doi.org/10.1016/j.jmaa.2008.08.031

    Article  MathSciNet  MATH  Google Scholar 

  3. Alvarez-Vázquez, L.J., Martínez, A., Muñoz-Sola, R., Rodríguez, C., Vázquez-Méndez, M.E.: The water conveyance problem: optimal purification of polluted waters. Math. Models Meth. Appl. Sci. 15, 1393–1416 (2005). https://doi.org/10.1142/S0218202505000790

    Article  MathSciNet  MATH  Google Scholar 

  4. Alvarez-Vázquez, L.J., Martínez, A., Rodríguez, C., Vázquez-Méndez, M.E.: Numerical optimization for the location of wastewater outfalls. Comput. Optim. Appl. 22, 399–417 (2002). https://doi.org/10.1023/A:1019767123324

    Article  MathSciNet  MATH  Google Scholar 

  5. Alvarez-Vázquez, L.J., Martínez, A., Rodríguez, C., Vázquez-Méndez, M.E.: Sediment minimization in canals: an optimal control approach. Math. Comput. Simul. 149, 109–122 (2018). https://doi.org/10.1016/j.matcom.2018.02.007

    Article  MathSciNet  Google Scholar 

  6. Casas, E., Ryll, C., Troltzsch, F.: Sparse optimal control of the Schlogl and FitzHugh-Nagumo systems. Comput. Meth. Appl. Math. 13, 415–442 (2013). https://doi.org/10.1515/cmam-2013-0016

    Article  MathSciNet  MATH  Google Scholar 

  7. Hecht, F.: New development in Freefem++. J. Numer. Math. 20, 251–265 (2012). https://doi.org/10.1515/jnum-2012-0013

    Article  MathSciNet  MATH  Google Scholar 

  8. Mani, D., Kumar, C.: Biotechnological advances in bioremediation of heavy metals contaminated ecosystems: an overview with special reference to phytoremediation. Int. J. Environ. Sci. Technol. 11, 843–872 (2014). https://doi.org/10.1016/j.jmaa.2008.08.031

    Article  Google Scholar 

  9. Martínez, A., Alvarez-Vázquez, L.J., Rodríguez, C., Vázquez-Méndez, M.E., Vilar, M.A.: Optimal shape design of wastewater canals in a thermal power station. In: Fontes, M., Gunther, M., Marheineke, N. (eds.) Progress in Industrial Mathematics at ECMI 2012, pp. 59–64. Springer, New York (2014)

    Chapter  Google Scholar 

  10. MIKE 21: User guide and reference manual. Danish Hydraulic Institute, Horsholm (2001)

    Google Scholar 

  11. Perales-Vela, H., Peña-Castro, J., Cañizares-Villanueva, R.: Heavy metal detoxification in eukaryotic microalgae. Chemosphere 64, 1–10 (2006). https://doi.org/10.1016/j.chemosphere.2005.11.024

    Article  Google Scholar 

  12. Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25–57 (2006). https://doi.org/10.1007/s10107-004-0559-y

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors thank the funding from project MTM2015-65570-P of MINECO/ FEDER (Spain). The support provided by DHI with modelling system MIKE21 is also greatly appreciated.

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Authors and Affiliations

  1. E.I. Telecomunicación, Universidade de Vigo, 36310, Vigo, Spain

    Lino J. Alvarez-Vázquez & Aurea Martínez

  2. Fac. Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago, Spain

    Carmen Rodríguez

  3. E.P.S. Enxeñería, Universidade de Santiago de Compostela, 27002, Lugo, Spain

    Miguel E. Vázquez-Méndez & Miguel A. Vilar

Authors
  1. Lino J. Alvarez-Vázquez
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  2. Aurea Martínez
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  3. Carmen Rodríguez
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  4. Miguel E. Vázquez-Méndez
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  5. Miguel A. Vilar
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Corresponding author

Correspondence to Lino J. Alvarez-Vázquez .

Editor information

Editors and Affiliations

  1. Mechanical Engineering Department, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    H.C. Rodrigues

  2. Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    J. Herskovits

  3. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    C.M. Mota Soares

  4. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    A.L. Araújo

  5. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    J.M. Guedes

  6. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    J.O. Folgado

  7. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    F. Moleiro

  8. IST, IDMEC – Instituto de Engenharia Mecânica, Lisbon, Portugal

    J. F. A. Madeira

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Alvarez-Vázquez, L.J., Martínez, A., Rodríguez, C., Vázquez-Méndez, M.E., Vilar, M.A. (2019). Optimal Control of Phytoremediation Techniques for Heavy Metals Removal in Shallow Water. In: Rodrigues, H., et al. EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization. EngOpt 2018. Springer, Cham. https://doi.org/10.1007/978-3-319-97773-7_32

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  • DOI: https://doi.org/10.1007/978-3-319-97773-7_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-97772-0

  • Online ISBN: 978-3-319-97773-7

  • eBook Packages: EngineeringEngineering (R0)

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