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Numerical Solution of a PDE System with Non-Linear Steady State Conditions that Translates the Air Stripping Pollutants Removal

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Nonlinear Science and Complexity

Abstract

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

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References

  1. E. Bouwer, M.C. Kavanaugh, Coping with groundwater contamination. J. Water Polut. Control Fed. 60, 1415–1427 (1988)

    Google Scholar 

  2. A.O. Bradley, Remove VOCs from wastewater by air stripping. Chem. Eng. Progr. 60, 89–93 (1992)

    Google Scholar 

  3. W.V. Chang, Stripping of TCE from water at low air/water ratios. Environ. Progr. 14, 111–114 (1995)

    Article  Google Scholar 

  4. D. Hand, Design and evaluation of an air stripping tower for removing VOCs from groundwater. J. Am. Water Works Assoc., 87–97 (1986)

    Google Scholar 

  5. J.G. Kunesh, Recent developments in packed columns. Can. J. Chem. Eng. 65, 907–913 (1987)

    Article  Google Scholar 

  6. A. Mersmann, A. Deixler, Packed columns. Ger. Chem. Eng., 265–276 (1986)

    Google Scholar 

  7. R.W. Rousseau, Analyzing chemical absorbers and strippers. Chem. Eng. June, 91–95 (1985)

    MathSciNet  Google Scholar 

  8. W. Yang, Removal of trihalomethanes from water by air stripping. Water Treat. June, 267–282 (1991)

    Google Scholar 

  9. A.C.M. Castro, Projecto e simulação dinâmica utilizando um sistema de parâmetros distribuidos, PhD Thesis, Faculdade de Engenharia da Universidade do Porto, Portugal, 2004

    Google Scholar 

  10. J.D. Seader, E.J. Henley, Separation Process Principles (Wiley, New York, 1998)

    Google Scholar 

  11. J.L. Schnoor, Environmental Modelling—Fate and Transport of Pollutants in Water, Air and Soil (Wiley, New York, 1996)

    Google Scholar 

  12. I.A. Furzer, Liquid dispersion in packed columns I. Chem. Eng. Sci. 39, 70–76 (1984)

    Google Scholar 

  13. I.A. Furzer, Liquid dispersion in packed columns II. Chem. Eng. Sci. 39, 77–80 (1984)

    Google Scholar 

  14. E. James, W. Byers, Limitations and practical use of mass transfer model for predicting air stripper performance. Environ. Progr. 12, 61–66 (1993)

    Article  Google Scholar 

  15. W. Ball, M.C. Kavanaugh, Mass transfer of volatile organic compounds in packed tower aeration. J. Water Polut. Control Fed. 56, 127–136 (1984)

    Google Scholar 

  16. P. Lamarche, R. Droste, Air stripping mass transfer correlations for volatile organics. J. Am. Water Works Assoc., 78–89 (1989)

    Google Scholar 

  17. M. Leva, Reconsider packed-tower pressure-drop correlations. Chem. Eng. Progr. January, 65–72 (1992)

    Google Scholar 

  18. K. Onda, Mass transfer coefficients between gas and liquid phases in packed columns. J. Chem. Eng. Jpn. 1, 56–62 (1968)

    Article  Google Scholar 

  19. C. Yaws, Henry’s law constants for organic compounds in water. Chem. Eng. November, 179–185 (1991)

    Google Scholar 

  20. V. Stanek, Transients of the hydrodynamics of counter-current packed-bed columns. Chem. Eng. Sci. 45, 449–455 (1990)

    Article  Google Scholar 

  21. C. Lanczos, Trigonometric interpolation of empirical and analytical functions. J. Math. Phys. 17, 123–199 (1938)

    Google Scholar 

  22. C. Lanczos, Applied Analysis (Pitman, London, 1957)

    Google Scholar 

  23. J. Matos, M.J. Rodrigues, P.B. Vasconcelos, New implementation of the Tau method for PDEs. J. Comput. Appl. Math. 164–165, 555–567 (2004)

    Article  MathSciNet  Google Scholar 

  24. E.L. Ortiz, The Tau method. SIAM J. Numer. Anal. Optim. 12, 480–492 (1969)

    Article  MathSciNet  Google Scholar 

  25. M.R. Silva, Numerical treatment of differential equations with the Tau method. J. Comput. Appl. Math. 20, 167–173 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  26. M.R. Silva, M.J. Rodrigues, A simple alternative principle for rational τ-method approximation, in Nonlinear Numerical Methods and Rational Approximation, ed. by A. Cuyt (Reidel, Dordrecht, 1988), pp. 427–434

    Chapter  Google Scholar 

  27. M. Hosseini Ali Abadi, E.L. Ortiz, Numerical treatment of moving and free boundary value problems with the Tau method. Comput. Math. Appl. 35, 53–61 (1998)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. LEMA—Laboratório de Engenharia Matemática, Porto, Portugal

    Ana C. Meira Castro, J. Matos & A. Gavina

  2. ISEP—Instituto Superior de Engenharia do Porto, Porto, Portugal

    Ana C. Meira Castro, J. Matos & A. Gavina

  3. CIGAR—Centro de Investigação em Geo-Ambiente e Recursos, Porto, Portugal

    Ana C. Meira Castro

  4. CMUP—Centro de Matemática da Universidade do Porto, Porto, Portugal

    J. Matos

Authors
  1. Ana C. Meira Castro
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  2. J. Matos
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  3. A. Gavina
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Corresponding author

Correspondence to Ana C. Meira Castro .

Editor information

Editors and Affiliations

  1. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    J.A. Tenreiro Machado

  2. Dept. of Mech. & Industr. Engineering, Southern Illinois Univ. Edwardsville, Edwardsville, 62026-1805, Illinois, USA

    Albert C.J. Luo

  3. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Ramiro S. Barbosa

  4. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Manuel F. Silva

  5. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Lino B. Figueiredo

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Meira Castro, A.C., Matos, J., Gavina, A. (2011). Numerical Solution of a PDE System with Non-Linear Steady State Conditions that Translates the Air Stripping Pollutants Removal. In: Machado, J., Luo, A., Barbosa, R., Silva, M., Figueiredo, L. (eds) Nonlinear Science and Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9884-9_26

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  • DOI: https://doi.org/10.1007/978-90-481-9884-9_26

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9883-2

  • Online ISBN: 978-90-481-9884-9

  • eBook Packages: EngineeringEngineering (R0)

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