Advertisement

A Strategy for Bioremediation of Marine Shorelines by Using Several Nutrient Release Points

  • David Parra-GuevaraEmail author
  • Yuri N. Skiba
Chapter
Part of the The Reacting Atmosphere book series (REAT, volume 2)

Abstract

In this chapter, a strategy for the bioremediation of marine shorelines polluted with oil is presented. Several discharge points are chosen in a limited region in order to release a nutrient and reach critical concentration of this substance in the oil-polluted shorelines. The strategy is optimal in the sense that the location of the discharge points and the release rates are planned so as to minimize the amount of the nutrient introduced into the aquatic system. To accomplish this task, a variational problem is solved to find the location of the discharge point in each oil-polluted zone, and to determine a basic (preliminary) shape of its release rate. After that, a quadratic programming problem is solved to specify the strength of these release rates in order to reach the critical concentration in all the polluted zones during the same time interval. An initial-boundary value 3D advection-diffusion problem and its adjoint problems are considered in a limited area to model, estimate and control the dispersion of the nutrient. It is shown that the advection-diffusion problem is well posed, and its solution satisfies the mass balance equation. In each oil-polluted zone, the mean concentration of nutrient is determined by means of an integral formula in which the adjoint model solution serves as the weight function showing the relative contribution of each source. Critical values of these mean concentrations are used as the constraints for the variational problem as well as for the quadratic programming problem. The ability of new method is demonstrated by numerical experiments on the remediation in oil-polluted channel using three control zones.

Notes

Acknowledgments

This work was supported by the PAPIIT projects IN103313-2 and IN101815-3 (UNAM, México) and by the grants 14539 and 25170 of National System of Researches (CONACyT, México). The authors are grateful to Marco Antonio Rodríguez García for his help in preparing the final version of this manuscript in Open image in new window .

References

  1. 1.
    Alvarez-Vázquez, L.J., García-Chan, N., Martínez, A., Vázquez-Méndez, M.E., Vilar, M.A.: Optimal control in wastewater management: a multi-objective study. Commun. Appl. Ind. Math. 1(2), 62–77 (2010)MathSciNetGoogle Scholar
  2. 2.
    Boufadel, M.C., Suidan, M.T., Venosa, A.D.: Tracer studies in laboratory beach simulating tidal influences. J. Environ. Eng. 132(6), 616–623 (2006)CrossRefGoogle Scholar
  3. 3.
    Boufadel, M.C., Suidan, M.T., Venosa, A.D.: Tracer studies in a laboratory beach subjected to waves. J. Environ. Eng. 133(7), 722–732 (2007)CrossRefGoogle Scholar
  4. 4.
    Bragg, J.R., Prince, R.C., Harner, E.J., Atlas, R.M.: Effectiveness of bioremediation for the Exxon Valdez oil spill. Nature 368, 413–418 (1994)CrossRefGoogle Scholar
  5. 5.
    Cheney, E.W.: Introduction to Approximation Theory. Chelsea Publishing Company, New York (1966)zbMATHGoogle Scholar
  6. 6.
    Coleman, T.F., Li, Y.: A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables. SIAM J. Optim. 6(4), 1040–1058 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Coulon, F., McKew, B.A., Osborn, A.M., McGenity, T.J., Timmis, K.N.: Effects of temperature and biostimulation on oil-degrading microbial communities in temperate estuarine waters. Environ. Microbiol. 9(1), 177–186 (2006)CrossRefGoogle Scholar
  8. 8.
    Crank, J., Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proc. Camb. Philos. Soc. 43, 50–67 (1947)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Dang, Q.A., Ehrhardt, M., Tran, G.L., Le, D.: Mathematical modeling and numerical algorithms for simulation of oil pollution. Environ. Model. Assess. 17(3), 275–288 (2012)CrossRefGoogle Scholar
  10. 10.
    Dieudonné, J.: Foundations of Modern Analysis. Academic Press, New York (1969)zbMATHGoogle Scholar
  11. 11.
    Folland, G.B.: Real Analysis: Modern Techniques and Their Applications. Wiley, New York (1999)zbMATHGoogle Scholar
  12. 12.
    Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, London (1981)zbMATHGoogle Scholar
  13. 13.
    Hadamard, J.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale University Press, New Haven (1923)zbMATHGoogle Scholar
  14. 14.
    Head, M., Swannell, R.P.J.: Bioremediation of petroleum hydrocarbon contaminants in marine habitats. Curr. Opin. Biotechnol. 10(3), 234–239 (1999)CrossRefGoogle Scholar
  15. 15.
    Hinze, M., Yan, N.N., Zhou, Z.J.: Variational discretization for optimal control governed by convection dominated diffusion equations. J. Comput. Math. 27(2–3), 237–253 (2009)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Hongfei, F.: A characteristic finite element method for optimal control problems governed by convection-diffusion equations. J. Comput. Appl. Math. 235(3), 825–836 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Kreyszig, E.: Introductory Functional Analysis with Applications. Wiley, New York (1989)zbMATHGoogle Scholar
  18. 18.
    Kreyszig, E.: Advanced Engineering Mathematics. Wiley, New Jersey (2006)Google Scholar
  19. 19.
    Ladousse, A., Tramier, B.: Results of 12 years of research in spilled oil bioremediation: Inipol EAP22. In: Hildrew, J.C., Ludwigson, J. (eds.) Proceedings of the 1991 International Oil Spill Conference, vol. 1, pp. 577–582. American Petroleum Institute, Washington DC (1991)Google Scholar
  20. 20.
    Liu, F., Zhang, Y.H., Hu, F.: Adjoint method for assessment and reduction of chemical risk in open spaces. Environ. Model. Assess. 10(4), 331–339 (2005)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Marchuk, G.I.: Numerical Solution of Problems of the Dynamics of Atmosphere and Ocean. Leningrad, Gidrometeoizdat (in Russian) (1974)Google Scholar
  22. 22.
    Marchuk, G.I.: Mathematical Models in Environmental Problems. Elsevier, New York (1986)zbMATHGoogle Scholar
  23. 23.
    Marchuk, G.I., Skiba, Y.N.: Role of adjoint functions in studying the sensitivity of a model of the thermal interaction of the atmosphere and ocean to variations in input data. Izv., Atmos. Ocean. Phys. 26, 335–342 (1990)Google Scholar
  24. 24.
    Marchuk, G.I.: Adjoint Equations and Analysis of Complex Systems. Kluwer, Dordrecht (1995)CrossRefzbMATHGoogle Scholar
  25. 25.
    Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2, 575–601 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Mills, M.A., Bonner, J.S., Simon, M.A., McDonald, T.J., Autenrieth, R.L.: Bioremediation of a controlled oil release in a wetland. In: Proceedings of the 24th Arctic and Marine Oil Spill (AMOP) Program Technical Seminar, vol. 1, pp. 609–616. Environment Canada, Ottawa, Ontario, Canada (1997)Google Scholar
  27. 27.
    National Research Council: Oil in the Sea III: Inputs. Fates and Effects, National Academy of Sciences, Washington DC (2002)Google Scholar
  28. 28.
    Parra-Guevara, D., Skiba, Y.N., Reyes-Romero, A.: Existence and uniqueness of the regularized solution in the problem of recovery the non-steady emission rate of a point source: application of the adjoint method. In: Rodrigues, H.C., et al. (eds.) Proceedings of the International Conference on Engineering Optimization (ENGOPT 2014), Engineering Optimization IV, pp. 181–186. CRC Press/Balkema, The Netherlands (2015)Google Scholar
  29. 29.
    Parra-Guevara, D., Skiba, Y.N.: A variational model for the remediation of aquatic systems polluted by biofilms. Int. J. Appl. Math. 20(7), 1005–1026 (2007)zbMATHMathSciNetGoogle Scholar
  30. 30.
    Parra-Guevara, D., Skiba, Y.N., Pérez-Sesma, A.: A linear programming model for controlling air pollution. Int. J. Appl. Math. 23(3), 549–569 (2010)zbMATHMathSciNetGoogle Scholar
  31. 31.
    Parra-Guevara, D., Skiba, Y.N., Arellano, F.N.: Optimal assessment of discharge parameters for bioremediation of oil-polluted aquatic systems. Int. J. Appl. Math. 24(5), 731–752 (2011)zbMATHMathSciNetGoogle Scholar
  32. 32.
    Parra-Guevara, D., Skiba, Y.N.: An optimal strategy for bioremediation of aquatic systems polluted by oil. In: Daniels, J.A. (ed.) Advances in Environmental Research, vol. 15, pp. 165–205. Nova Science Publishers Inc, New York (2011)Google Scholar
  33. 33.
    Parra-Guevara, D., Skiba, Y.N.: A linear-programming-based strategy for bioremediation of oil-polluted marine environments. Environ. Model. Assess. 18(2), 135–146 (2013)CrossRefGoogle Scholar
  34. 34.
    Parra-Guevara, D., Skiba, Y.N.: Adjoint approach to estimate the non-steady emission rate of a point source. Int. J. Eng. Res. Appl. 3(6), 763–776 (2013)Google Scholar
  35. 35.
    Prince, R.C., Bare, R.E., Garrett, R.M., Grossman, M.J., Haith, C.E., Keim, L.G., Lee, K., Holtom, G.J., Lambert, P., Sergy, G.A., Owens, E H., Guénette, C.C.: Bioremediation of a marine oil spill in the Arctic. In: Alleman, B.C., Leeson, A. (eds.) In Situ Bioremediation of Petroleum Hydrocarbon and Other Organic Compounds, pp. 227–232, Battle Press, Columbus (1999)Google Scholar
  36. 36.
    Prince, R.C., Clark, J.R., Lindstrom, J.E., Butler, E.L., Brown, E.J., Winter, G., Grossman, M.J., Parrish, R.R., Bare, R.E., Braddock, J.F., Steinhauer, W.G., Douglas, G.S., Kennedy, J.M., Barter, P.J., Bragg, J.R., Harner, E.J., Atlas, R.M.: Bioremediation of the Exxon Valdez oil spill: monitoring safety and efficacy. In: Hinchee, R.E., Alleman, B.C., Hoeppel, R.E., Miller, R.N. (eds.) Hydrocarbon Remediation, pp. 107–124. Lewis Publishers, Boca Raton (1994)Google Scholar
  37. 37.
    Prince, R.C., Bragg, J.R.: Shoreline bioremediation following the Exxon Valdez oil spill in Alaska. Bioremediation J. 1, 97–104 (1997)CrossRefGoogle Scholar
  38. 38.
    Prince, R.C., Lessard, R.R., Clark, J.R.: Bioremediation of marine oil spills. Oil Gas Sci. Technol. 58(4), 463–468 (2003)CrossRefGoogle Scholar
  39. 39.
    Pudykiewicz, J.: Application of adjoint tracer transport equations for evaluating source parameters. Atmos. Environ. 32, 3039–3050 (1998)CrossRefGoogle Scholar
  40. 40.
    Ramsay, M.A., Swannell, R.P.J., Shipton, W.A., Duke, N.C., Hill, R.T.: Effect of bioremediation on the microbial community in oiled mangrove sediments. Mar. Pollut. Bull. 41, 413–419 (2000)CrossRefGoogle Scholar
  41. 41.
    Skiba, Y.N.: Balanced and absolutely stable implicit schemes for the main and adjoint pollutant transport equations in limited area. Rev. Int. Contam. Ambient. 9, 39–51 (1993)Google Scholar
  42. 42.
    Skiba, Y.N.: Dual oil concentration estimates in ecologically sensitive zones. Environ. Monit. Assess. 43, 139–151 (1996)CrossRefGoogle Scholar
  43. 43.
    Skiba, Y.N., Parra-Guevara, D.: Industrial pollution transport part I: formulation of the problem and air pollution estimates. Environ. Model. Assess. 5, 169–175 (2000)CrossRefGoogle Scholar
  44. 44.
    Smith, D.R.: Variational Methods in Optimization. Dover Publications, New York (1998)zbMATHGoogle Scholar
  45. 45.
    Swannell, R.P.J., Mitchell, D., Jones, D.M., Petch, S., Head, I.M., Wilis, A., Lee, K., Lepo, J.E.: Bioremediation of oil-contaminated fine sediment. In: Marshall, S. (ed.) Proceedings of the 1999 International Oil Spill Conference, vol. 1, pp. 751–756. American Petroleum Institute, Washington DC (1999)Google Scholar
  46. 46.
    Swannell, R.P.J., Mitchell, D., Lethbridge, G., Jones, D., Heath, D., Hagley, M., Jones, M., Petch, S., Milne, R., Croxford, R., Lee, K.: A field demonstration of the efficacy of bioremediation to treat oiled shorelines following the Sea Empress incident. Environ. Technol. 20, 863–873 (1999)CrossRefGoogle Scholar
  47. 47.
    Venosa, A.D.: Oil spill bioremediation on coastal shorelines: a critique. In: Sikdar, S.K., Irvine, R.I. (eds.) Bioremediation: Principles and Practice, Vol. III. Bioremediation Technologies, pp. 259–301. Technomic, Lancaster (1998)Google Scholar
  48. 48.
    Venosa, A.D., Suidan, M.T., Wrenn, B.A., Strohmeier, K.L., Haines, J.R., Eberhart, B.L., King, D., Holder, E.: Bioremediation of an experimental oil spill on the shoreline of Delaware Bay. Environ. Sci. Technol. 30, 1764–1775 (1996)CrossRefGoogle Scholar
  49. 49.
    Yan, N.N., Zhou, Z.J.: A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection-dominated diffusion equation. J. Comput. Appl. Math. 223(1), 198–217 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  50. 50.
    Yee, E.: Theory for reconstruction of an unknown number of contaminant sources using probabilistic inference. Bound.-Layer Meteorol. 127(3), 359–394 (2008)CrossRefMathSciNetGoogle Scholar
  51. 51.
    Zhang, Y.: Solving large-scale linear programs by interior-point methods under the MATLAB environment. Technical report TR96-01, Department of Mathematics and Statistics, University of Maryland (1995)Google Scholar
  52. 52.
    Zhu, X., Venosa, A.D., Suidan, M.T., Lee, K.: Guidelines for the Bioremediation of Marine Shorelines and Freshwater Wetlands. U.S. Environmental Protection Agency, Cincinnati (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, Circuito ExteriorCiudad UniversitariaMexico, D.F.Mexico

Personalised recommendations