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

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Mathematical Modelling and Numerical Simulation of Oil Pollution Problems

Part of the book series: The Reacting Atmosphere ((REAT,volume 2))

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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.

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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 .

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  1. Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, C.P 04510, Mexico, D.F., Mexico

    David Parra-Guevara & Yuri N. Skiba

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  1. David Parra-Guevara
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  2. Yuri N. Skiba
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Correspondence to David Parra-Guevara .

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  1. Fachbereich C, Chair of Applied Mathematics / Numerical Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    Matthias Ehrhardt

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Parra-Guevara, D., Skiba, Y.N. (2015). A Strategy for Bioremediation of Marine Shorelines by Using Several Nutrient Release Points. In: Ehrhardt, M. (eds) Mathematical Modelling and Numerical Simulation of Oil Pollution Problems. The Reacting Atmosphere, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-16459-5_2

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