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A Linear-Programming-Based Strategy for Bioremediation of Oil-Polluted Marine Environments

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Abstract

A linear programming problem is considered with the aim to determine the optimal discharge point and the optimal discharge rate of a nutrient to be released to a marine environment polluted with oil. The objective is to minimize the total discharge of nutrient into the system provided that the concentrations of nutrient will reach critical values sufficient to eliminate oil residuals in certain affected zones through bioremediation. An initial boundary-value 3D problem for the advection–diffusion equation and its adjoint problems are considered to model, estimate, and control the dispersion of nutrient in a limited region. 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 a weight function. Critical values of these mean concentrations are used as the constraints of linear programming problem. Some additional constraints are posed in order to limit not only the local discharge of the nutrient, but also the mean concentration of this substance in the whole region. Both constraints serve for environmental protection. The ability of the new method is demonstrated by numerical experiments on the remediation in oil-polluted channel using three control zones. The experiments show that the optimal discharge rate can always be got with a simple combination of step functions.

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Acknowledgments

This work was supported by the projects PAPIIT IN104811-3 (UNAM, México) and PAPIME PE103311 (UNAM, México), and by the grants 14539 and 25170 of National System of Researches (CONACyT, México).

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

    David Parra-Guevara & Yuri N. Skiba

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  1. David Parra-Guevara
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Correspondence to David Parra-Guevara.

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Parra-Guevara, D., Skiba, Y.N. A Linear-Programming-Based Strategy for Bioremediation of Oil-Polluted Marine Environments. Environ Model Assess 18, 135–146 (2013). https://doi.org/10.1007/s10666-012-9337-z

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