A Strategy for Bioremediation of Marine Shorelines by Using Several Nutrient Release Points - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 23

Chapter 2
A Strategy for Bioremediation of Marine
Shorelines by Using Several
Nutrient Release Points

David Parra-Guevara and Yuri N. Skiba

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.