Accounting for spatial inhomogeneity in the minimal-time bioremediation of natural water resources

Antoine Rousseau (1)

1 MOISE - Modelling, Observations, Identification for Environmental Sciences

We study minimal time strategies for the treatment of pollution of large volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists in feeding the bioreactor from the resource, the clean output returning to the resource with the same flow rate.

We first present the results of a former paper that characterizes the optimal policies among constant and feedback controls, under the assumption of a uniform concentration in the resource. In a second part, we study the influence of an inhomogeneity in the resource, considering two measurements points.

We end with a presentation of numerical results in which the spatial inhomogeneity is simulated thanks to the Navier-Stokes equations for incompressible fluids. In this case the optimal strategy seems much more difficult to obtain. However, the numerical simulations provide an interesting tool to choose one suboptimal strategy or another.

Domaines: Analyse numérique [math.NA]

Antoine Rousseau. Accounting for spatial inhomogeneity in the minimal-time bioremediation of natural water resources. JFCO-7 - Seventh Franco-Chilean days of Optimization - 2011, Dec 2011, Perpignan, France. ⟨hal-00648241⟩