Controlling recirculation rate in minimal-time bioremediation of natural water resources

Victor Riquelme (1) , Alain Rapaport (2)

1 Departamento de Matematicas, Univesidad Tecnica Federico Santa-Maria (Valparaiso)
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

We revisit the minimal time problem of in-situ decontamination of large water resources with a bioreactor, considering a recirculation flow rate in the resource as an additional control. This new problem has two manipulated inputs : 1. the flow rate of the treatment in the bioreactor (which enters nonlinearly in the dynamics because of the biological dependancy between the flow rate and the concentration at the output of the bioreactor) 2. the flow rate of the recirculation in the resource between the pumping and reinjection locations (which enters linearly the dynamics). Although the velocity set of the dynamics is non convex, we show that the optimal control is reached among non-relaxed controls. The optimal strategy consists in three sequential steps: 1. do not recirculate water and take the flow rate of treatment that maximizes the concentration decay in the resource. 2. recirculate water at maximum rate and carry on with the flow rate that maximizes the concentration decay. 3. carry on with recirculation but do not treat the water (i.e. bypass the bioreactor). Finally, we show on numerical simulations that significant gains in processing time can be achieved when controlling the recirculation flow rate.

Domaines: Optimisation et contrôle [math.OC]

Victor Riquelme, Alain Rapaport. Controlling recirculation rate in minimal-time bioremediation of natural water resources. EURO 2018 - 29th European Conference of Operational Research, Jul 2018, Valencia, Spain. ⟨hal-01838401⟩