Minimal-time bioremediation of natural water resources

TL;DR

This paper investigates optimal control strategies for the rapid bioremediation of large water bodies using autonomous bioreactors, highlighting the benefits of non-constant flow rates in heterogeneous conditions.

Contribution

It characterizes optimal control policies for bioremediation in both homogeneous and inhomogeneous water resources, revealing non-monotonic control laws and the impact of resource heterogeneity.

Findings

Optimal policies differ between homogeneous and inhomogeneous cases.

Non-monotonic control laws are optimal in inhomogeneous conditions.

Using non-constant flow rates can significantly improve remediation efficiency.

Abstract

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 characterize 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. With the help of the Maximum Principle, we show that the optimal control law is non-monotonic and terminates with a constant phase, contrary to the homogeneous case for which the optimal flow rate is decreasing with time. This study allows the decision makers to identify situations for which the benefit of using non-constant flow rates is significant.