Minimal time bioremediation of natural water resources

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.

Modeling and control of in-situ decontamination of large water resources

“…The proof of this proposition can be found in [4], where the existence and uniqueness of the best constant control is shown.…”

Modeling and optimization of activated sludge bioreactors for wastewater treatment taking into account spatial inhomogeneities

“…Since we assume homogeneous distribution of substrate in the water resource, its dynamics can be described as follows [17]:…”

“…The biological purification of waste water is an example of application of continuous bioreactors (see [16], [17] and [18]). Specifically, the influence of inhomogeneity was studied in [17] [19] [20], where the problem of water treatment was tackled when considering non homogeneous substrate concentration in the water resource.…”

“…Specifically, the influence of inhomogeneity was studied in [17] [19] [20], where the problem of water treatment was tackled when considering non homogeneous substrate concentration in the water resource.…”

“…We aim at studying the influence of this gradient on the optimal inlet volumetric flow rate control problem. Following [17], we consider a natural resource polluted with a substrate concentration S r . The objective of the treatment is to decrease S r , as fast as possible, to a target value S lim , with the help of a bioreactor.…”