Optimization of a photobioreactor biomass production using natural light

TL;DR

This paper develops an optimal control strategy for maximizing long-term biomass productivity in photobioreactors using natural light, considering day/night cycles and biomass constraints, with various control regimes depending on parameters.

Contribution

It introduces a simple bioreactor model with light attenuation and derives an optimal control law using Pontryagin's maximum principle, accounting for long-term productivity constraints.

Findings

Optimal control laws include bang-bang, bang-singular-bang, or constant maximal dilution regimes.

A bifurcation diagram illustrates parameter conditions for different control behaviors.

The model provides insights into biomass management under natural light conditions.

Abstract

We address the question of optimization of the biomass long term productivity in the framework of microalgal biomass production in photobioreactors under the influence of day/night cycles. For that, we propose a simple bioreactor model accounting for light attenuation in the reactor due to biomass density and obtain the control law that optimizes productivity over a single day through the application of Pontryagin's maximum principle, with the dilution rate being the control. An important constraint on the obtained solution is that the biomass in the reactor should be at the same level at the beginning and at the end of the day so that the same control can be applied everyday and optimizes the long term productivity. Several scenarios are possible depending on the microalgae's strain parameters and the maximal admissible value of the dilution rate: bang-bang or bang-singular-bang control or, if the growth rate of the algae is very strong in the presence of light, constant maximal dilution. A bifurcation diagram is presented to illustrate for which values of the parameters these different behaviors occur.