Résumé
In this work, we solve an optimization problem which aims to minimize the volume of a continuous bioreactor, with an outflow substrate concentration maintained with a desired threshold, by choosing a suitable bioreactor shape. We have used a mathematical model that couples hydrodynamics (described with the incompressible Navier-Stokes equations) with biological phenomena (described with an Advection-Diffusion-Reaction system). We have presented a discrete optimization problem related to the design of our device and solved it by using a Hybrid Genetic Algorithm. We show that the optimal reactor has height much larger than width and its exterior wall is concavely curved. The advantage of these shape features in the reactor performance could be attributed to the fact that the resulting reactor contains areas of biomass storage and helps to decrease the vertical flow velocity (in absolute value), which in turn favor the reaction between species.