Shape optimization of spatial chemostat models




Crespo, Maria
Ivorra, Benjamin
Ramos, Angel M.
Rapaport, Alain

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Texas State University, Department of Mathematics


In this work, we study the shape optimization of a continuous bioreactor in which a substrate is degraded by a microbial ecosystem in a nonhomogeneous environment. The bioreactor considered here is a three-dimensional vertically oriented cylindrical tank. The behavior of reactants is described with a spatial chemostat model based on an Advection-Diffusion-Reaction system while the fluid flow is modeled using incompressible Navier-Stokes equations. We consider that the reaction rate between biomass and nutrient shows either monotonic or non-monotonic behavior. We tackle an optimization problem which aims to minimize the considered total reactor volume, with an output concentration (at stationary state) maintained below a desired threshold, by choosing a suitable bioreactor shape. We propose a methodology to create three different discrete parametrizations of the bioreactor geometry and obtain the optimized shapes with the help of a Hybrid Genetic Algorithm. We show that the optimized reactors exhibit height much larger than width and their exterior wall is concavely curved (the concavity at the upper part of the exterior wall being more pronounced for non-monotonic functions).



Shape optimization, Optimal design, Continuous bioreactor, Spatial chemostat model, Advection-diffusion-reaction, Hybrid genetic algorithm


Crespo, M., Ivorra, B., Ramos, A. M., & Rapaport, A. (2019). Shape optimization of spatial chemostat models. Electronic Journal of Differential Equations, 2019(84), pp. 1-26.


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