Convex Optimization of Bioprocesses

We optimize a general model of bioprocesses, which is nonconvex due to the microbial growth in the biochemical reactors. We formulate a convex relaxation and give conditions guaranteeing its exactness in both the transient and steady-state cases. When the growth kinetics are modeled by the Contois or, under constant biomass, Monod or Powell functions, the relaxation is a second-order cone program, which can be solved efficiently at large scales. We implement the model on a numerical example based on a wastewater treatment system.