  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 Monod function under
constant biomass or the Contois function, 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.
