Second-order cone optimization of the gradostat

The gradostat consists of multiple chemostats interconnected by mass flows and diffusion. It has been used to model biochemical systems such as wastewater treatment networks microbial activity in soil. In this paper we maximize the production biogas a at steady state. physical decision variables are water, substrate, biomass entering each tank through interconnecting pipes. Our main technical focus is nonconvex constraint describing growth. We formulate relaxation prove that it exact when outflow connected, its system matrix irreducible, growth rate satisfies simple condition. second-order cone representations for Monod Contois rates. extend state models case time periods replacing derivatives with numerical approximations instead setting them zero. resulting optimizations programs, which can be solved large scales using standard industrial software.