Convex Optimization of Wastewater Treatment

Josh Taylor, PhD
New Jersey Institute of Technology

Abstract: In this talk, we begin by optimizing the gradostat, in which several bioreactors are interconnected by mass flow and diffusion. The gradostat is of interest both as a classical nonlinear system and because the basic network structure and nonlinearities appear in a broad range of bioprocesses, including wastewater treatment. We formulate a convex relaxation for optimizing the gradostat. The relaxation is exact under several conditions, for example, if the network is outflow connected and irreducible. When the microbial growth in the bioreactors is described by the Monod or Contois functions, the relaxation is a secondorder cone program, which can be solved at scales of over 10^5 variables in minutes with existing software. In a case study based on the Paris wastewater treatment system, we use our results to design a model predictive controller that minimizes flooding and overflow during wet weather, and minimizes pollutant release at other times. We also discuss related work on metabolic networks, in which we use a second-order cone representation of the Michaelis-Menten kinetics to augment polyhedral models of reaction networks with metabolite concentrations.
 

Bio: Josh Taylor received the B.S. from Carnegie Mellon University in 2006 and the Ph.D. from the Massachusetts Institute of Technology in 2011, all in Mechanical Engineering. From 2011 to 2012, he was a postdoctoral researcher at the University of California, Berkeley. He was an assistant and then associate professor at the University of Toronto from 2013 to 2023. He is currently an associate professor of Electrical and Computer Engineering at the New Jersey Institute of Technology. His research focuses on control and optimization of energy and water infrastructure.