Optimal Control of Chromate Removal via Enhanced Modeling using the Method of Moments

TL;DR

This paper develops a stochastic optimal control strategy for chromate removal in water treatment, using the method of moments and Pontryagin's maximum principle to optimize resin capacity and process efficiency under uncertain conditions.

Contribution

It introduces a novel stochastic control approach combining the method of moments with Pontryagin's principle for improved chromate removal process management.

Findings

Enhanced chromate removal efficiency through flow rate adjustments.

Maximized resin capacity and column efficiency.

Effectively managed process uncertainties using stochastic modeling.

Abstract

Single-use anion-exchange resins can reduce hazardous chromates to safe levels in drinking water. However, since most process control strategies monitor effluent concentrations, detection of any chromate leakage leads to premature resin replacement. Furthermore, variations in the inlet chromate concentration and other process conditions make process control a challenging step. In this work, we capture the uncertainty of the process conditions by applying the Ito process of Brownian motion with drift into a stochastic optimal control strategy. The ion exchange process is modeled using the method of moments which helps capture the process dynamics, later formulated into mathematical objectives representing desired chromate removal. We then solved our developed models as an optimal control problem via Pontryagin's maximum principle. The objectives enabled a successful control via flow rate adjustments leading to higher chromate extraction. Such an approach maximized the capacity of the resin and column efficiency to remove toxic compounds from water while capturing deviations in the process conditions.