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

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 a 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 maximizes the capacity of the resin and column efficiency to remove toxic compounds from water while capturing deviations in the process conditions. When dealing with highly toxic compounds like chromium, it is critical that its concentration in drinking water is kept at a low, safe level. As single-use ion-exchange resins are used to extract the hazardous chemical, changes in inlet concentrations can lead to premature leakage. Hence, an optimal control strategy is needed for the purification system while monitoring the inlet concentration rather than the outlet concentration to avoid a process control delay. For a successful optimization, predicting the output concentration based on the inlet conditions becomes necessary to maximize the performance of the extraction process. In this work, predictive modeling while capturing the uncertainties of the system maximized the chromate removal in less time than running the process at a constant flow rate. The results demonstrate that changing the flow rate with time is an improved strategy to achieve such performance. The flow rate change is a unique approach to an industry that designs its processes around a constant flow rate and reacts too late when system deviations have already occurred. Therefore, applying the approach described in this work will maximize the utilization of the purification process resulting in less waste produced and safer drinking water.