Two-Stage Robust Optimization of Water Treatment Network Design and Operations under Uncertainty

This paper presents a study of two-stage adaptive nonlinear robust optimization in dealing with uncertainty in the optimal design and operation of water treatment systems. This work aims to obtain (i) a robust process design and (ii) robust operational policies for the water treatment network, which are easily applicable for any realization of uncertainty that the problem has been modeled to handle. The approach uses a two-stage nonlinear robust optimization technique, which is based on the linearization around the nominal value of the uncertainty. The intractable adaptive robust optimization model is transformed into its tractable robust counterpart by applying the linear decision rule over the control variables. To handle the issue of concentration target violation caused by an inaccurate linear approximation model, a modified optimization model with additional constraints on the extreme points of the uncertainty set is further presented. The performance and advantages of the approach are then analyzed and contrasted on two case studies, a small water treatment model and a larger SAGD water treatment network.