Multi-contaminant wastewater treatment: conflicting multi-objective optimisation with limited computational budget

One of the biggest challenges in treating industrial wastewater, such as hydraulic fracturing (fracking) water, is its complex and variable composition. The composition varies based on the fracking fluids injected into a well and the geology of the formation. The performance of water treatment technologies is highly sensitive to the composition of wastewater, requiring customized water treatment processes and optimized operating conditions for each wastewater type. Moreover, designing these systems often involves multi-objective optimization with conflicting goals, such as maximizing water recovery while achieving high water purity. Traditional design of experiments can be time-consuming and expensive, creating a need to develop efficient tools to analyze trade-offs. This study presents a highly efficient data-driven method for the design of experiments and multi-objective optimization of wastewater treatment technologies. Using Bayesian optimization (BO), the method explores the search space efficiently, minimizing the number of test iterations. It enables performance characterization and efficient prediction of the Pareto front of optimal solutions. We demonstrate the method on SCEPTER, a demo-unit industrial wastewater treatment technology developed at Oregon State University. The procedure successfully guided the experiments by exploring promising regions of the design space, significantly reducing time and effort. Experimental results and BO model predictions showed strong agreement, with a Mean Absolute Percentage Error (MAPE) of 2.4% for water recovery and 5.8% for contaminant separation. The procedure successfully predicted the Pareto front of optimal solutions using fewer than 20 experiments as training data, compared to 1920 experiments required for full-factorial analysis.