Modeling the activated sludge process with gravity clarification using mixed-integer nonlinear programming

Abstract

The activated sludge process (ASP) is widely used to remove organics and nutrients from domestic wastewater. Traditional ASP designs are based on a paradigm of strict regulation, cheap energy, and overdesign. Because of this regulation first paradigm, engineers rely heavily on experience based design approaches, empirical studies, and iterative methods to produce ASP designs that meet regulatory targets. This dissertation improves upon these typical design approaches by applying a rigorous mathematical methodology for reducing combined investment and operating costs associated with ASP designs. An explicit mathematical programming model, using the Activated Sludge Model 3 and the double exponential layered settling model, was used to find ASP designs that represent the lowest combined costs. The model was presented as a Mixed-Integer Nonlinear Programming (MINLP) problem with complementarity constraints and solved using a random-multi start method. Uncertain factors were varied singly, and as a group, allowing the model to draw probabilistic inference about the reliability of least-cost ASP designs. Multiple solutions to the problem were obtained that reduced costs compared to a typical design solution by up to 25%. Perturbation of optimization model parameters was used to identify important parameters contributing to cost variability in excess of 40%. Quantitative safety factors (QSFs) were calculated using sample-averaged approximation optimization that included the probabilistic nature of model parameters. Lastly, a robust-optimal ASP design was obtained using QSFs that reduced costs compared to a typical design by 18% and which represented a risk of performance degradation due to uncertainty of less than 5%. Synthesis of the activated sludge and settler models with MINLP produced the following improvements from typical designs: High numbers of solutions improved confidence that MINLP methods can be used to design and control ASPs more efficiently and at a lower cost. Uncertainty was decreased by identifying important parameters that significantly impact optimal ASP costs. QSFs were used to decide which unit processes and operations required overdesigned to account for parameter uncertainty. In addition, the inclusion of equilibrium conditions as complementarity constraints increased model credibility as compared to earlier ASP optimizations.