Analysis of mathematical models using non-linear ordinary differential equations with application to activated sludge process

Abstract

The activated sludge process has been successfully applied to treat both municipal sewage and industrial wastewater since the beginning of the 20th century. Today, across the world, more than 90% of modern municipal water treatment plants use the activated sludge process. The process consists of three major components: an aeration tank, a clarification or settling tank, and a method for returning some activated sludge to the input line. The procedure’s effectiveness is contingent on employing microorganisms, which consume the organic contaminants in the wastewater and generate new microorganisms. This self-replication means that, in theory, the process may continue indefinitely. The main disadvantage of the activated sludge process (ASP) is the expense of disposing of excess sludge, which can account for between fifty to sixty percent of the operating costs of a treatment plant. In recent decades the development of the green economy has driven interest in either finding a positive use for excess sludge or finding mechanisms to reduce its production. Mathematical modelling is a powerful tool for investigating the design of wastewater processing systems, including the monitoring, predicting and controlling the progress of the process. The ASM1 model was the first internationally accepted model for the treatment of municipal wastewater using the activated sludge process. In this thesis, we use a simplified ASM1 model with five state variables, rather than the complete model’s thirteen. This is achieved by retaining terms related to the removal of organic carbon materials whilst omitting terms related to nitrogen removal. The advantages of investigating this simplified version of the ASM1 was mentioned by Billing and Dold immediately after the ASM1 model was published.