Why We Need Mathematical Models

We address the need for mathematical models in this chapter only in reference to treatment processes in biological wastewater technology. The main compounds which must be removed from water during treatment are:

• Organics, dissolved molecules, colloids and solid particles.

• Inorganic, dissolved compounds containing nitrogen (NH+, NO-, NO-) and phosphorus (PO4-).

All these compounds are removable in the activated sludge process in different parts of the reactor (see Chapters 6 and 10):

• The organics in the anaerobic, anoxic and aerobic sections.

• PO4- in the anoxic and aerobic sections by the formation of polyphosphates or, if chemical precipitation is used, by the formation of undissolved phosphatohy-droxy compounds with iron or aluminium.

Flow rates and concentrations change over time, in the aerobic part air must be dispersed, oxygen dissolved and wastewater and also sludge must be recycled. The entire process has to be controlled continously to ensure adherence with legal regulations and to minimize costs, especially for energy.

A mathematical model describing the process in whole or in part provides some of the following advantages for design and operation:

• To find the best construction for the basins, mixing and aeration system.

• To optimize the process design and the process controls.

• To develop automatic process controls.

• To use a program for training the staff.

In Chapters 5 and 6, some kinetic and reaction engineering fundamentals of modelling are discussed. In this chapter various models of the activated sludge process, their structure and their application are explained.

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