Modeling of chlorine disinfection and kaolin dispersion systems with control applications

This dissertation presents an analysis of a chlorine disinfection process and on a kaolin dispersion process with the goals of developing models and additional insight that would be ultimately useful for the purpose of designing effective automatic control schemes. The chlorine disinfection study focuses on the fact that the large contact times required for effective wastewater treatment involve a large and variable time-delay which in turn makes the design of a control system more challenging. This monograph uses a plug-flow reactor model to represent the dynamics of the process, resulting in a partial differential equation. It is shown that the method of characteristics can be used to reduce the model to an ordinary differential equation which still captures the key dynamic features of the original model but that is more amenable to analysis using conventional process control techniques. Finally, an odometric transformation is introduced to take advantage of the fact that the variations in time delay are introduced exclusively by changes in flow rate. The odometrically-transformed model features a constant dead time that is shown to be equal to the length of the reactor. It is also shown that the constant-delay transformed model can be used as the basis for the design of a Smith Predictor scheme for time delay compensation, which is free from the undesirable performance degradation typically observed when the time delay varies. Preliminary closed-loop simulation studies suggest that effective control of the chlorine disinfection process could be achieved using a cascade control scheme coupled with a modified Smith Predictor master controller designed using the odometrically transformed process.; In the kaolin dispersion study the effect of pH and three different anionic dispersants (sodium polyacrylate, sodium hexametaphosphate and sodium silicate) were investigated on the dissolution capacity of metal ions from kaolin particles. The dosage of dispersing agent, pH, solid concentration and aging significantly affected the solubility of metal ion concentrations. Released aluminum ions precipitated as Al(OH)₃ with increasing and decreasing suspension pH. Analogously, increasing the pH of the suspension results in the formation of alumino-silicate surface on the silica surface of particles, and this situation prohibited the release of silicon ions from the kaolin particles. Some of the aluminum ions adsorbed onto the surface of released silicon ions, and formed alumino-silicate gel. The complete and best models were obtained for the dissolution of aluminum and silicon ions from kaolin particles. These models are useful for future designs of appropriate controllers to maintain the surface properties of kaolin at a desired value.