## Year

2013

## Degree Name

Doctor of Philosophy

## Department

School of Mathematics and Applied Statistics

## Recommended Citation

Alqahtani, Rubayyi Turki, Modelling of biological wastewater treatment, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2013. https://ro.uow.edu.au/theses/3951

## Abstract

Many models have been proposed in the literature for the specific growth rate of biomass, including those of Tessier, Monod, Moser and Contois kinetics. Of these models the Monod model has become the default model used in bioreactor engineering. However, there is growing experimental evidence showing that in a number of industrial processes, in particular wastewater treatment, the specific growth rate is more accurately described by Contois kinetics rather than other models. Thus in this thesis, we construct and analyze models for wastewater treatment where the specific growth rate of biomass on biodegradable organic matter is assumed to be given by the Contois growth rate.

This thesis is organized into four parts. Part 1 consists of three chapters (1, 2 and 3) which contain general information on the wastewaster treatment and the pertinent modeling studies.

For remaining parts, specific issues related to wastewater treatment modelling are investigated. In part 2, which contain three chapters (4, 5 and 6), we develop a model for wastewater treatment. In chapter (4), the analysis of wastewater treatment in a single reactor with recycle is presented. In chapter (5), we consider a n-cascade reactor with recycle around each reactor. We investigate how to tune the parameters of a settling unit to minimize the effluent concentration leaving the reactor cascade. If only one settling unit is to be used, we ask the question, ”Where should it be placed in order to optimized the performance of the reactor cascade?” The chapter (6) deals with the scenario in which the settling unit is placed after the final cascade reactor and the effluent stream from the settling unit is recycled back into the first reactor. We show that there is a critical value of the total residence time. If the total residence time is below the critical value then the settling unit improves the performance of the reactor cascade whereas if the residence time is above the critical value the performance of the cascade is reduced compared to that of a cascade without a settling unit. We conclude by noting that the configuration of the cascade where recycle occurs around each reactor (chapter (5)), outperforms the configuration of the cascade where recycle is present around the whole cascade at high total residence time. This is noteworthy as the latter is often used in industry. A further three chapters (7, 8 and 9) are contained in part 3. In this part, we extend the standard Contois expression to include both substrate inhibition and a variable yield coefficient. These extensions are important in both the theoretical and practical application of wastewater treatment. We investigate parameter regions in which either natural oscillations or bistable behaviour can occur. In this first of these chapters, we consider the case when the yield coefficient is variable with decay coefficient whilst in the second of these chapter, the substrate inhibition is analyzed. In the final chapter of this part, the combination of substrate inhibition and a variable yield coefficient is investigated.

The final part of this thesis investigates the use of a sludge disintegration unit to minimize the sludge production inside the reactor, represented by chapters (10 and 11). This is important to reduce the operation cost associated with the wastewater process. In chapter (10), we investigate Yoon’s model with infinite reaction rate by replacing Monod kinetic with Contois Kinetic. The operation condition for two configurations of reactor, continuous flow reactor and membrane reactor under which a sludge disintegration unit is required are investigated. In chapter (11), we extend Yoon’s model to include finite reaction rates and Contois kinetics and establish that the infinite reaction rate assumption of Yoon’s model is only correct for specific value of the sludge solubilization efficiency but a viable approximation in only certain practical cases. The effect of the finite reaction rate and the relative volume of the sludge disintegration unit (n) upon the production of activate sludge inside the reactor are investigated. Finally, chapter (12) will summarize the thesis findings and give future research directions.

## FoR codes (2008)

0102 APPLIED MATHEMATICS, 010202 Biological Mathematics, 010204 Dynamical Systems in Applications, 0307 THEORETICAL AND COMPUTATIONAL CHEMISTRY

**Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.**