Mathematical modelling of biological wastewater treatment of oxidation pond and constructed wetland systems

Abstract

Wastewater treatment methods are intended to improve the quality of wastewater to prevent many health problems stemming from water sources. Among popular treatment methods are oxidation pond and constructed wetland (CW) treatment. There are some mathematical models for simulating oxidation pond process where some important parameters are considered such as bacteria (cleansing agent), pollutants and dissolved oxygen (DO). However, previous results did not provide good approximation of the required parameters. Meanwhile, for constructed wetland models, the stability analysis was rarely considered. However, the steadystate and bifurcation analyses are usually crucial in determining the reliability of the models that is under study. In this thesis, dynamic mathematical models are developed to allow simulation and prediction of the wastewater treatment process for both oxidation pond and CW case studies. The nonlinear system of ordinary differential equations (ODE) using multiple substrate limiting factors with interactive reactions and partial differential equations (PDE) using advection-diffusion-reaction equations are implemented for CW and oxidation pond, respectively. Water quality indexes considered in this study are chemical oxygen demand (COD), biochemical oxygen demand (BOD), ammonium nitrogen (NH+4 ), nitrate (NO3), and DO. For oxidation pond system, the input of microbe-based product (mPHO) is added to the model, whereas the effect of living plants (Typha Angustifolia) is introduced in the CW treatment system to mimic the natural behaviour of the wetland system. Since the models are nonlinear, coupled, and dynamic, computational algorithms with specific numerical methods are employed to simulate the dynamical behaviour of the system. Implicit Runge-Kutta method is selected for solving the ODE model. Whereas, for the PDE, the implicit Crank-Nicolson method is used. The process model built is then optimised using gradient-free optimisation method (least squares) algorithms NonlinearModelFit in Mathematica to identify the optimal solution for improving the efficiency of the simulation process. Stability, bifurcation, and numerical analyses are presented to illustrate the dynamical behaviour of the proposed model. Numerical results also revealed that the proposed models have good accuracy when compared to the experimental data. The two separate mathematical models for oxidation pond and constructed wetland, both are then applied to simulate a wastewater treatment site with pond-constructed wetland system. The combined mathematical model results in a further removal of COD as well as an increase of DO up to 94.1% and 97.4% respectively when compared to a single oxidation pond model.