# Nonlinear Partial Dierential Equations Model Related to Oxidation Pond Treatment System: A Case Study of mPHO at Taman Timor Oxidation Pond, Johor Bahru

## Authors

• Amir Syafiq Syamin Syah Hamzah Department of Mathematical Sciences, Universiti Teknologi Malaysia 81310 UTM Johor Bahru, Malaysia
• Ali Hassan Mohamed Murid UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu Sina Institute for Scientic and Industrial Research (ISI-SIR), Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

## Abstract

This study presents a mathematical model examining wastewater pollutant removal
through an oxidation pond treatment system. This model was developed to describe
the reaction between microbe-based product mPHO (comprising Phototrophic bac-
teria (PSB)), dissolved oxygen (DO) and pollutant namely chemical oxygen demand
(COD). It consists of coupled advection-diusion-reaction equations for the microor-
ganism (PSB), DO and pollutant (COD) concentrations, respectively. The coupling
of these equations occurred due to the reactions between PSB, DO and COD to pro-
duce harmless compounds. Since the model is nonlinear partial dierential equations
(PDEs), coupled, and dynamic, computational algorithm with a specic numerical
method, which is implicit Crank-Nicolson method, was employed to simulate the dy-
namical behaviour of the system. Furthermore, numerical results revealed that the
proposed model demonstrated high accuracy when compared to the experimental data.

Keywords Oxidation pond; nonlinear PDEs; PSB; implicit Crank-Nicolson.

30-12-2018

## How to Cite

Hamzah, A. S. S. S., & Murid, A. H. M. (2018). Nonlinear Partial Dierential Equations Model Related to Oxidation Pond Treatment System: A Case Study of mPHO at Taman Timor Oxidation Pond, Johor Bahru. MATEMATIKA, 34(2), 293–311. https://doi.org/10.11113/matematika.v34.n2.1038

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