Proceedings of the Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021)

# Stability Analysis of Biological Wastewater Treatment in Facultative Stabilization Ponds: Mathematical Model

Authors
Mia Nur Islami*, 1, Sunarsih Sunarsih1, sunarsih@lecturer.undip.ac.id, R Heru Tjahjana1
1Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Semarang, Indonesia
*Corresponding author. Email: mianurislami11@gmail.com.
Corresponding Author
Mia Nur Islami
Available Online 25 May 2022.
DOI
10.2991/apr.k.220503.010How to use a DOI?
Keywords
Wastewater Treatment; Facultative Stabilization Pond; Jacobian Matrix; Stability Analysis; System of Non-Linear Differential Equations
Abstract

Wastewater stabilization pond is a very large pond where wastewater is stored for a long time, in that pond there is a biological process of organic matter in the sludge produced from primary deposition, and it’s resulting in stable biological treatment of wastewater. Wastewater treatment is used to reduce organic matter and remove pathogens to a level that complies with water quality standards. Many biological processes are carried out using microorganisms such as bacteria. The purpose of this paper is to develop a simple mathematical model of a system nonlinear differential equations in biological wastewater treatment by considering the inflow and outflow during the treatment process. The system of equations is built using the basic Monod equations. Then linearize the system by finding the Jacobian matrix. Stability of the system differential equations around the equilibrium point is analyzed by looking for characteristic equations, eigenvalues and phase portraits and its shows that the model is asymptotically stable. Numerical simulations to determine the changes that occur at each concentration over time were carried out using the Fourth-order Runge Kutta method. The data were obtained from the facultative stabilization pond in Sewon, Bantul, Yogyakarta. The simulation shows that the concentration of DO (dissolved oxygen) has increased to stable, while the concentration of OM (organic matter) and B (bacteria) has decreased to stable. Computational calculations and visualization system to get the equilibrium point using Maple 18 and finding the solution using the Matlab (R2015a).

Open Access

Volume Title
Proceedings of the Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021)
Series
Publication Date
25 May 2022
ISBN
10.2991/apr.k.220503.010
ISSN
2352-541X
DOI
10.2991/apr.k.220503.010How to use a DOI?
Open Access

TY  - CONF
AU  - Mia Nur Islami
AU  - Sunarsih Sunarsih
AU  - R Heru Tjahjana
PY  - 2022
DA  - 2022/05/25
TI  - Stability Analysis of Biological Wastewater Treatment in Facultative Stabilization Ponds: Mathematical Model
BT  - Proceedings of the Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021)
PB  - Atlantis Press
SP  - 44
EP  - 49
SN  - 2352-541X
UR  - https://doi.org/10.2991/apr.k.220503.010
DO  - 10.2991/apr.k.220503.010
ID  - Islami2022
ER  -