A reduced-order ODE-PDE model for the activated sludge process in wastewater treatment: Classification and stability of steady states
(2013) In Mathematical Models and Methods in Applied Sciences 23(3). p.369-405- Abstract
- Most wastewater treatment plants contain an activated sludge process, which consists of a biological reactor and a sedimentation tank. The purpose is to reduce the incoming organic material and dissolved nutrients (the substrate). This is done in the biological reactor where micro-organisms (the biomass) decompose the substrate. The biomass is then separated from the water in the sedimentation tank under continuous in- and outflows. One of the outflows is recirculated to the reactor. The governing mathematical model describes the concentration of substrate and biomass as functions of time for the biological reactor, and as functions of time and depth for the sedimentation tank. This gives rise to a system of two ODEs for the reactor... (More)
- Most wastewater treatment plants contain an activated sludge process, which consists of a biological reactor and a sedimentation tank. The purpose is to reduce the incoming organic material and dissolved nutrients (the substrate). This is done in the biological reactor where micro-organisms (the biomass) decompose the substrate. The biomass is then separated from the water in the sedimentation tank under continuous in- and outflows. One of the outflows is recirculated to the reactor. The governing mathematical model describes the concentration of substrate and biomass as functions of time for the biological reactor, and as functions of time and depth for the sedimentation tank. This gives rise to a system of two ODEs for the reactor coupled with two spatially one-dimensional PDEs for the sedimentation tank. The main mathematical difficulty lies in the nonlinear PDE modeling the continuous sedimentation of the biomass. Previous analyses of models of the activated sludge process have included excessively simplifying assumptions on the sedimentation process. In this paper, results for nonlinear hyperbolic conservation laws with spatially discontinuous flux function are used to obtain a classification of the steady states for the coupled system. Their stability to disturbances are investigated and some phenomena are demonstrated by a numerical simulation. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3412345
- author
- Diehl, Stefan LU and Farås, Sebastian LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Conservation law, discontinuous coefficient, clarifier-thickener, biological reactor, continuous sedimentation
- in
- Mathematical Models and Methods in Applied Sciences
- volume
- 23
- issue
- 3
- pages
- 369 - 405
- publisher
- World Scientific Publishing
- external identifiers
-
- wos:000318013300001
- scopus:84872371192
- ISSN
- 1793-6314
- DOI
- 10.1142/S0218202512500509
- language
- English
- LU publication?
- yes
- id
- 3d8021d8-17cb-493f-8c9e-4f11e5ac0c7b (old id 3412345)
- date added to LUP
- 2016-04-01 10:40:24
- date last changed
- 2022-01-26 01:24:33
@article{3d8021d8-17cb-493f-8c9e-4f11e5ac0c7b,
abstract = {{Most wastewater treatment plants contain an activated sludge process, which consists of a biological reactor and a sedimentation tank. The purpose is to reduce the incoming organic material and dissolved nutrients (the substrate). This is done in the biological reactor where micro-organisms (the biomass) decompose the substrate. The biomass is then separated from the water in the sedimentation tank under continuous in- and outflows. One of the outflows is recirculated to the reactor. The governing mathematical model describes the concentration of substrate and biomass as functions of time for the biological reactor, and as functions of time and depth for the sedimentation tank. This gives rise to a system of two ODEs for the reactor coupled with two spatially one-dimensional PDEs for the sedimentation tank. The main mathematical difficulty lies in the nonlinear PDE modeling the continuous sedimentation of the biomass. Previous analyses of models of the activated sludge process have included excessively simplifying assumptions on the sedimentation process. In this paper, results for nonlinear hyperbolic conservation laws with spatially discontinuous flux function are used to obtain a classification of the steady states for the coupled system. Their stability to disturbances are investigated and some phenomena are demonstrated by a numerical simulation.}},
author = {{Diehl, Stefan and Farås, Sebastian}},
issn = {{1793-6314}},
keywords = {{Conservation law; discontinuous coefficient; clarifier-thickener; biological reactor; continuous sedimentation}},
language = {{eng}},
number = {{3}},
pages = {{369--405}},
publisher = {{World Scientific Publishing}},
series = {{Mathematical Models and Methods in Applied Sciences}},
title = {{A reduced-order ODE-PDE model for the activated sludge process in wastewater treatment: Classification and stability of steady states}},
url = {{http://dx.doi.org/10.1142/S0218202512500509}},
doi = {{10.1142/S0218202512500509}},
volume = {{23}},
year = {{2013}},
}