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A moving-boundary model of reactive settling in wastewater treatment. Part 2 : Numerical scheme

Bürger, Raimund ; Careaga, Julio LU ; Diehl, Stefan LU and Pineda, Romel (2022) In Applied Mathematical Modelling 111. p.247-269
Abstract

A numerical scheme is proposed for the simulation of reactive settling in sequencing batch reactors (SBRs) in wastewater treatment plants. Reactive settling is the process of sedimentation of flocculated particles (biomass; activated sludge) consisting of several material components that react with substrates dissolved in the fluid. An SBR is operated in cycles of consecutive fill, react, settle, draw, and idle stages, which means that the volume in the tank varies and the surface moves with time. The process is modelled by a system of spatially one-dimensional, nonlinear, strongly degenerate parabolic convection-diffusion-reaction equations. This system is coupled via conditions of mass conservation to transport equations on a half... (More)

A numerical scheme is proposed for the simulation of reactive settling in sequencing batch reactors (SBRs) in wastewater treatment plants. Reactive settling is the process of sedimentation of flocculated particles (biomass; activated sludge) consisting of several material components that react with substrates dissolved in the fluid. An SBR is operated in cycles of consecutive fill, react, settle, draw, and idle stages, which means that the volume in the tank varies and the surface moves with time. The process is modelled by a system of spatially one-dimensional, nonlinear, strongly degenerate parabolic convection-diffusion-reaction equations. This system is coupled via conditions of mass conservation to transport equations on a half line whose origin is located at a moving boundary and that models the effluent pipe. A finite-difference scheme is proved to satisfy an invariant-region property (in particular, it is positivity preserving) if executed in a simple splitting way. Simulations are presented with a modified variant of the established activated sludge model no. 1 (ASM1).

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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convection-diffusion-reaction PDE, Degenerate parabolic PDE, Moving boundary, Numerical scheme, Sedimentation, Sequencing batch reactor
in
Applied Mathematical Modelling
volume
111
pages
23 pages
publisher
Elsevier
external identifiers
  • scopus:85133276123
ISSN
0307-904X
DOI
10.1016/j.apm.2022.06.030
language
English
LU publication?
yes
id
346eac60-0f87-46fe-858b-1f55e2d3be58
date added to LUP
2022-09-05 14:20:06
date last changed
2022-09-05 14:20:06
@article{346eac60-0f87-46fe-858b-1f55e2d3be58,
  abstract     = {{<p>A numerical scheme is proposed for the simulation of reactive settling in sequencing batch reactors (SBRs) in wastewater treatment plants. Reactive settling is the process of sedimentation of flocculated particles (biomass; activated sludge) consisting of several material components that react with substrates dissolved in the fluid. An SBR is operated in cycles of consecutive fill, react, settle, draw, and idle stages, which means that the volume in the tank varies and the surface moves with time. The process is modelled by a system of spatially one-dimensional, nonlinear, strongly degenerate parabolic convection-diffusion-reaction equations. This system is coupled via conditions of mass conservation to transport equations on a half line whose origin is located at a moving boundary and that models the effluent pipe. A finite-difference scheme is proved to satisfy an invariant-region property (in particular, it is positivity preserving) if executed in a simple splitting way. Simulations are presented with a modified variant of the established activated sludge model no. 1 (ASM1).</p>}},
  author       = {{Bürger, Raimund and Careaga, Julio and Diehl, Stefan and Pineda, Romel}},
  issn         = {{0307-904X}},
  keywords     = {{Convection-diffusion-reaction PDE; Degenerate parabolic PDE; Moving boundary; Numerical scheme; Sedimentation; Sequencing batch reactor}},
  language     = {{eng}},
  pages        = {{247--269}},
  publisher    = {{Elsevier}},
  series       = {{Applied Mathematical Modelling}},
  title        = {{A moving-boundary model of reactive settling in wastewater treatment. Part 2 : Numerical scheme}},
  url          = {{http://dx.doi.org/10.1016/j.apm.2022.06.030}},
  doi          = {{10.1016/j.apm.2022.06.030}},
  volume       = {{111}},
  year         = {{2022}},
}