# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### A model for continuous sedimentation with reactions for wastewater treatment

; Diehl, S. LU and Mejías, C. (2017) In Lecture Notes in Civil Engineering 4. p.596-601
Abstract

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the under- lying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble constituents of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved... (More)

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the under- lying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble constituents of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively in each time step by an explicit numerical scheme. This scheme combines a difference scheme for conservation laws with discontinuous flux with an approach of numerical percentage propagation for multi-component flows. The main result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.

(Less)
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Multi-Component flow, Percentage propagation, Secondary settling tank, Wastewater treatment
host publication
Lecture Notes in Civil Engineering
series title
Lecture Notes in Civil Engineering
volume
4
pages
6 pages
publisher
Springer
external identifiers
• scopus:85060246936
ISSN
2366-2557
2366-2565
DOI
10.1007/978-3-319-58421-8_93
language
English
LU publication?
yes
id
1124a8c9-757d-4fea-807d-ae62a59456cd
2019-02-04 13:54:17
date last changed
2020-01-13 01:26:47
```@inbook{1124a8c9-757d-4fea-807d-ae62a59456cd,
abstract     = {<p>Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the under- lying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble constituents of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively in each time step by an explicit numerical scheme. This scheme combines a difference scheme for conservation laws with discontinuous flux with an approach of numerical percentage propagation for multi-component flows. The main result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.</p>},
author       = {Bürger, R. and Diehl, S. and Mejías, C.},
booktitle    = {Lecture Notes in Civil Engineering},
issn         = {2366-2557},
language     = {eng},
pages        = {596--601},
publisher    = {Springer},
series       = {Lecture Notes in Civil Engineering},
title        = {A model for continuous sedimentation with reactions for wastewater treatment},
url          = {http://dx.doi.org/10.1007/978-3-319-58421-8_93},
doi          = {10.1007/978-3-319-58421-8_93},
volume       = {4},
year         = {2017},
}

```