## A finite-difference solution of solute transport through a membrane bioreactor

dc.contributor.author | Godongwana, B | |

dc.contributor.author | Solomons, D | |

dc.contributor.author | Sheldon, M S | |

dc.date.accessioned | 2021-10-08T07:08:21Z | |

dc.date.available | 2021-10-08T07:08:21Z | |

dc.date.issued | 2015 | |

dc.description.abstract | The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR), immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod) rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM). An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i) the radial and axial convective velocity, (ii) the convective mass transfer rates, (iii) the reaction rates, (iv) the fraction retentate, and (v) the aspect ratio. | |

dc.identifier.apacitation | Godongwana, B., Solomons, D., & Sheldon, M. S. (2015). A finite-difference solution of solute transport through a membrane bioreactor. <i>Mathematical Problems in Engineering</i>, 2015(4), 174 - 177. http://hdl.handle.net/11427/34562 | en_ZA |

dc.identifier.chicagocitation | Godongwana, B, D Solomons, and M S Sheldon "A finite-difference solution of solute transport through a membrane bioreactor." <i>Mathematical Problems in Engineering</i> 2015, 4. (2015): 174 - 177. http://hdl.handle.net/11427/34562 | en_ZA |

dc.identifier.citation | Godongwana, B., Solomons, D. & Sheldon, M.S. 2015. A finite-difference solution of solute transport through a membrane bioreactor. <i>Mathematical Problems in Engineering.</i> 2015(4):174 - 177. http://hdl.handle.net/11427/34562 | en_ZA |

dc.identifier.issn | 1024-123X | |

dc.identifier.issn | 1026-7077 | |

dc.identifier.issn | 1563-5147 | |

dc.identifier.ris | TY - Journal Article AU - Godongwana, B AU - Solomons, D AU - Sheldon, M S AB - The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR), immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod) rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM). An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i) the radial and axial convective velocity, (ii) the convective mass transfer rates, (iii) the reaction rates, (iv) the fraction retentate, and (v) the aspect ratio. DA - 2015 DB - OpenUCT DP - University of Cape Town IS - 4 J1 - Mathematical Problems in Engineering LK - https://open.uct.ac.za PY - 2015 SM - 1024-123X SM - 1026-7077 SM - 1563-5147 T1 - A finite-difference solution of solute transport through a membrane bioreactor TI - A finite-difference solution of solute transport through a membrane bioreactor UR - http://hdl.handle.net/11427/34562 ER - | en_ZA |

dc.identifier.uri | http://hdl.handle.net/11427/34562 | |

dc.identifier.vancouvercitation | Godongwana B, Solomons D, Sheldon MS. A finite-difference solution of solute transport through a membrane bioreactor. Mathematical Problems in Engineering. 2015;2015(4):174 - 177. http://hdl.handle.net/11427/34562. | en_ZA |

dc.language.iso | eng | |

dc.publisher.department | Department of Chemical Engineering | |

dc.publisher.faculty | Faculty of Engineering and the Built Environment | |

dc.source | Mathematical Problems in Engineering | |

dc.source.journalissue | 4 | |

dc.source.journalvolume | 2015 | |

dc.source.pagination | 174 - 177 | |

dc.source.uri | https://dx.doi.org/10.1155/2015/810843 | |

dc.subject.other | Engineering (General) | |

dc.subject.other | Civil engineering (General) | |

dc.subject.other | TA1-2040 | |

dc.subject.other | QA1-939 | |

dc.subject.other | Mathematics | |

dc.title | A finite-difference solution of solute transport through a membrane bioreactor | |

dc.type | Journal Article | |

uct.type.publication | Research | |

uct.type.resource | Journal Article |

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