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A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor
Joint Authors
Sheldon, M. S.
Godongwana, B.
Solomons, D.
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-25
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Godongwana, B.& Solomons, D.& Sheldon, M. S.. 2015. A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1074783
Modern Language Association (MLA)
Godongwana, B.…[et al.]. A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor. Mathematical Problems in Engineering No. 2015 (2015), pp.1-8.
https://search.emarefa.net/detail/BIM-1074783
American Medical Association (AMA)
Godongwana, B.& Solomons, D.& Sheldon, M. S.. A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1074783
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074783