A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor
This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diff...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Chemical Engineering |
| Online Access: | http://dx.doi.org/10.1155/2010/738482 |
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| author | B. Godongwana D. Solomons M. S. Sheldon |
| author_facet | B. Godongwana D. Solomons M. S. Sheldon |
| author_sort | B. Godongwana |
| collection | DOAJ |
| description | This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR) systems (e.g., dead-end, open-shell, or closed-shell mode), as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR. |
| format | Article |
| id | doaj-art-4a1920e40a3d4b3c8e7bf2441c26f0cb |
| institution | Kabale University |
| issn | 1687-806X 1687-8078 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Chemical Engineering |
| spelling | doaj-art-4a1920e40a3d4b3c8e7bf2441c26f0cb2025-02-03T05:48:13ZengWileyInternational Journal of Chemical Engineering1687-806X1687-80782010-01-01201010.1155/2010/738482738482A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane BioreactorB. Godongwana0D. Solomons1M. S. Sheldon2Department of Chemical Engineering, Cape Peninsula University of Technology, P.O. Box 652, Cape Town 8000, South AfricaDepartment of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Ronderbosch 7700, South AfricaDepartment of Chemical Engineering, Cape Peninsula University of Technology, P.O. Box 652, Cape Town 8000, South AfricaThis paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR) systems (e.g., dead-end, open-shell, or closed-shell mode), as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.http://dx.doi.org/10.1155/2010/738482 |
| spellingShingle | B. Godongwana D. Solomons M. S. Sheldon A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor International Journal of Chemical Engineering |
| title | A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor |
| title_full | A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor |
| title_fullStr | A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor |
| title_full_unstemmed | A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor |
| title_short | A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor |
| title_sort | solution of the convective diffusion equation for solute mass transfer inside a capillary membrane bioreactor |
| url | http://dx.doi.org/10.1155/2010/738482 |
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