# Mathematical modelling of deep bed filtration

Jegatheesan, V., and Vigneswaran, S. (2003) Mathematical modelling of deep bed filtration. In: Proceedings of MODSIM 2003 International Congress on Modelling and Simulation (4), pp. 1805-1810. From: MODSIM 2003 International Congress on Modelling and Simulation, 14-17 July 2003, Townsville, QLD, Australia.

 PDF (Published Version) Restricted to Repository staff only
View at Publisher Website: http://www.mssanz.org.au/MODSIM03/Volume...

## Abstract

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective-diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. O’Melia and Ali’s model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This paper evaluates those models and their applicability under different operating conditions of filtration.

Item ID: 7671 Conference Item (Refereed Research Paper - E1) filtration; initial stage; mathematical modelling; transient stage http://www.mssanz.org.au/ 978-1-74052-098-0 20 Jun 2010 23:18 09 ENGINEERING > 0907 Environmental Engineering > 090702 Environmental Engineering Modelling @ 100% 96 ENVIRONMENT > 9699 Other Environment > 969999 Environment not elsewhere classified @ 100% Total: 1 More Statistics

Actions (Repository Staff Only)

 Item Control Page