Hall, David; (2001) A mathematical model for rapid gravity filter backwashing. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

A mathematical model for backwashing rapid gravity filters using a fluidising water wash has been developed. The model development has benefited from previous research carried out using a high speed video camera to obtain fundamental insights into the physical mechanisms of the backwash process. The model is developed in two parts. The first part develops an expression to describe the volume of deposit dislodged into suspension. The second develops a mass balance expression describing the change in backwash suspension concentration. Common to both parts of the model are the backwash processes that have been termed the transient and steady state stages. The transient stage has been defined as the initial backwash period between application of the backwash water and up to the time when the bed expansion is complete. During the transient stage a fraction of deposit is dislodged from media grains into suspension. A new term, the 'expansion fraction', has been introduced to model the volume of deposit dislodged into suspension during the transient stage. The steady state stage commences after the bed expansion is complete. A suitable filtration model is used to establish the initial conditions in the filter bed prior to backwashing. Experimental work has also been undertaken to measure and investigate the development of backwash suspension concentration profiles throughout the filter bed. Three backwash regimes were used: fluidising water wash only; air scour followed by a fluidising water wash; simultaneous air and water. Backwash suspension concentration profiles at various depths within the bed have been obtained for the three types of backwash regime. The concentration profiles obtained for the fluidising water backwash experiments have also been used to validate the results generated by the model. The profiles predicted by the model were reasonably accurate for water only backwashing up to water velocities of 10 mm/s. Uneven flow profiles and mixing of the top bed layers during bed expansion contribute to the inaccuracy of the model at higher backwash velocities.

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