New hydraulic insights into rapid sand filter bed backwashing using the Carman–Kozeny model

O.J.I. Kramer, P.J. de Moel, J.T. Padding, Eric T. Baars, Sam B. Rutten, Awad H.E. Elarbab, Jos F.M. Hooft, Edo S. Boek, J.P. van der Hoek

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Fluid flow through a bed of solid particles is an important process that occurs in full-scale water treatment operations. The Carman–Kozeny model remains highly popular for estimating the resistance across the bed. It is common practice to use particle shape factors in fixed bed state to match the predicted drag coefficient with experimentally obtained drag coefficients. In fluidised state, however, where the same particles are considered, this particle shape factor is usually simply omitted from the model without providing appropriate reasoning. In this research, it is shown that a shape factor is not a constant particle property but is dependent on the fluid properties as well. This dynamic shape factor for irregularly shaped grains increases from approximately 0.6 to 1.0 in fluidised state.

We found that unstable packed beds in moderate up-flow conditions are pseudo-fixed and in a setting state. This results in a decreasing bed voidage and simultaneously in a decreasing drag coefficient, which seems quite contradictory. This can be explained by the collapse of local channels in the bed, leading to a more uniform flow distribution through the bed and improving the available surface for flow-through. Our experimental measurements show that the drag coefficient decreases considerably in the laminar and transition regions. This is most likely caused by particle orientation, realignment and rearrangement in particles’ packing position.

A thorough hydraulic analysis shows that up-flow filtration in rapid sand filters under backwash conditions causes the particle bed to collapse almost imperceptibly. In addition, an improved expression of the drag coefficient demonstrated that the Carman–Kozeny model constant, however often assumed to be constant, is in fact not constant for increasing flow rates. Furthermore, we propose a new pseudo-3D image analysis for particles with an irregular shape. In this way, we can explain the successful method using optimisation of the extended terminal sub-fluidisation wash (ETSW) filter backwashing procedure, in which turbidity and peaks in the number of particles are reduced with a positive effect on water quality.
Original languageEnglish
Article number117085
Number of pages12
JournalWater Research
Publication statusPublished - 2021


  • Drinking Water Treatment
  • Multiphase Flows
  • Filter-Backwash
  • Hydraulics Drag Relations
  • Particle Orientation
  • Dynamic Particle Shape Factors


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