Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics

Onno Kramer, Peter de Moel, E.T. Baars, W.H. van Vugt, Johan Padding, Jan Peter van der Hoek

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29 Citations (Scopus)
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One of the most popular and frequently used models for describing homogeneous liquid-solid fluidised suspensions is the model developed by Richardson & Zaki in 1954. The superficial fluid velocity and terminal settling velocity together with an index makes it possible to determine the fluid porosity in a straightforward way. The reference point for the Richardson-Zaki model is the terminal settling velocity at maximum porosity conditions. To be able to predict porosity in the proximity of minimum fluidisation conditions, either the minimum fluidisation velocity must be known or the Richardson-Zaki index must be very accurate. To maintain optimal process and control conditions in multiphase drinking water treatment processes, the porosity is kept relatively low. Unfortunately, the Richardson-Zaki index models tends to overestimate the minimum fluidisation velocity and therefore also results in less accurate predictions with respect to porosity values. We extended the Richardson-Zaki model with proven hydraulics-based models. The minimum fluidisation velocity is acquired using the model proposed by Kozeny (1927), Ergun (1952) and Carman (1937). The terminal settling velocity is obtained through the model developed by Brown & Lawler (2003), which is an improved version of the well-known model developed by Schiller & Naumann (1933). The proposed models are compared with data from expansion experiments with calcium carbonate grains, crushed calcite and garnet grains applied in drinking water softening using the fluidised bed process. With respect to porosity, prediction accuracy is improved, with the average relative error decreasing from 15% to 3% when the classic Richardson-Zaki model is extended with these hydraulics-based models. With respect to minimum fluidisation velocity, the average relative error decreases from 100% to 12%. In addition, simplified analytical equations are given for a straightforward estimation of the index n.

Original languageEnglish
Pages (from-to)465-478
JournalPowder Technology
Publication statusPublished - 2019


  • Drinking water
  • Hydraulic models
  • Liquid-solid fluidisation
  • Minimal fluidisation
  • Richardson-Zaki
  • Terminal settling velocity


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