Abstract
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.
Highlights
The accurate calculation of porosity in water is of major importance in drinking water treatment processes because it determines the process conditions and treatment results
Examples include pellet-softening in fluidised bed reactors [1], sedimentation, flotation and flocculation, filtration processes [2], backwashing of filter media and washing columns in which fine material and impurities are separated from seeding material
The softening process involves the dosing of caustic soda, soda ash or lime in a cylindrical up-flow fluidised-bed reactor, which leads to an alteration of the calcium carbonate equilibrium in which
Summary
The accurate calculation of porosity in water is of major importance in drinking water treatment processes because it determines the process conditions and treatment results. Examples include pellet-softening in fluidised bed reactors [1], sedimentation, flotation and flocculation, filtration processes [2], backwashing of filter media and washing columns in which fine material and impurities are separated from seeding material. In these processes, particle size mostly varies between 0.3 - 2.0 mm, and particle density between 2.5 - 4.0 kg/L. It is important that the largest pellets, usually those that are larger than 1–2 mm, are extracted from the reactor These pellets can be used as a by-product in other processes, for instance in industrial and agricultural processes, or they can be re-used as seeding material
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