Abstract
In full-scale drinking water production plants in the Netherlands, central softening is widely used for reasons related to public health, client comfort, and economic and environmental benefits. Almost 500 million cubic meters of water is softened annually through seeded crystallisation in fluidised bed reactors. The societal call for a circular economy has put pressure on this treatment process to become more sustainable. By optimising relevant process conditions, the consumption of chemicals can be reduced, and raw materials reused. Optimal process conditions are feasible if the specific crystallisation surface area in the fluidised bed is large enough to support the performance of the seeded crystallisation process. To determine the specific surface area, crucial variables including voidage and particle size must be known. Numerous models can be found in the literature to estimate the voidage in liquid-solid fluidisation processes. Many of these models are based on semi-empirical porous-media-based drag relations like Ergun or semi-empirical terminal-settling based models such as Richardson-Zaki and fitted for monodisperse, almost perfectly round particles. In this study, we present new voidage prediction models based on accurate data obtained from elaborate pilot plant experiments and non-linear symbolic regression methods. The models were compared with the most popular voidage prediction models using different statistical methods. An explicit model for voidage estimation based on the dimensionless Reynolds and Froude numbers is presented here that can be used for a wide range of particle sizes, fluid velocities and temperatures and that can therefore be directly used in water treatment processes such as drinking water pellet softening. The advantage of this model is that there is no need for applying numerical solutions; therefore, it can be explicitly implemented. The prediction errors for classical models from the literature lie between 2.7 % and 11.4 %. With our new model, the voidage prediction error is reduced to 1.9 %.
Highlights
We examined two kinds of particles, calcite pellets (100 % CaCO3), and crushed calcite seeding material grains [28], both applied in drinking water softening [11]
Graphical exploration The prediction models presented in this work, i.e. voidage prediction polynomials, dimensionless number applications, and symbolic regression models, were compared with the most popular and familiar models known from the literature (Table 1)
The accurate calculation of voidage and specific surface area is of major importance in drinking water treatment processes like pellet softening, because it determines the process conditions and treatment results
Summary
Central softening of drinking water is currently frequently applied in several countries (e.g. the Netherlands, Belgium, Germany, France, and the USA) while domestic softening is the most frequently applied way of softening in other countries [2,3,4]. In full-scale drinking water production plants in the Netherlands, central softening is widely used for reasons related to public health, client comfort, and economic and environmental benefits [5,6,7]. In areas with high water hardness, centralised drinking water softening can reduce the consumption of soap, detergents, and other household chemicals and increase the service life and energy efficiency of household appliances such as coffee machines due to a reduction in calcium carbonate scaling [8,9].
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