Drinking water softening is an essential treatment step that provides multiple benefits, including public health, reduction of environmental impact, decrease in clogging potential and improvement in heating efficiency. With approximately 35 billion cubic meters of water being softened annually worldwide, the predominant methods are conventional lime/soda-ash softening, nanofiltration, ion exchange, and seeded crystallization through pellet-water softening. This study addresses the limitations in existing predictive models for calcium carbonate (CaCO₃) precipitation kinetics in industrial-scale pellet-water softening by experimentally investigating the integral and multivariate effects of particle-, fluid-, water matrix- and reactor properties, on CaCO₃ precipitation kinetics. Fluid characterization experiments were conducted at lab-scale continuous-stirred tank reactors (CSTR), pilot-scale plug-flow reactors (PFR), and full-scale fluidized bed reactors (FBR) at the Waternet Weesperkarspel treatment plant in Amsterdam, The Netherlands. In parallel, solid characterization was performed with image analysis software on pellets and SEM on fines extracted from water samples, where both pellet and water samples were collected during FBR experiments. The calcium removal data obtained from experiments were compared with modeled CaCO₃ precipitation rates using and extending the most recently developed water softening model for pellet-water softening. The results predominantly highlight the critical role of mixing dynamics — between softening chemicals, hard influent water and seeding material — for accurate CaCO₃ precipitation predictions across various reactor types and other reactor-specific properties such as the residence time of influent hard water. Additional enhancements can be achieved by targeting fluid properties, followed by water matrix properties, and finally particle properties, though these factors exhibit a progressively smaller impact on overall water softening improvement. By implementing these prioritized optimization strategies, the operational control strategy for calcium removal will be enhanced, leading to improvements in cost-effectiveness, sustainability, and reliability in drinking water treatment processes.

Drinking water softening has primarily prioritized public health, environmental benefits, social costs and enhanced client comfort. Annually, over 35 billion cubic meters of water is softened worldwide, often utilizing three main techniques: nanofiltration, ion exchange and seeded crystallization by pellet softening. However, recent modifications in pellet softening, including changes in seeding materials and acid conditioning used post-softening, have not fully achieved desired flexibility and optimization. This highlights the need of an integral approach, as drinking water softening is just one step in the drinking water treatment chain, which includes ozonation, softening, biological active carbon filtration (BACF) and sand filtration among others. In addition, pellet softening is often practiced based on operator knowledge, lacking practical key reactor performance indicators (KPIs) for efficient control. For that reason, we propose a newly and improved integral mechanistic model designed to accurately predict (1) calcite removal rates in drinking water through seeded crystallization in pellet softening reactors, (2) the saturation of the filter bed in the subsequent treatment step, (3) values for the KPIs steering the softening efficiency. Our new mechanistic model integrates insights from hydrodynamics, thermodynamics, mass transfer kinetics, nucleation and reactor engineering, focussing on critical variables such as temperature, linear velocity, pellet particle size and saturation index with respect to calcite. Our model was validated with data from the Waternet Weesperkarspel drinking water treatment plant in Amsterdam, The Netherlands, but implies universal applicability for addressing industrial challenges beyond drinking water softening. The implementation of our model proposes five effective KPIs to optimize the softening process, chemical usage, and reactor design. The advantage of this model is that it eliminates the application of numerical methods and fills a significant gap in the field by providing predictions of the carry-over (i.e., the produced CaCO₃ fines leaving the fluidized bed) from water softening practices. With our model, the calcium removal rate is predicted with an average standard deviation (SD) of 40 % and the consequential clogging prediction of the BACF bed with an average SD of 130 %. Ultimately, our model provides crucial insights for operational management and decision-making in drinking water treatment plants, steering towards a more circular and environmentally sustainable process.

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.

Natural particles are frequently applied in drinking water treatment processes in fixed bed reactors, fluidised bed reactors, and sedimentation processes to clarify water and to concentrate solids. When particles settle, it has been found that, in terms of hydraulics, natural particles behave differently when compared to perfectly round spheres. To estimate the terminal settling velocity of single solid particles in a liquid system, a comprehensive collection of equations is available. For perfectly round spheres, the settling velocity can be calculated quite accurately. However, for naturally polydisperse non-spherical particles, experimentally measured settling velocities of individual particles show considerable spread from the calculated average values.

This work aims to analyse and explain the different causes of this spread. To this end, terminal settling experiments were conducted in a quiescent fluid with particles varying in density, size, and shape. For the settling experiments, opaque and transparent spherical polydisperse and monodisperse glass beads were selected. In this study, we also examined drinking-water-related particles, like calcite pellets and crushed calcite seeding material grains, which are both applied in drinking water softening. Polydisperse calcite pellets were sieved and separated to acquire more uniformly dispersed samples. In addition, a wide variety of grains with different densities, sizes, and shapes were investigated for their terminal settling velocity and behaviour. The derived drag coefficient was compared with well-known models such as the one of Brown and Lawler (2003).

A sensitivity analysis showed that the spread is caused, to a lesser extent, by variations in fluid properties, measurement errors, and wall effects. Natural variations in specific particle density, path trajectory instabilities, and distinctive multi-particle settling behaviour caused a slightly larger degree of the spread. In contrast, a greater spread is caused by variations in particle size, shape, and orientation.

In terms of robust process designs and adequate process optimisation for fluidisation and sedimentation of natural granules, it is therefore crucial to take into consideration the influence of the natural variations in the settling velocity when using predictive models of round spheres.

For an accurate prediction of the porosity of a liquid-solid homogenous fluidized bed, various empirical prediction models have been developed. Symbolic regression machine learning techniques are suitable for analyzing experimental fluidization data to produce empirical expressions for porosity as a function not only of fluid velocity and viscosity but also of particle size and shape. On the basis of this porosity, it becomes possible to calculate the specific surface area for reactions for seeded crystallization in a fluidized bed.