A macroscopic agglomeration kernel model for gibbsite precipitation in turbulent and laminar flows

A macroscopic agglomeration kernel model has been developed that is capable of describing gibbsite agglomeration over a broad range of process conditions, including both the laminar and turbulent flow regimes. The agglomeration kernel model was derived using chemical reaction engineering principles and data from an extensive experimental program covering a wide range of temperatures, supersaturations, seed sizes, shear rates and mixing regimes. The experimental precipitation data in the laminar flow regime were generated using a novel Taylor-Couette precipitator. Data in the turbulent regime were generated in a stirred reactor. The developed agglomeration kernel model incorporates terms for the collision, capture, rupture and cementation rates affecting the formation of agglomerates. The model is shown to be able to predict the data from independent experiments. The proposed model also captures the complex non-linear shear rate and size-dependency observed experimentally, e.g. (1) for small particles the agglomeration kernel exhibits a maximum with respect to the shear rate, increasing at low shear rates in the laminar flow, but decreasing in the unstable Taylor-Couette flows and turbulent regimes; (2) for large particles the agglomeration kernel decreases monotonically with increasing shear.     

The influence of organic additives on the crystallization and agglomeration of gibbsite

During the crystallization of gibbsite Al(OH)₃, which leads to the synthesis of alumina in the Bayer process, crystals go through a step of agglomeration. In this work, we present a study concerning the influence of different organic compounds, polycarboxylic acids and polyalcohols on the crystallization and agglomeration of gibbsite crystals. It has been determined that they act as crystal habit modifiers and inhibitors of the agglomeration occurring during the formation of alumina crystallites. Simply by following the kinetics of the reaction, it has been observed that polyalcohols are stronger inhibitors than polycarboxylic acids, which can be linked to the structure of gibbsite crystals. The influence of the characteristics of the additive, such as the number of carboxylic groups and the distance between them for polyacids, the stereochemistry and the length of the carbon chain in the case of polyalcohols, is demonstrated to have a significant effect.     

Particle distribution model of gibbsite precipitation process in alumina production

The precipitation is a process involving complicated crystallization and mass transfer. As a key step in the Bayer process in alumina production, it has great influences on both outputs and quality of alumina products. Thus laboratory experiments, industrial tests and numerical simulations have been carried out to study the precipitation. Based on the dynamics law and particle population balance, a combined model is developed with MATLAB/Simulink to study the process of crystal nucleation, growth and agglomeration, the model also take the variation characteristics of the particle size of the MSMPR (mixed-suspension, mixed product removal) gibbsite precipitation process into account. The particle size distribution is predicted through the method of moments at different conditions. The deviation between the model prediction and the test data is less than 9%, which is within the acceptable accuracy range for the process control.     

Development of a networks-of-zones fluid mixing model for an unbaffled stirred vessel used for precipitation

Reactive acid-alkali tracers have been deployed to capture the macromixing and partial segregation behaviour in an unbaffled stirred vessel. This configuration is often used in precipitators to avoid inadvertent solid accretions on vessel internals. The macromixing behaviour for semi-batch addition with visualisation of reactive (acid-alkali) tracers has been acquired via video images which are rendered visible using phenolphthalein as indicator. By means of visual reality modelling, in which computer graphics are used to reconstruct and closely mimic the experimentally visualised fluid mixing “scenes”, the parameters for a networks-of-zones mixing model for the unbaffled semi-batch case have been established. The model can then be used for predicting precipitation behaviour for single-jet and other modes of operation. Some illustrative examples for barium sulphate, showing the underlying supersaturation fields in 3-D and the consequent time evolving particle size distributions, are presented and discussed for a single jet case.     

Tomographic imaging during reactive precipitation in a stirred vessel: Mixing with chemical reaction

Electrical resistance tomography (ERT) allows the user to non-invasively ‘see inside their process’ through the manipulation and measurement of electrical properties enabling a powerful real-time visualisation of the time evolving three-dimensional conductivity distributions within the process unit. A 4-plane 16-sensor ERT array retrofitted to a 7.5 l stirred vessel has been used to rigorously interrogate the single feed semi-batch precipitation of barium sulphate, providing over 1000 spatially varying data points per ‘captured’ frame. A variety of reactant concentrations and agitation intensities were investigated. The results obtained reflect both the hydrodynamics and complex reaction kinetics involved with reactions and detail a number of very distinct regions during the experimental runs. This is achieved through the direct visualisation of the induced feed plume, quantification of the homogeneity (‘mixedness’) within the vessel, time evolving conductivity trends and a further analysis into the rates of conductivity changes as the reaction proceeds. For some experimental runs the predicted conductivity trends for a perfectly mixed state have been calculated using a conductivity-concentration correlation. ERT offers many spatially varying data points as opposed to point wise measurements which offers a significant improvement for the validation of mathematical models which attempt to deal with reactive crystallisation. As well as data collection, specifically for model validation, ERT may offer the means to control the spatio-temporal distributions of reactants and phases within the reactor to aid the suppression of unwanted by-products for industrial processes whilst offering a means to monitor the process unit to ensure the required mixing intensity is always achieved. Also included is an analysis of the mean volume diameter of the precipitate for each experimental run with scanning electron microscope (SEM) images.     

Modelling of multiple-mechanism agglomeration in a crystallization process

A three-level agglomeration model coupled with crystal growth is developed. It accounts for Brownian, laminar, and turbulent agglomeration. The desupersaturation profiles, the particle size distributions, the average sizes, and variances (or standard deviations), as well as the instantaneous agglomeration degrees for each mechanism, can be calculated as functions of time. The model is applied to the crystallization of an amorphous solid into a crystalline polymorph in a batch crystallizer. A runaway phenomenon is detected for agglomeration when crystals are switching over from the Brownian regime to the laminar one: this switchover significantly affects the desupersaturation curve and the crystal shapes.     

Inline monitoring the effect of chemical inhibitor on the calcium carbonate precipitation and agglomeration

The formation of mineral scale particularly calcium carbonate is a problem for industries ranging from oil and gas to desalination plants. Various techniques have been studied to prevent the formation of scale. The use of chemical inhibitors to prevent calcium carbonate agglomeration is widely studied. The present study attempts to show that the inline monitoring technique is a useful tool for laboratory experimental investigation of agglomeration phenomenon. This method is successful in providing the induction time of starting agglomeration. It was shown that the presence of inhibitor delays the agglomeration and affects the deposition of calcium carbonate.In addition the method is found useful in determining the minimum inhibitor concentration and also to screen various types of inhibitors for the selection. The influence of an inhibitor is studied on scaling solution of various calcium ion concentrations. Finally, the result of inline technique was validated by comparing with the conventional one called offline technique. The SEM images reveal that the mechanism of inhibition might be the surface adsorption or distortion of inhibitor molecules on the growing calcium carbonate crystals.     

A 1-D non-isothermal dynamic model for the thermal decomposition of a gibbsite particle

A 1-D mathematical model describing the thermal decomposition, or calcination, of a single gibbsite particle to alumina has been developed and validated against literature data. A dynamic, spatially distributed, mass and energy balance model enables the prediction of the evolution of chemical composition and temperature as a function of radial position inside a particle. In the thermal decomposition of gibbsite, water vapour is formed and the internal water vapour pressure plays a significant role in determining the rate of gibbsite dehydration. A thermal decomposition rate equation, developed by closely matching experimental data reported previously in the literature, assumes a reaction order of 1 with respect to gibbsite concentration, and an order of −1 with respect to water vapour pressure. Estimated values of the transformation kinetic parameters were k₀ = 2.5 × 10¹³ mol/(m³ s) for the pre-exponential factor, and E_a = 131 kJ/mol for the activation energy. Using these kinetic parameters, the gibbsite particle model is solved numerically to predict the evolution of the internal water vapour pressure, temperature and gibbsite concentration. The model prediction was shown to be very sensitive to the values of heat transfer coefficient, effective diffusivity, particle size and external pressure, but relatively less sensitive to the mass transfer coefficient and particle thermal conductivity. The predicted profile of the water vapour pressure inside the particle helps explain some phenomena observed in practice, including particle breakage and formation of a boehmite phase.     

Dynamic modeling of a batch crystallization process: A stochastic approach for agglomeration and attrition process

This paper deals with the dynamic modeling of a batch crystallizer. A complete model taking into account primary and secondary nucleations, crystal growth, agglomeration and attrition mechanisms is established. The proposed model is not restricted to binary agglomeration and breakage phenomena. From markovian considerations, continuous kernel functions are built and the basic balance equations are then presented. The complete model is solved using a finite difference method for the discretization of the size variable. As to distinguish agglomeration and breakage parameters from the others, on line measurement of the Crystal Size Distribution is necessary, a new on line measurement strategy is proposed. Finally, simulations of the crystal size distribution are compared with experimental results at different times. It appears that simulated curves are in good agreement with the experimental data.     

Modelling of agglomeration in suspension: Application to salicylic acid microparticles

The agglomeration in suspension technique consists of adding directly into the suspension a small amount of a second liquid which acts as an interparticle bonding agent. The system (salicylic acid particles, aqueous solution, chloroform) is studied experimentally by in situ image analysis. After a brief period of wetting of the particles by the binding liquid, the agglomerates grow by a coalescence-like process until they reach a maximum size. Porosity measurements reveal that the agglomerates are then getting more compact. Eventually, the agglomeration mechanism is likely governed by the agglomerate deformability, as it is often suggested in granulation. A population balance modelling is proposed to describe the growth period. The agglomeration kernel is built according to the experimental observations. It is expressed as the product of two factors which relate the meeting probability and the sticking efficiency, respectively. The probability of encounter is governed by the hydrodynamics. The sticking efficiency compares the sticking force, directly linked to the deformation induced by the agglomerate-agglomerate impact under consideration, with the shear-induced disruptive force. This phenomenological model fits well the experimental results obtained for the salicylic acid particles.     

A refined model for ozone mass transfer in a semibatch stirred vessel

The mathematical model proposed by Anselmi et al. (1984) for a semibatch stirred gas‐liquid contactor is refined to describe the mass transfer of ozone absorption and decomposition in aqueous solution with the decomposition rate expression of general reaction orders (not necessarily integers). Three system equations are employed to describe the ozone concentrations in the bulk liquid (C_ALb), the hold‐up gas (C_AGi), and the outlet gas in the free volume above the liquid surface (C_AGe), respectively. The effect of ozone decomposition on the mass transfer, which is reflected by the enhancement factor (E_r) defined as the ratio of mass absorbed per unit area in time t with chemical reaction (r) to that without chemical reaction or of the purely physical absorption, is considered in the refined model. Furthermore, the refined model also takes into account the variation of E_r with C_ALb, which changes with time during the course of gas‐liquid contacting. Thus this analysis extends the applicability of the model of Anselmi et al. (1984) and is of special importance for ozone mass transfer in the cases of basic solutions and of low mass transfer coefficients, in which the effect of decomposition on absorption is significant, and in the system with variable liquid phase ozone concentration.     

Barium Sulphate Agglomeration in a Pipe – An Experimental Study and CFD Modeling

Agglomeration effects, observed during precipitation of barium sulphate in the unpremixed feed two‐dimensional tubular precipitator, are studied experimentally and interpreted theoretically. Effects of process parameters on precipitation–agglomeration phenomena are predicted using a CFD based model that describes micromixing (the multiple‐time‐scale turbulent mixer model is used) and precipitation (including nucleation, growth and agglomeration of crystals). Agglomeration rate is defined as a product of the collision frequency and the probability of agglomeration.     

Parameter estimation in a multidimensional granulation model

A new multidimensional model for wet granulation is presented, which includes particle coalescence, compaction, reaction, penetration, and breakage. In the model, particles are assumed to be spherical and consist of two kinds of solid, two kinds of liquid, and pore volume. The model is tested against experimental results (Simmons, Turton and Mort. Proceedings of Fifth World Congress on Particle Technology, paper 9d, 2006) from the granulation of sugar particles with different PEG based binders in a bench scale mixer, being carried out for different impeller speeds, binder compositions and process durations. The unknown rate constants for coalescence, compaction, reaction, and breakage were fitted to the experiments and the sensitivities of the mass of agglomerates were calculated with respect to these parameters. This is done by employing experimental design and a response surface technique. The simulations with the established set of parameters show that the model predicts the trends, not only in time, but also for crucial process conditions such as impeller speed and the binder composition. As such it is found that more viscous binder promotes the formation of porous particle ensembles. Furthermore, the statistics of the different events such as collisions, coalescence and breakage reveal for instance that successful coalescence events outnumber the breakage events by a factor of up to three for low impeller speeds.     

Powder coating efficiency of small particles and their agglomeration in circulating fluidized bed

The coating efficiency of fluidizing small particles and their agglomeration were investigated to evaluate the possibility of powder coating by the use of a circulating fluidized bed. Glass beads, whose mean diameter was 43 Μm, and silica powder of 1 Μm were used as a core and a coating material. Polyvinyl alcohol was used as a binder and its solution was supplied together with silica powder from a spray nozzle equipped in the circulating fluidized bed. Glass beads of 43 Μm, which had been impossible to coat in a conventional fluidized bed coater, were successfully coated with silica powder in a circulating fluidized bed, and agglomeration among core particles was prevented. From this result, it was confirmed that a circulating fluidized bed performs excellently as a coater, especially for fine core particles, so a circulating fluidized bed coater has bright prospects for particle coating.     

Kinetics identification of salicylic acid precipitation through experiments in a batch stirred vessel and a T-mixer

This work aims to identify the mechanisms and kinetics of salicylic acid precipitation. A large supersaturation domain is covered (initial supersaturation ratios between 2.7 and 65.0) and two experimental set-ups are used. At low supersaturations, precipitations are performed in a stirred vessel, whereas a T-mixer must be used at high supersaturations in order to avoid hydrodynamic effects. In each case, the precipitation mechanisms actually involved are different and their kinetics are identified by solving the population balance with the method of classes. Thus, at low supersaturations in the stirred vessel, the primary nucleation is of heterogeneous type and the secondary nucleation is dominant, whereas homogeneous primary nucleation dominates in the T-mixer at high supersaturations. The crystal growth is diffusion controlled in the stirred vessel and turns into an integration limited mechanism in the T-mixer.     

Influence of shear on particle size and fractal dimension of whey protein precipitates: implications for scale-up and centrifugal clarification efficiency

Whey protein fractionation was carried out at laboratory scale by applying the required temperature and pH conditions in a standard configuration batch agitated vessel to cause selective precipitation and aggregation of proteins. Scale-up of this operation to pilot scale was achieved on the basis of impeller power input per unit volume resulting in similar particle sizes. Separation was subsequently achieved by high-speed disc-stack centrifugation.Processing of precipitates in pumps, valves and at the centrifuge inlet zone can lead to substantial breakage, depending on the strength of the precipitates formed and aged in the batch vessel. Such turbulent processing was mimicked at lab scale by passing the precipitate solution through a ball-valve rig while monitoring the effects on particle size and fractal geometry. Measurement of fractal dimension were used to assess the compactness of precipitates. Precipitates subjected to higher batch vessel impeller shear-rates during formation and ageing were found to be smaller, more compact and better able to resist turbulent breakage and thus should provide better feed-stock for disc-stack centrifugation at pilot scale. Clarification efficiency curves obtained for pilot-scale disc-stack centrifugation confirmed these lab-scale predictions. Recommendations for improved process design in terms of selecting suitable batch vessel shear-rates that ultimately lead to improved separation efficiencies have been made.     

A study on some effects of a drag-reducing agent on the performance of a stirred vessel

The influence of the addition of a drag reducing agent (100 ppm PAA) to a pure liquid (water) in a stirred vessel has been studied. The vessel was stirred with two types of agitators, a Rushton turbine and an axial A310 impeller.This study was meant to implement previous findings with new data and various types of measurements were performed to determine a number of parameters. It is confirmed that the drag-reducing agent decreases power draw and increases mixing time. Mean flow and the fluctuating velocities were determined (with the PIV technique) and notable reduction in turbulence intensity was detected. The mechanism of tracer dispersion (followed by the PLIF technique) was also documented qualitatively. Finally, the influence of the drag-reducing agent on the particle size distribution of the solid product of a precipitation reaction (reaction of barium chloride and sodium sulphate) was shown.     

Experimental validation studies on a multi-dimensional and multi-scale population balance model of batch granulation

In this study, a dynamic model is presented for the granulation process, employing a three-dimensional population balance framework. As a first attempt to account for the multi-scale character of the process, the nucleation and aggregation kernels used in the population balance model are derived using mechanistic representations of the underlying particle physics such as wetting kinetics and energy dissipation effects. Thus, the fundamental properties of the powder and the liquid were used as parameters in the model to predict the granulator dynamics and granule properties. The population balance model is validated against experimental data from a calcite/PVOH-H₂O recipe obtained using a lab-scale drum granulator for granule size, fractional binder content and porosity. A reasonably good agreement between experimental and simulation results were obtained for the granule size distribution under different experimental conditions. In addition, accurate model predictions were made for the evolution of the average properties (i.e., size, fractional binder content and porosity) for various operating conditions.