Ag Jones

Programmed cooling crystallization of potassium sulphate solutions

Abstract The crystal size distribution from a batch cooling crystallizer is predicted by the numerical solution of a mathematical model which uses empirical kinetics of nucleation and crystal growth. The predictions clearly point out the potential advantages of controlled cooling at a constant nucleation rate for improving the product crystal size over that obtained by either natural or linear cooling. Experimental runs following programmed cooling curves for seeded potassium sulphate solutions showed reasonable agreement with the theoretical predictions. A size dispersion of the crystals was observed which contributes to a slight deviation from theory. Nevertheless, controlled cooling significantly reduced the quantity of nuclei formed and improved the product crystal size distribution.

Liquid circulation in a draft-tube bubble column

Abstract A study of liquid circulation in a draft-tube bubble column (250 mm diameter, 60l. capacity) using a flow-follower technique is reported. It was observed that annulus liquid circulation velocity increased to a maximum with air flowrate and a maximum in the volumetric liquid circulation rate occurred at a tube: column diameter ratio of about 0.5. A simple model based on air-lift pump theory is used to predict liquid circulation velocity using either pressure drop or air flowrate data. Reasonable agreement is found for narrow draft-tubes (≤ 121 mm) at low gas flowrates (≤ 400 ml./s) but with significant deviations occurring with larger draft-tube diameters. These are thought to be due to secondary liquid flow within the draft-tube reducing primary liquid circulation. At higher gas flowrates bubble entrainment into the annulus becomes increasingly significant at all diameter ratios and the simple air-lift model is then inapplicable.

Optimal operation of a batch cooling crystallizer

Abstract A theory of programmed cooling crystallization is presented based on the moment transformation of the population balance. Numerical predictions for the behaviour of a batch crystallizer agree closely with those from an alternative theory based on the discrete-supersaturation balance. A potential advantage of the present approach is shown to lie in the application of the Continuous Maximum Principle in optimal control theory to facilitate the numerical computation of optimal cooling curves. The transient behavior of a computed “size-optimal” operating policy which maximises the terminal size of the largest crystals is shown to be significantly different from either natural of linear cooling or from crontrolled cooling at a constant nucleation rate. A peak in the nucleation rate towards the end of the operation and an increased terminal crystal size is predicted for the conditions considered and this is supported by preliminary experimental work with potassium sulphate solutions in a laboratory-scale crystallizer.

On the influence of mixing on crystal precipitation processes - application of the segregated feed model

Abstract The segregated feed model (SFM), a compartmental mixing model, is used to predict the influence of mixing on crystal precipitation. In this method, the population balance is solved simultaneously with the mass balances using crystallisation kinetic, solubility and computational fluid dynamics (CFD) mixing data. Mean properties are calculated for the three different zones of the reactor (two feed zones and bulk zone). It is predicted that during continuous operation, the product particle size exhibits oscillating behaviour before reaching steady state after about ten residence times. In contrast, the second moment (surface area) sharply increases during the first residence time and remains constant thereafter. Different mixing conditions are modelled by varying the mesomixing and micromixing times, which can be regarded as convective and diffusive exchange parameters between the compartments of the reactor. The overall nucleation rate is found to strongly depend on the mixing conditions, as it depends in a highly non-linear manner on the level of supersaturation. In consequence, the nucleation rate varies over three orders of magnitude between ‘good’ and ‘poor’ mixing conditions. Using the SFM, the effect of different feed points, feed rates, feed tube diameters, energy dissipation rates, impeller types and vessel sizes on the nucleation rate and the particle size during crystal precipitation is illuminated. Predictions of the model compare favourably with batch and continuous experimental data for calcium oxalate.

A hybrid CFD - reaction engineering framework for multiphase reactor modelling: basic concept and application to bubble column reactors

The coupling of turbulent mixing and chemical phenomena lies at the heart of multiphase reaction engineering, but direct CFD approaches are usually confronted with excessive computational demands. In this hybrid approach, the quantification of mixing is accomplished through averaging the flow and concentration profiles resulting from a CFD flow field calculation and a computational (“virtual”) tracer experiment. Based on these results, we construct a mapping of the CFD grid into a generalised compartmental model where the chemistry calculations can be efficiently carried out. In contrast to the empirical models used in the residence time distribution (RTD) approach, the compartmental model in this methodology, owning to its CFD origins, retains the essential features of the equipment geometry and flow field. A procedure for extracting the mixing information from k–e based CFD codes is outlined, but the main concept of the approach is not restricted to any particular type of turbulence modelling, and will therefore benefit from future developments. A phenomenological model of mass transfer and chemical reaction, based on the penetration theory, is employed to simulate the interfacial phenomena in gas–liquid reactors, and a study of CO2 absorption into alkali solution is presented to demonstrate the method.

Crystal break-up in dilute turbulently agitated suspensions

An analysis of particle attrition in dilute stirred suspensions is developed to predict both the impact attrition rate as a consequence of crystal collisions and the turbulent attrition rate caused by the liquid motion. Detailed attrition experiments designed for model discrimination were carried out in a 1.5 l vessel fitted with four wall baffles and agitated by means of stainless steel and silicone rubber (RTV) coated turbines, respectively, for dilute suspensions (< 3.2% v/v) in the unit power input range 0.6–1.5W/kg and parent particle size range 100–1000 μm, using potassium sulphate and potash alum crystals in saturated ethanol solutions respectively. The experimental results are consistent with predictions of attrition fragments arising from crystal-impeller collisions, with a strong effect of impeller hardness on the average attrition rate, together with turbulent fluid drag-induced particle attrition. It is also predicted, however, that the total attrition rate decreases on vessel scale-up at constant power input, with an increasing proportion of fine particles being due to turbulence, arising from the independence of turbulent forces of the vessel scale and a decrease in the corresponding collisional impact forces.

MASS-TRANSFER WITH CHEMICAL-REACTION AND PRECIPITATION

Precipitation involving three steps, namely gas-liquid mass transfer, chemical reaction and crystallization, is analysed in terms of the coupled equations for the film theory of gas-liquid mass transfer with chemical reaction and the mass and population balances of crystallization. The equations are solved numerically using literature data for the absorption of carbon dioxide gas into lime water. Non-uniform spatial distributions of supersaturation and nucleated particles due to the mass transfer resistance are reflected in the predicted crystal size distributions: larger particles are formed under conditions of high mass transfer into a large liquid volume (small specific surface area), while small particles of low variance are produced when the mass transfer coefficient is low.

Crystallization and precipitation engineering

New computational techniques for the analysis and design of systems for the manufacture of particulate crystals have become available, and the more complex precipitation processes whereby crystallization follows fast chemical reactions have also been analysed more deeply. This progress has been aided by the growing power of the population balance and kinetic models, computational fluid dynamics (CFD) and mixing theory, respectively. These aspects are selectively reviewed and areas requiring further progress are identified.

Flow dynamics in a draft-tube bubble column using various liquids

Abstract Gas hold-up and liquid circulation rates in a draft-tube bubble column (0.22 m diameter, 85 l capacity) fitted with various diameter draft-tubes are measured for water and aqueous solutions of ethanol, glycerol and carboxymethylcellulose (CMC), respectively. The data are analyzed in terms of a development of the simple energy balance incorporating flow contraction coefficients to quantify deviations from ideal flow. Ethanol and glycerol enhance the entrainment of gas bubbles into the downcomer compared with pure water and inhibit liquid circulation. In CMC solutions, however, large coalesced bubbles are easily disengaged at the top of the column with little entrainment into the downcomer and promote the highest liquid circulation rate. Bubble column geometry, i.e. draft-tube diameter, affects both bubble entrainment and the flow contraction coefficients, and interacts with the fluid properties to affect both gas hold-up and liquid circulation.

Hydrodynamics of secondary nucleation in suspension crystallization

Abstract Hydrodynamic models of secondary nucleus generation in mechanically agitated suspension crystallizers are analysed in detail and their predictions compared with experimental measurements using potassium sulphate crystals. The data indicate that, under operating conditions similar to those found in industrial crystallizers, secondary nuclei are produced by a particle attrition process consistent with a turbulent fluid-induced breeding mechanism having critical eddies in the viscous dissipation subrange of the turbulent energy spectrum.