Comprehensive Study of Crystal Growth from Solution

Crystal growth is an essential phase in crystallization kinetics. The rate of crystal growth provides significant information for the design and control of crystallization processes; nevertheless, obtaining accurate growth rate data is still challenging due to a number of factors that prevail in crystal growth. In industrial crystallization, crystals are generally grown from multi-componentand multi-particle solutions under complicated hydrodynamic conditions; thus, it is crucial to increase the general understanding of the growth kinetics in these systems. The aim of this work is to develop a model of the crystal growth rate from solution. An extensive literature review of crystal growth focuses on themodelling of growth kinetics and thermodynamics, and new measuring techniques that have been introduced in the field of crystallization. The growth of a singlecrystal is investigated in binary and ternary systems. The binary system consists of potassium dihydrogen phosphate (KDP, crystallizing solute) and water (solvent), and the ternary system includes KDP, water and an organic admixture. The studied admixtures, urea, ethanol and 1-propanol, are employed at relatively highconcentrations (of up to 5.0 molal). The influence of the admixtures on the solution thermodynamics is studied using the Pitzer activity coefficient model. Theprediction method of the ternary solubility in the studied systems is introduced and verified. The growth rate of the KDP (101) face in the studied systems aremeasured in the growth cell as a function of supersaturation, the admixture concentration, the solution velocity over a crystal and temperature. In addition, the surface morphology of the KDP (101) face is studied using ex situ atomic force microscopy (AFM). The crystal growth rate in the ternary systems is modelled on the basis of the two-step growth model that contains the Maxwell-Stefan (MS) equations and a surface-reaction model. This model is used together with measuredcrystal growth rate data to develop a new method for the evaluation of the model parameters. The validation of the model is justified with experiments. The crystal growth rate in an imperfectly mixed suspension crystallizer is investigatedusing computational fluid dynamics (CFD). A solid-liquid suspension flow that includes multi-sized particles is described by the multi-fluid model as well as by a standard k-epsilon turbulence model and an interface momentum transfer model. The local crystal growth rate is determined from calculated flow information in a diffusion-controlled crystal growth regime. The calculated results are evaluated experimentally.

Particle transport method for convection-diffusion-reaction problems

Convective transport, both pure and combined with diffusion and reaction, can be observed in a wide range of physical and industrial applications, such as heat and mass transfer, crystal growth or biomechanics. The numerical approximation of this class of problemscan present substantial difficulties clue to regions of high gradients (steep fronts) of the solution, where generation of spurious oscillations or smearing should be precluded. This work is devoted to the development of an efficient numerical technique to deal with pure linear convection and convection-dominated problems in the frame-work of convection-diffusion-reaction systems. The particle transport method, developed in this study, is based on using rneshless numerical particles which carry out the solution along the characteristics defining the convective transport. The resolution of steep fronts of the solution is controlled by a special spacial adaptivity procedure. The serni-Lagrangian particle transport method uses an Eulerian fixed grid to represent the solution. In the case of convection-diffusion-reaction problems, the method is combined with diffusion and reaction solvers within an operator splitting approach. To transfer the solution from the particle set onto the grid, a fast monotone projection technique is designed. Our numerical results confirm that the method has a spacial accuracy of the second order and can be faster than typical grid-based methods of the same order; for pure linear convection problems the method demonstrates optimal linear complexity. The method works on structured and unstructured meshes, demonstrating a high-resolution property in the regions of steep fronts of the solution. Moreover, the particle transport method can be successfully used for the numerical simulation of the real-life problems in, for example, chemical engineering.

Particle model for simulating limestone reactions in novel fluidised bed energy applications

The development of carbon capture and storage (CCS) has raised interest towards novel fluidised bed (FB) energy applications. In these applications, limestone can be utilized for S02 and/or CO2 capture. The conditions in the new applications differ from the traditional atmospheric and pressurised circulating fluidised bed (CFB) combustion conditions in which the limestone is successfully used for SO2 capture. In this work, a detailed physical single particle model with a description of the mass and energy transfer inside the particle for limestone was developed. The novelty of this model was to take into account the simultaneous reactions, changing conditions, and the effect of advection. Especially, the capability to study the cyclic behaviour of limestone on both sides of the calcination-carbonation equilibrium curve is important in the novel conditions. The significances of including advection or assuming diffusion control were studied in calcination. Especially, the effect of advection in calcination reaction in the novel combustion atmosphere was shown. The model was tested against experimental data; sulphur capture was studied in a laboratory reactor in different fluidised bed conditions. Different Conversion levels and sulphation patterns were examined in different atmospheres for one limestone type. The Conversion curves were well predicted with the model, and the mechanisms leading to the Conversion patterns were explained with the model simulations. In this work, it was also evaluated whether the transient environment has an effect on the limestone behaviour compared to the averaged conditions and in which conditions the effect is the largest. The difference between the averaged and transient conditions was notable only in the conditions which were close to the calcination-carbonation equilibrium curve. The results of this study suggest that the development of a simplified particle model requires a proper understanding of physical and chemical processes taking place in the particle during the reactions. The results of the study will be required when analysing complex limestone reaction phenomena or when developing the description of limestone behaviour in comprehensive 3D process models. In order to transfer the experimental observations to furnace conditions, the relevant mechanisms that take place need to be understood before the important ones can be selected for 3D process model. This study revealed the sulphur capture behaviour under transient oxy-fuel conditions, which is important when the oxy-fuel CFB process and process model are developed.