Kinetic model for quartz and spinel dissolution during melting of high-level-waste glass batch
The dissolution of quartz particles and the growth and dissolution of crystalline phases during the conversion of batch to glass potentially affects both the glass melting process and product quality. Crystals of spinel exiting the cold cap to molten glass below can be troublesome during the vitrification of iron-containing high-level wastes. To estimate the distribution of quartz and spinel fractions within the cold cap, we used kinetic models that relate fractions of these phases to temperature and heating rate. Fitting the model equations to data showed that the heating rate, apart from affecting quartz and spinel behavior directly, also affects them indirectly via concurrent processes, such as the formation and motion of bubbles. Because of these indirect effects, it was necessary to allow one kinetic parameter (the pre-exponential factor) to vary with the heating rate. The resulting kinetic equations are sufficiently simple for the detailed modeling of batch-to-glass conversion as it occurs in glass melters. The estimated fractions and sizes of quartz and spinel particles as they leave the cold cap, determined in this study, will provide the source terms needed for modeling the behavior of these solid particles within the flow of molten glass in the melter.
Cold-cap reactions in vitrification of nuclear waste glass: Experiments and modeling
a b s t r a c t Cold-cap reactions are multiple overlapping reactions that occur in the waste-glass melter during the vitrification process when the melter feed is being converted to molten glass. In this study, we used simultaneous differential scanning calorimetry-thermogravimetry (DSC-TGA) to investigate cold-cap reactions in a high-alumina high-level waste melter feed. To separate the reaction heat from both the heat associated with the heat capacity of the feed and experimental artifacts, we employed the run/rerun method, which enabled us to define the degree of conversion based on the reaction heat and to estimate the heat capacity of the reacting feed. Assuming that the reactions are nearly independent and can be approximated by an nth order kinetic model, we obtained the kinetic parameters using the Kissinger method combined with least squares analysis. The resulting mathematical simulation of the cold-cap reactions provides a key element for the development of an advanced cold-cap model.
Diffusion-controlled mass transfer to or from spheres with concentration-dependent diffusivity
Abstract Analytical solutions for the growth of an isolated sphere from zero initial size have been derived with diffusivity an explicit function of concentration. Numerical methods have also been developed to treat either growth or dissolution with concentration-dependent diffusivity. Diffusivity is here taken to be an exponential function of concentration but several other forms have been studied. The predictions of the two methods show the same asymptotic behaviour (rate of change in size and concentration distribution) for growing spheres and this is considered to validate the numerical procedures. When appropriately normalized the change in size of a sphere can be described by a constant property model. However, the equivalent diffusivity is equal to the expected average over the appropriate concentration range only for very low solubility; the equivalent diffusivity can be estimated for higher solubilities.