Mathematical modeling of cold cap
The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass, and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.
Application of evolved gas analysis to cold-cap reactions of melter feeds for nuclear waste vitrification
Abstract In the vitrification of nuclear wastes, the melter feed (a mixture of nuclear waste and glass-forming and modifying additives) experiences multiple gas-evolving reactions in an electrical glass-melting furnace. We employed the thermogravimetry-gas chromatography–mass spectrometry (TGA-GC–MS) combination to perform evolved gas analysis (EGA). Along with identifying the gases evolved, we performed quantitative analysis relating the weighted sum of intensities of individual gases in linear proportion with the differential thermogravimetry. The proportionality coefficients were obtained by three methods based on the stoichiometry, least squares, and calibration. The linearity was shown to be a good first-order approximation, in spite of the complicated overlapping reactions.
Kinetics of growth of spinel crystals in a borosilicate glass
Three aspects of the kinetics of spinel crystallization in a high-level waste (HLW) glass were studied: (1) the effect of nucleation agents on the number density (ns) of spinel crystals, (2) crystallization kinetics in a crushed glass, and (3) crystallization kinetics in a glass preheated at T > TL (liquidus temperature). In glass lacking in nucleation agents, ns was a strong function of temperature. In glasses with noble metals (Rh, Ru, Pd, and Pt), ns increased by up to four orders of magnitude and was nearly independent of temperature. The kinetics of spinel crystallization in crushed glass lacking nucleation agents was dominated by surface crystallization and was described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation with the Avrami exponent n {at} 0.5. For application to HLW glass melter processing, it was necessary to preheat glass at T > TL to eliminate the impact of temperature history and surface crystallization on crystal nucleation and growth. In the temperature range of glass processing, crystals descend under gravity when they reach a critical size. Below this critical size, crystallization kinetics is described by the KJMA equation and above the critical size by the Hixson-Crowell equation. At low temperatures, at which glass viscosity is high andmore » diffusion is slow, the KJMA equation represents crystal growth from nucleation to equilibrium. As ns increases, the temperature interval of the transition from the KJMA to Hixson-Crowell regime shifts to a higher temperature.« less