Mathematical Modeling of Conversion Kinetics during Vitrification of Nuclear Waste

The last part of the high-level waste (HLW) glass melter that has not yet been fully understood, not to mention mathematically modeled, is the cold cap. Cold cap is a layer of dry melter feed, a mixture of the HLW with glass forming and modifying additives. It floats on the pool of molten glass from which it receives the heat necessary for melting. Mathematical modeling of the cold cap solves differential equations that express the mass and energy balances for the feed-to-glass conversion within the cold cap. The feed-to-glass conversion consists of multiple chemical reactions and phase transitions. Reaction enthalpies and mass losses to gases evolved provide an important input for the cold cap modeling. In this study, we measured the kinetics of cold cap reactions using the non-isothermal thermo-gravimetric analysis (TGA) and differential scanning calorimetry (DSC). These thermoanalytical techniques show multiple overlapping peaks, necessitating the development of a deconvolution method for the determination of the kinetics of major reactions needed for cold cap modeling. Assuming that the cold cap reactions are independent, we expressed the overall rate as a sum of rates of individual reactions that we treat as Arrheniustype processes with a power-law based kinetics. Accordingly, we fitted to experimental data the following equation: dx/dT=1/ΦNΣ1wiAi(1-xi)ni exp(-Bi/T) (1) where x is the fraction of material reacted, T is temperature, Φ is the heating rate, wi the weight of the ith reaction (the fraction of the total mass loss caused by the ith reaction), Ai is the ith reaction pre-exponential factor, Bi is the ith reaction activation energy, and ni is the ith reaction (apparent) reaction order. Because HLW melter feeds contain a large number of constituents, such as oxides, acids, hydroxides, oxyhydrates, and ionic salts, the number of cold cap reactions is very large indeed. For example, hydroxides, oxyhydrates, boric acid, and various crystalline forms release chemically bonded water, and reactions of nitrates with organics and molten salts with solid silica release copious amounts of NOx, COx, and O2. Because it is formidable to identify the chemistry of reactions associated with individual peaks, we focused on obtaining the kinetic parameters needed for cold cap modeling. The number of kinetic parameters in Equation (1) is rather large. Therefore, in our recent study, we fitted TGA data using solely a first-order reaction kinetics, i.e., ni = 1, for each reaction peak. In this study, we present an improved model in which the reaction order is a variable parameter