Nuclear Waste Vitrification Efficiency: Cold Cap Reactions

Journal of Non-Crystalline Solids 358 (2012) 3559–3562 Contents lists available at SciVerse ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol Nuclear waste vitrification efficiency: Cold cap reactions P. Hrma a,b,⁎, A.A. Kruger c, R. Pokorny d a Division of Advanced Nuclear Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea b Pacific Northwest National Laboratory, Richland, WA 99352, USA c U.S. Department of Energy Hanford Tank Waste Treatment and Immobilization Plant Federal Project Office, Engineering Division, Richland, WA 99352, USA d Institute of Chemical Technology, Prague, Czech Republic article info abstract Article history: Batch melting takes place within the cold cap, i.e., a batch layer floating on the surface of molten glass in a Received 26 July 2011 glass-melting furnace. The conversion of batch to glass consists of various chemical reactions, phase transi- Received in revised form 5 January 2012 tions, and diffusion-controlled processes. This study introduces a one-dimensional (1D) mathematical Available online 7 March 2012 model of the cold cap that describes the batch-to-glass conversion within the cold cap as it progresses in a vertical direction. With constitutive equations and key parameters based on measured data, and simplified Keywords: boundary conditions on the cold-cap interfaces with the glass melt and the plenum space of the melter, Glass melting; Glass foaming; the model provides sensitivity analysis of the response of the cold cap to the batch makeup and melter con- Waste vitrification; ditions. The model demonstrates that batch foaming has a decisive influence on the rate of melting. Under- Cold cap standing the dynamics of the foam layer at the bottom of the cold cap and the heat transfer through it appears crucial for a reliable prediction of the rate of melting as a function of the melter-feed makeup and melter operation parameters. Although the study is focused on a batch for waste vitrification, the authors expect that the outcome will also be relevant for commercial glass melting. © 2012 Elsevier B.V. All rights reserved. 1. Introduction borate melt with molten salts and amorphous solids, precipitation of intermediate crystalline phases, formation of a continuous glass- The cold cap, or batch blanket, is the layer of glass batch floating forming melt, growth and collapse of primary foam, dissolution of re- on molten glass in an electrical glass-melting furnace (a melter). In sidual solids, and the formation of secondary foam at the bottom of melters producing commercial glasses, the batch is typically spread the cold cap. In the present model, this complex situation is simplified in a layer of uniform thickness on the whole top surface area of the by assuming that the feed consists of two major phases: the con- melt. In melters for nuclear waste glass, the melter feed, typically a densed phase and the gas phase. slurry containing 40–60% water, is charged through one or more noz- The authors expect that the 1D two-phase model presented in this zles. The cold cap covers 90–95% of the melt surface. Mathematical paper will be extended in the future to a two-dimensional (2D) models of melters have been well developed [1–5] in all aspects ex- multi-phase model to be incorporated in a complete 3D model of cept for the batch melting, which has rarely been addressed in other the waste glass melter. than a simplified manner [6–12]. This work presents an initial step toward the modeling of a cold 2. Theory cap in a melter for high-level-waste glass while taking advantage of the availability of data for the key properties and the reaction kinetics The 1D model views the cold cap as a blanket of uniform thickness for a high-alumina melter feed [13–16] considered for the Waste that receives steady uniform heat fluxes from both the molten glass Treatment and Immobilization Plant, currently under construction below and the plenum space above (Fig. 1). The mass balances of at the Hanford Site in Washington State, USA. The 1D model is the condensed phase and the gas phase are based on the ideas by Hrma [9] and Schill [10,11]. ρ ðÞρ Though the 1D modeling greatly simplifies mathematical treat- d b þ d bvb ¼ ð Þ rb 1 ment, the main challenge lies in the complexity of the conversion dt dx process, which consists of a host of phenomena: water evaporation, ρ gas evolution, melting of salts, borate melt formation, reactions of dρ d gvg g þ ¼ r ð2Þ dt dx g ⁎ Corresponding author at: Pacific Northwest National Laboratory, Richland, WA ρ 99352, USA. where t is the time, the spatial density, v the velocity, r the mass E-mail address: [email protected] (P. Hrma). source associated with reactions, and the subscripts b and g denote 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.01.051 3560 P. Hrma et al. / Journal of Non-Crystalline Solids 358 (2012) 3559–3562 Table 1 Melter feed composition (in g) to make 1 kg of glass. Compound g/kg Al(OH)3 367.49 SiO2 305.05 B(OH)3 269.83 NaOH 97.14 Li2CO3 88.30 Fe(OH)3 73.82 CaO 60.79 NaF 14.78 Bi(OH)3 12.80 Fe(H2PO2)3 12.42 Na2CrO4 11.13 NiCO3 6.36 Pb(NO3)2 6.08 Zr(OH) ·0.654H O 5.11 Fig. 1. Cold-cap structure. 4 2 NaNO3 4.93 Na2SO4 3.55 fl NaNO2 3.37 the condensed phase and the gas phase, respectively. The mass uxes, KNO 3.04 −ρ 3 jb and jg, respectively, are jb = bvb (the minus sign in is used Zn(NO3)2·4H2O 2.67 because the condensed phase moves in the negative direction) and Na2C2O4·3H2O 1.76 Mg(OH) 1.69 jg =ρgvg. The energy balance for the condensed phase is: 2 Total 1352.11 dT dT dq ρ c b ¼ −ρ v c b − b þ H þ s ð3Þ b b dt b b b dx dx and λEff(1100 °C)=4.56 W m− 1 K− 1, the value for molten glass where T is the temperature, c is the heat capacity, q is the heat flux, H (Schill [17]). To the best of our knowledge, the heat conductivity of is the internal heat source, and s is the heat transfer between phases. the foam layer at the cold cap bottom has not been determined exper- fl ¼ −λEff dT The heat ux is subjected to Fourier's law, qb dx, where the ef- imentally. The heat conductivity of the foam layer was estimated to fective value of heat conductivity, λEff, involves both conductive and be close to half of the heat conductivity of bubble-free melt. radiative modes of heat transfer in the feed. The boundary conditions are given in the term of both fluxes and temperatures, i.e., qb(0)=QB, qb(h)=QT, T(0)=TB, and T(h)=TT, 4. Results where h is the cold cap thickness, TB and TT are the bottom and top cold-cap temperatures, respectively, and QB and QT are the heat fluxes As Fig. 1 illustrates, a layer of boiling slurry rests on the top of the to cold-cap bottom and from cold-cap top, respectively. cold cap, which consists of two layers: the main layer in which batch To solve the energy balance equation, we used, for the sake of sim- reactions occur and batch gases are escaping through open pores, and plicity and comprehensibility, the finite difference method. For nu- the bottom foam layer. merical simulations, experimental data were used together with For the calculations, the cold-cap bottom temperature, TB =1100°C, constitutive equations that were taken from the literature and modi- was estimated as the temperature at which the motion of the con- fied for our problem as described in Section 3. All algorithms were densed phase can no longer be considered one-dimensional and the cir- coded in Mathworks MATLAB 7. cular convection of the melt takes over. The temperature at the interface between the cold cap and the slurry layer was TT =100 °C, the temper- 3. Material properties ature of the boiling slurry pool, ignoring the elevation of the boiling point by dissolved salts. The melter feed composition is shown in Table 1. Based on melter experiments reported by Matlack et al. [18],wechose Fig. 2 shows the degree of conversion, ξg, calculated as ξg(T) as the baseline case a slurry feed containing 52.2 mass% water and the −2 −1 =(m−mF)/(mM −mF), where m is the temperature-dependent feed glass production rate (the rate of melting) jM=0.0141 kg m s , −2 −1 mass, mF is the melter-feed mass, and mM is the glass mass; the sub- (1220 kg m day ). script g indicates that the degree of conversion is based on the release of gas from the feed. Because the ξg(T) function changed little with the rate of heating, we used the degree of conversion obtained by thermogravimetric analysis at the heating rate 15 K min− 1. Following Schill [11], the heat capacity of the gas phase (cg) was approximated by that of carbon dioxide: cg =1003+0.21T− 7 − 2 − 1 − 1 1.93⋅10 T (T≥373 K), where cg is in J kg K . The melter feed density decreased as the temperature increased as a result of mass loss and the nearly constant volume of the sample at Tb~700 °C, i.e., ρb =ρb0m/mF.

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