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he laye-meltins, the bwholess, the

Journal of Non-Crystalline Solids 358 (2012) 35593562

Contents lists available at SciVerse ScienceDirect

Journal of Non-Cr

evmodels of melters have been well developed [15] in all aspects ex-cept for the batch melting, which has rarely been addressed in otherthan a simplied manner [612].

This work presents an initial step toward the modeling of a coldcap in a melter for high-level-waste glass while taking advantage ofthe availability of data for the key properties and the reaction kineticsfor a high-alumina melter feed [1316] considered for the WasteTreatment and Immobilization Plant, currently under constructionat the Hanford Site in Washington State, USA. The 1D model isbased on the ideas by Hrma [9] and Schill [10,11].

multi-phase model to be incorporated in a complete 3D model ofthe waste glass melter.

2. Theory

The 1D model views the cold cap as a blanket of uniform thicknessthat receives steady uniform heat uxes from both the molten glassbelow and the plenum space above (Fig. 1). The mass balances ofthe condensed phase and the gas phase areThough the 1D modeling greatly simpliment, the main challenge lies in the compprocess, which consists of a host of phenomgas evolution, melting of salts, borate melt

Corresponding author at: Pacic Northwest Natio99352, USA.

E-mail address: pavel.hrma@pnl.gov (P. Hrma).

0022-3093/$ see front matter 2012 Elsevier B.V. Alldoi:10.1016/j.jnoncrysol.2012.01.051melter feed, typically arough one or more noz-lt surface. Mathematical

densed phase and the gas phase.The authors expect that the 1D two-phase model presented in this

paper will be extended in the future to a two-dimensional (2D)

slurry containing 4060% water, is charged thzles. The cold cap covers 9095% of the me1. Introduction

The cold cap, or batch blanket, is ton molten glass in an electrical glassmelters producing commercial glassein a layer of uniform thickness on themelt. In melters for nuclear waste glamelter operation parameters. Although the study is focused on a batch for waste vitrication, the authors ex-pect that the outcome will also be relevant for commercial glass melting.

2012 Elsevier B.V. All rights reserved.

r of glass batch oatingg furnace (a melter). Inatch is typically spreadtop surface area of the

borate melt with molten salts and amorphous solids, precipitationof intermediate crystalline phases, formation of a continuous glass-forming melt, growth and collapse of primary foam, dissolution of re-sidual solids, and the formation of secondary foam at the bottom ofthe cold cap. In the present model, this complex situation is simpliedby assuming that the feed consists of two major phases: the con-Cold cap standing the dynamics of the foam layer at the bottom of the cold cap and the heat transfer through itappears crucial for a reliable prediction of the rate of melting as a function of the melter-feed makeup andWaste vitrication; ditions. The model demonsNuclear waste vitrication efciency: Col

P. Hrma a,b,, A.A. Kruger c, R. Pokorny d

a Division of Advanced Nuclear Engineering, Pohang University of Science and Technology,b Pacic Northwest National Laboratory, Richland, WA 99352, USAc U.S. Department of Energy Hanford Tank Waste Treatment and Immobilization Plant Feded Institute of Chemical Technology, Prague, Czech Republic

a b s t r a c ta r t i c l e i n f o

Article history:Received 26 July 2011Received in revised form 5 January 2012Available online 7 March 2012

Keywords:Glass melting;Glass foaming;

Batch melting takes place wglass-melting furnace. Thetions, and diffusion-contromodel of the cold cap thatvertical direction. With conboundary conditions on ththe model provides sensitiv

j ourna l homepage: www.e lses mathematical treat-lexity of the conversionena: water evaporation,formation, reactions of

nal Laboratory, Richland, WA

rights reserved.cap reactions

ang, Republic of Korea

Project Ofce, Engineering Division, Richland, WA 99352, USA

in the cold cap, i.e., a batch layer oating on the surface of molten glass in aersion of batch to glass consists of various chemical reactions, phase transi-processes. This study introduces a one-dimensional (1D) mathematicalribes the batch-to-glass conversion within the cold cap as it progresses in autive equations and key parameters based on measured data, and simpliedld-cap interfaces with the glass melt and the plenum space of the melter,analysis of the response of the cold cap to the batch makeup and melter con-es that batch foaming has a decisive inuence on the rate of melting. Under-

ystalline Solids

i e r .com/ locate / jnoncryso ldbdt

d bvb dx

rb 1

dgdt

d gvg

dx rg 2

where t is the time, the spatial density, v the velocity, r the masssource associated with reactions, and the subscripts b and g denote

cold cap, which consists of two layers: the main layer in which batchreactions occur and batch gases are escaping through open pores, and

between the cold cap and the slurry layer was TT=100 C, the temper-ature of the boiling slurry pool, ignoring the elevation of the boilingpoint by dissolved salts.

Based onmelter experiments reported byMatlack et al. [18], we choseas the baseline case a slurry feed containing 52.2 mass% water and theglass production rate (the rate of melting) jM=0.0141 kg m2 s1,(1220 kg m2 day1).

Table 1Melter feed composition (in g) to make 1 kg of glass.

Compound g/kg

Al(OH)3 367.49SiO2 305.05B(OH)3 269.83NaOH 97.14Li2CO3 88.30Fe(OH)3 73.82CaO 60.79NaF 14.78Bi(OH)3 12.80Fe(H2PO2)3 12.42Na2CrO4 11.13NiCO3 6.36Pb(NO3)2 6.08Zr(OH)40.654H2O 5.11NaNO3 4.93Na2SO4 3.55

3560 P. Hrma et al. / Journal of Non-Crystalline Solids 358 (2012) 35593562the condensed phase and the gas phase, respectively. The mass uxes,jb and jg, respectively, are jb=bvb (the minus sign in is usedbecause the condensed phase moves in the negative direction) andjg=gvg. The energy balance for the condensed phase is:

bcbdTbdt

bvbcbdTbdx

dqbdx

H s 3

where T is the temperature, c is the heat capacity, q is the heat ux, His the internal heat source, and s is the heat transfer between phases.The heat ux is subjected to Fourier's law, qb Eff dTdx, where the ef-fective value of heat conductivity, Eff, involves both conductive andradiative modes of heat transfer in the feed.

The boundary conditions are given in the term of both uxes andtemperatures, i.e., qb(0)=QB, qb(h)=QT, T(0)=TB, and T(h)=TT,where h is the cold cap thickness, TB and TT are the bottom and topcold-cap temperatures, respectively, and QB and QT are the heat uxesto cold-cap bottom and from cold-cap top, respectively.

To solve the energy balance equation, we used, for the sake of sim-plicity and comprehensibility, the nite difference method. For nu-merical simulations, experimental data were used together withconstitutive equations that were taken from the literature and modi-ed for our problem as described in Section 3. All algorithms werecoded in Mathworks MATLAB 7.

3. Material properties

The melter feed composition is shown in Table 1.Fig. 2 shows the degree of conversion, g, calculated as g(T)

=(mmF)/(mMmF), where m is the temperature-dependent feedmass, mF is the melter-feed mass, and mM is the glass mass; the sub-script g indicates that the degree of conversion is based on the release

Fig. 1. Cold-cap structure.of gas from the feed. Because the g(T) function changed little withthe rate of heating, we used the degree of conversion obtained bythermogravimetric analysis at the heating rate 15 K min1.

Following Schill [11], the heat capacity of the gas phase (cg) wasapproximated by that of carbon dioxide: cg=1003+0.21T1.93107T2 (T373 K), where cg is in J kg1 K1.

The melter feed density decreased as the temperature increased asa result of mass loss and the nearly constant volume of the sample atTb~700 C, i.e., b=b0m/mF. Once the sample was shrinking be-tween ~700800 C, the density increased to a maximum. Then,above 800 C, the density decreased as the bubbly melt turned tofoam, reaching a minimum. The density was estimated from the ex-pansion data reported in [13,14].

For the heat conductivity, we used the relationship reported bySchill [17] for a high-level-waste melter feed: Eff=0.06571+0.002114T (373 KbTb1000 K), where is in Wm1 K1. ForT>1000 K, we used a linear interpolation between Eff at 1000 Kthe bottom foam layer.For the calculations, the cold-cap bottom temperature, TB=1100 C,

was estimated as the temperature at which the motion of the con-densed phase can no longer be considered one-dimensional and the cir-cular convection of themelt takes over. The temperature at the interfaceand Eff(1100 C)=4.56 Wm1 K1, the value for molten glass(Schill [17]). To the best of our knowledge, the heat conductivity ofthe foam layer at the cold cap bottom has not been determined exper-imentally. The heat conductivity of the foam layer was estimated tobe close to half of the heat conductivity of bubble-free melt.

4. Results

As Fig. 1 illustrates, a layer of boiling slurry rests on the top of the

NaNO2 3.37KNO3 3.04Zn(NO3)24H2O 2.67Na2C2O43H2O 1.76Mg(OH)2 1.69Total 1352.11Fig. 2. Degree of conversion with respect to gas phase versus temperature and heatingrate.

Fig. 5. Velocity prole within the cold cap.

3561P. Hrma et al. / Journal of Non-Crystalline Solids 358 (2012) 35593562The major part of the total heat ux to convert the slurry to mol-ten glass at 1100 C comes from the cold-cap bottom (QB), of whicha part enters the boiling slurry (QT), while the remaining heat owsto boiling slurry from the plenum space (QU). We have computedthe temperature distributions within the cold cap as a function oftwo parameters: QF, the total heat ux to convert the slurry to1100 C melt, and the fractional heat ux from above, QU/QS, whereQS is the heat ux to turn the slurry into dry feed. Fig. 3 comparesthe temperature distributions within the cold cap for three values ofQU, while the total heat ux supplied to the slurry layer is constant.The proles exhibit three intervals with distinct temperature gradi-ents. Between 250 and 350 C, the temperature gradient is affectedby endothermic reactions. As Fig. 4 shows, most of the heat for melt-ing is consumed in the upper part of the cold cap, 0.5 to 4 cm belowthe top surface. Within 350 and 800 C, the presence of moltenphase results in an increased heat conductivity and a relatively mildtemperature gradient as compared to the temperature interval of800 to 1100 C, where a steeper temperature gradient is caused bythe low Eff of the foam layer.

Fig. 5 shows the condensed phase velocity versus the vertical po-sition within the cold cap, x, for QU/QS=0.8. The higher velocity ofthe condensed phase in the foam layer results from the high porosity,while the lowest velocity occurs where the porosity is minimum; ve-locity changes little with x in the upper part of the cold cap.

Fig. 6 displays the thickness of the cold cap as a function of QU/QSfor three values of QF, i.e., different rates of melting, showing that ahigher melting rate makes the cold cap thinner.

5. Discussion

Understanding the dynamics of the foam layer at the bottom ofthe cold cap and the heat transfer through it appears crucial for a re-

Fig. 3. Cold-cap temperature prole for three heat uxes from plenum space.liable prediction of the rate of melting as a function of the melter-feed

Fig. 4. Effective heat capacity distributions within the cold cap.makeup and melter operation parameters. Foam continuously arisesfrom batch reactions and redox reactions within molten glass. Be-cause foam has low heat conductivity, the foam layer hinders theheat transfer to the cold cap and leads to a lower melting rate [15].However, because the rate of melting affects the cold-cap thickness,thus affecting the temperature gradient (i.e., the heating rate thatthe feed experiences), the resulting shifts in the reaction peaks affectthe rate of foaming [19]. Hence, a self-regulating mechanism existsthat balances foaming, cold-cap thickness, and the heat uxes fromthe top and bottom of the cold cap. Accordingly, batch foaming hasa decisive inuence on the rate of melting.

In the temperature interval of 700800 C at which the density isminimum, a continuous layer of high-viscosity melt presents a barrierthrough which neither bubbles can ascend nor low-viscosity moltensalts can drain. The foam continuously collapses vial bubble coales-cence into cavities that are presumed to release the gas through thefree melt surface in the vent holes and around the cold-cap edges.This process is clearly at least 2-dimensional.

An advanced cold-cap model, to be incorporated into the overallmelter model, should describe at least two 2D phenomena, the hori-zontal movement of bubbles and cavities toward cold cap edges anda horizontal ow of migrating molten salts. Horizontal migration ofthe salt melt into the vent holes and around the cold-cap edges candisrupt the steady state, leading to cold-cap freezing because of de-pletion of uxes. Restoring the process requires melter idling, causinga loss of efciency. The 2D model will determine the conditions for anuninterrupted steady state.

Apart from foam dynamics and molten salt migration, the futuremodel will also address the fate of quartz particles (their dissolutionFig. 6. Cold-cap thickness versus upper and total heat ux; numbers represent QF inkWm2.

and clustering [16]), the fractions and sizes of solid particles (spineland quartz residues) leaving the cold cap into the melt pool, andthe thermal analysis-based reaction kinetics for gas evolution and en-thalpy changes.

In a commercial electric glass melter, the top surface of the coldcap is dry, and the top-surface boundary condition is not limited to100 C as in a slurry-fed waste glass melter. Because the melting pro-cesses in both types of cold caps are similar in other aspects, the au-thors expect that the cold-cap model presented in this paper can beadapted for commercial glass melting.

6. Conclusions

1. At a constant total heat ux to the cold cap, the cold-cap thicknessincreases as the fraction of heat ux from above increases.

2. At a constant fractional heat ux from above, the cold-cap thick-ness decreases as the total heat ux to the cold cap increases.

3. As the cold-cap thickness changes, the reaction zone shifts, affect-ing the rate of foaming at the cold-cap bottom.

4. An advanced 2D cold-cap model should include behaviors of themain liquid and solid phases within the cold cap, and the foamlayer under the cold cap. The model will be incorporated into thecomplete model of the melter.

Acknowledgements

The authors are grateful to the U.S. Department of Energy FederalProject Ofce Engineering Division for the Hanford TankWaste Treat-ment and Immobilization Plant for nancial support. Richard Pokornyis also pleased to acknowledge support from Czech Grant Agency

calorimetry data. Pacic Northwest National Laboratory is operatedfor the U.S. Department of Energy by Battelle under Contract DE-AC05-76RL01830. In its nal stages, this research was supported byWCU (World Class University) program through the National ResearchFoundation of Korea funded by the Ministry of Education, Science andTechnology (R31-30005).

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Nuclear waste vitrification efficiency: Cold cap reactions1. Introduction2. Theory3. Material properties4. Results5. Discussion6. ConclusionsAcknowledgementsReferences