Seeds

ICG – EFONGA Spring School Montpellier 4-5 May 2009 1

Chemical & Physical Processes

in Glass Melting

Quality of glass

melting process

Ruud Beerkens

TNO Glass Group

Eindhoven, The Netherlands

Glass Service

Buchmayer


Contents

• Overview of processes essential for glass melting

• Tools of analysis of industrial glass melting

• Melting-in of Raw materials

• Kinetics of Sand Dissolution

• Removal of Gas bubbles & Dissolved gases

• Evaporation processes

• Homogenisation


foaming

water infiltration

evaporation:

NaOH, KOH,

HBO2,

PbO, NaCl,

HF, SO2 etc.

refractory corrosion

refractory corrosion

fining and redox

deposition and

dust formation

emissions: Na2SO4, Na2B4O7 and PbO dust

HCl, HF, SO2, SO3 , SeO2, HBO2, H3BO3 etc.

NOx and

heat transfer

flue gas

chemistry

1. Overview

Chemistry & Physics

of Glass

Melting Processes

melting kinetics


Raw materials mixed

Furnace

Or

Crucible

Homogeneous molten glass

Melting-in of batch – chemical reactions/endothermic effects

Sand* grain dissolution

Removal of bubbles/gases

Dissolution of seed (fine bubbles) residue

Homogenisation

- Diffusion (slow)

- Velocity gradients – stretching of inhomogeneities

Side-effects

• Evaporation from melt

• Refractory corrosion

• Combustion & heating

• Emissions from evaporation & combustion


Parameters for processes in melting

Important parameters:

• Heat transfer �Temperature � viscosity, surface tension,

chemical activity, reaction kinetics, gas evolution..

• Flow characteristics – convection in melt, stirring

• Residence time: time-temperature history

• Exposure of melt to (reactive) atmosphere and refractory

lining

How to assess:

Temperatures and flows in glass melt ?


• Discretize total volume of furnace in small volume cells (> 1 million)

cells LxBxH: (1-10) x (1-10) x (1-10) cm

– GRID / mesh

• Input data process: pull, batch composition, fuel distribution, air

number

• Input furnace:

– Design

– Wall construction, including insulation

• Input glass: viscosity, heat conductivity, density, thermal

expansion, electric conductivity, solubility sand, solubility gases,…

• For each volume cell in tank & combustion chamber

– Energy conservation

– Momentum conservation

– Mass conservation (continuity) for melt and each chemical element

– Respect electro-neutrality

2. Tools: CFD Simulation Models Glass Furnaces


CFD Simulation Models

example: local conservation of energy

Energy equation, conservation law for

energy in each volume element

increase sensible convection heat conduction local

heat of heat boosting or

cooling

( ) ( ) ( ) qT Tct

Tc+λ+ρ−=

∂

ρ∂ grad divv div p

p r


Results of CFD simulation models

• Temperatures at all possible positions

– Combustion space

– Glass melt

– Refractory

• Glass melt and Combustion gas velocities

• Trajectories (particle tracing) in tank

– Thousands of different paths can be identified from charging end to throat or

spout

• Redox and dissolved gases

– Redox state of melt at each position (pO2 or Fe2+/Fe3+)

• Residence time distribution

– Minimum residence time is of importance for melting process

• Glass melt quality indices per trajectory

– Trajectory with minimum melting or fining index is decisive for glass


Application of CFD models

• For furnace design (lowest energy, highest glass quality)

– Optimum depth of tank

– Position bubblers or dam or burners

– Size and design of throat

– Design combustion chamber (LowNOx, less evaporation)

• For optimum process settings

– Optimum fuel-boosting ratio

– Temperature profile (energy distribution)

– Bubbling rate

– Creation of distinct spring zone to avoid short cut

• Time-transient (time dependent) for colour or pull change

– Optimize colour change process: reduce transition time

• Time-transient for process control (rMPC)

– Sensors give model continuous new information: model tracking

– Model continuously gives recommendation for input parameter changes to

follow optimum process path (low energy, high glass quality, constant T)


Geometry & Grid

for computational fluid dynamics (CFD)

analysis of glass furnace

Deep Refiner

Port Necks

Batch Boosting electrodes

tankBurner port

crown


Example result CFD computation

Temperature contours


NOxEnd-port fired furnace horizontal cross section at level of burners

Base case

4 inch higher crown


NOxEnd-port fired furnace vertical cross section at 25 % from furnace length from port

Base case

4 inch

higher crown

NOx scaling in mole fraction

Lower NOx-concentration in exit

Burner port Exit port (flue gas)


Glass melt path with lowest ‘temperature‘ index

Temperature course of glass (melt) in typical float glass furnace with

minium temperature index

0

200

400

600

800

1000

1200

1400

1600

1800

0 2 4 6 8 10 12 14

Time in hours

Temperature in oC

dtT

indexeTemperaturcanal

doghouse

ipath ∫ η=


Sensors (short overview)• Combustion gases

• gas composition: • laser optics

• electrochemical sensors (oxygen)

• Glass melt

• chemical composition

• LIBS = laser induced breakdown spectroscopy

• redox / colour parameters• Potentiometry

• Voltammetry

t/c

Type B

(mV)

Alumina rod

Pt measuring

electrode

Ni/NiO-

reference mix

Zirconia cell

emf

(mV)

Pt / Ni-NiO // ZrO2 // pO2 (glass) / Pt

O)(ref.Ni/NipO

(glass)pOln

nF

RTEMF

2

2⋅=


3. Melting-in of batch

• In glass furnaces (industrial)

– Kinetics determined by heat transfer through

batch blanket

• In small crucibles:

– Kinetics determined by contact between

different batch constituents and temperature


Day hopper

Spring zone& primary fining

Return flow from working end

Batch melting• 40-60 minutes• 80-90 % of net heat flux

Zone for sand grain dissolution

Hot spot &evaporation

Return flowfor batch heating

Generation blisters from refractory

RefiningBubble absorption

Conditioning of meltThermal homogeneity


Scheme of melting process of batch blanket, charging velocity vg(m/s)

heat transfer

gas release

combustion space

reaction zone

thick-

ness normal batch

temperature

profile

reaction zone

glass melt layer

figure 1b

glassmelt

flowheat

transferred

figure 1c

glass

levelZipfel


Detailed re-presentation of the batch melting process

in glass furnace

batch

b. top of batch blanketc. bottom side of batch

blanket

glass melt 1400 oC

meltingreactionsmelting

reactions

Dissolutionsand grains sand

grains

carbonates(soda/lime)

dissolution sandgrains

sandgrains

gas

gas

melts

Layerglassmelt

loose batch

1500 oC


Example:

Melting reactions of soda lime (dolomite) silica batch

• De-hydratation (100 oC physical bonded water & > 100 oC hydrates) – Important for energy consumption: water evaporation is energy intensive

• Solid state reactions, formation of silicates, e.g.:

Carbonate route < 900 oC at fast heating rate

Na2CO3 + CaCO3 � Na2Ca(CO3)2 (melts at ±820 oC) (550-850 oC)

Na2Ca(CO3)2 +2SiO2 � Na2SiO3/CaSiO3 + 2CO2↑ reaction enhances > 820 oC

Na2CO3 + 2SiO2 � Na2SiO3 + CO2↑ (790-850 oC)

• Formation of primary melt phases (alkali rich carbonates), e.g.:

Tm Na2CO3 = 850 oC

Tm Na2Ca(CO3)2 = 820 oC

Tm K2CO3 = 890 oC

High amount of

heat required


• Decomposition reactions of (Ca- and Mg-) carbonates:

• Dissolution reactions of SiO2, e.g. (coarse limestone)

Melting reactions of soda lime silica batchlimited kinetics may shift some reactions to higher temperatures

heat required

CaCO3 + heat � CaO + CO2↑ (910 oC at pressure 1 bar)

MgCO3 + heat � MgO + CO2↑ (540 oC at pressure of 1 bar)

MgCO3·CaCO3 + heat � MgO + CaCO3 + CO2↑ (650 oC, 1 bar)

MgO still present up to 1150 oC.

Reactive calcination: Na2CO3 + 2SiO2 � Na2O·2SiO2 + CO2↑ T > 790 oC

� forms with SiO2 an eutectic melt

Or at further heating � fast Na2O·SiO2 formation (850 oC) –

limestone decomposes and:

2CaO + (SiO2 + Na2O·2SiO2 )eutectic melt � Na2O·2CaO·3SiO2 (> 900 oC)

Silicate route: Silicate melt + SiO2 � silica enriched melt T > 1000-1100 oC

Eutectic melt phases are formed above ±800-840 oC


Phase diagram for the system Na2O – SiO2 showing

eutectic sodium silicate melt phases

100 % SiO2


Scheme of melting reactions of soda lime glass batch

1080 oC: T

s Na

2SiO

3

910 oC : CaCO

3 �� CaO + CO

2 (gas)

850 oC : T

s Na

2CO

3

820 oC : T

s Na

2Ca(CO

3)2

790 oC : T

eut Na

2O.2SiO

2 + SiO

2

740 oC : T

eut Na

2Ca(CO

3)2 + Na

2CO

3

650 oC : MgCO

3.CaCO

3 �� MgO+CaCO

3+CO

2 (gas)

540 oC : MgCO

3 -> MgO + CO

2 (gas)

0 200 400 600 800 1000 1200 1400

� temperature in oC

volatilisation of water

solid state reactions

decomposition

carbonates

primary melts

Dissolution of SiO2, CaO,

MgO, Al2O3 e.d. in melt phases


-2

0

2

4

6

8

10

600 650 700 750 800 850 900 950 1000

Temperature [°C]

Chemical energy consumption rate [kJ·kgbatch-1·K

-1]

Overall chemical energy demand

MgCO3·CaCO3(s) -> MgO(s) + CO2(g) + CaCO3(s)

CaCO3(s) -> CaO(s) + CO2(g)

Na2CO3(s) + SiO2(q) -> Na2O·SiO2(s) + CO2(g)

Na2CO3(s) -> Na2CO3(l)

Na2CO3(l) + SiO2(q) -> Na2O·SiO2(s) + CO2(g)

Na2O·SiO2(s) + SiO2(q) -> NS(l)

CaO(s) + melt

Chemical enthalpy of batch reactions for float glass

from soda-sand-dolomite and limestone (positive: endothermic effects)


4. Dissolution of ‘refractory’ type raw material

in silicate melt

example: sand grains


Glass meltSand grain

100

CSiO2

Ce (T)

Ce(T) = saturation level SiO2 in melt

Cb = bulk SiO2 level in melt

(depends on amount

dissolved sand)

Cb

Diffusion of SiO2 in melt

Moving boundary


Dissolving material

One-dimensional dissolution in multi-component liquid

dissolution

Multi-component liquid

Dissolution front

a x

Mass fraction SiO2 in saturated melt: we

w

ax

w

∂∂

we

)1(2

eeA

a

e

SiOwV

x

w

Ddt

da

⋅⋅−

∂∂

⋅⋅−=⋅

ρρρρ

ρρρρρρρρ

w is mass fraction SiO2 in melt


Mathematical description(Ready & Cooper 1966)

- Spherical symmetry – diffusion in 3 dimensions

- Assuming constant diffusion coefficient in melt

- Ideal solution, partial molar volume of SiO2 in melt is constant

- Convection (term u) due to change of partial molar volume of SiO2 in sand versus in melt

- Moving boundary: dissolving sand is partly staying in volume it came from

J = mass flux of SiO2

D = diffusion coefficient of SiO2 in silicate melt (m2/s)

r = radial co-ordinate (distance from sand grain centre) (m)

R = radius sand grain (m)

t = time (s)

ρ = density of melt (kg/m3)

C = local SiO2 mass concentration (kg/m3)

u = mass average velocity radial direction due to expansion by dissolution

(change in molar volume) (m/s)

Mass flux (j) of dissolved SiO2


Solution dissolution sand grain

without forced convection

a = actual grain size radius (m)

VA = partial specific volume of SiO2 in molten glass (m3/kg)

Cs = density of sand grain (kg/m3)

Ca = mass concentration SiO2 in saturated melt (kg/m3)

Effect of moving boundary


Sand grain dissolution with convection by

glass melt velocity gradients & density

differences

h = mass transfer coefficient SiO2 into melt (m/s)

we = mass fraction SiO2 in saturated melt (depends on T, and glass) (kg/m3)

ws = mass fraction SiO2 in bulk melt (depends on dissolved sand)) (kg/m3)

VA = partial specific volume of SiO2 in molten glass (m3/kg)

a = actual radius sand grain (m)

t = time (s)

ρs = density of melt (kg/m3)

ρSiO2 = density sand grain (kg/m3)

D = diffusion coefficient of SiO2 in silicate melt (m2/s)

( ) )1/(2 eeAsseeSiO wVwwhdt

daρρρρρρρρρρρρρρρρ ⋅⋅−−⋅−=⋅


Mass transfer coefficient

h = mass transfer coefficient (m/s)

D = diffusion coefficient of SiO2 in the molten glass, based on concentration

profiles given in mass fraction (D in m2/s)

R = grain radius (m),

t = time (s),

Sh = Sherwood number for mass transfer from spherical grain,

≈ 2 + 0.89 {Re · Sc + (Gr · Sc)3/4}1/3 *

= 2 (no convection)

= f (R2/3 , D-1/3, (grad v)1/3) (convection flow of the glass melt)

= f (R3/4 , h-1/4 , D-1/4)

(free convection of surrounding melt relative to the sand grain: v = flow velocity of the

melt relative to the sand grain (m/s), η = viscosity (Pa.s)

⋅⋅⋅

+⋅⋅=

tDShR

DSh

h

2

11

2ππππ


0

5000

10000

15000

20000

25000

30000

1350 1450 1550 1650 1750 1850

T in K

Dissoltion tim

e in s

no convection

v-gradient

0.001 s-1

v-gradient

0.025 s-1

Dissolution time required for complete dissolution of sand grains in

almost static and stirred soda-lime silica glass melts (forced convection

with velocity gradient grad v) at different temperatures. Initial size Ao=100 mm.


Dissolution of sand and alumina grains in static and convective soda-

lime-silica glass melt at 1700 K, moving boundary effect taken into

account (not on concentration profiles)

0.00E+00

2.00E-05

4.00E-05

6.00E-05

8.00E-05

1.00E-04

1.20E-04

0 5000 10000 15000 20000 25000 30000 35000

time [s]

radius in m

alumina,

grad v = 0

sand,

grad v=0sand,

grad v=0.001 s-1

alumina,

grad v=0.001 s-1

alumina,

grad v=0.01 s-1

sand,

grad v=0.01 s-1

sand,

steady state

grad v=0.001 s-1

sand,

grad v= 0 steady state


5. Fining Processes


Seeds after batch melting

Fine sand

Seeds after batch melting

Coarse sand


Glass just after batch melting- sample thickness ± 5 mm

10 mm


0 to 8 mm


Bubbles & Seeds just after melting

• Many small seeds and bubbles (Blisters) in glass melt

(Mulfinger 1976 GTB)

– More than 100.000 per kg glass melt

– Most bubble diameters: 0.05 -0.4 mm

• In most glass melts (using carbonates):

– bubbles in batch melting area: contain often mainly CO2

• Large concentrations dissolved CO2 in melt

• During sand grain dissolution in melt: generation

of fine CO2 seeds (Gispen)

heat transfer

gas release

combustion space

reaction zone

thick-

ness normal batch

temperature

profile

reaction zone

glass melt layer

figure 1b

glassmelt

flow heat

transferred

figure 1c

glass

level

from Glass Service


Fining

Objective of Fining:

Removal of bubbles and dissolved gases from the glass melt

Rising velocity of bubble:

ρ = Density of the glass melt [kg/m3]

η = Viscosity of the melt [Pa·s]

R = Bubble radius [m]

g = Acceleration of gravity [m/s2]

c = Factor (e.g. Stokes c = 2/9)

η

Rgρcv

2

ascension

⋅⋅⋅=


Fining

Time to reach glass surface (1 meter)

0

50

100

150

200

250

0 100 200 300 400 500

Bubble diameter [µm]

Time to reach glass level at 1 meter [h]

1350 OC

1400 OC

1450 OC

1500 OC


II. start of fining:

gases diffuse into

bubble

I. static bubble

Reaction in melt: release of fining gases

Pgases melt > pt (pt is pressure in bubble)

III. Fining gases and

other dissolved

gases diffuse

strongly into bubble


Two fining steps

• First step: primary fining

– High temperatures

– Bubble agglomeration and bubble size growth

– Dissolved gases diffuse from melt in to bubbles (like

bubbles in soda drinks)

– Ascension to glass melt surface

• Second step: Secondary fining/Refining (secondary fining)

– Dissolution of (small) remaining bubbles

• Only effective if bubble contains gases (CO2, O2, SO2+O2)

that dissolve in cooling melts

• Glass melt should be lean in dissolved gases


Mechanism sulfate primary fining

Fining process in glass melt

pSO2 · pO21/2 ·aNa2O

aNa2SO4

K =

Increasing temperatures lead to increasing K-values →

extra oxygen gas & SO2 gas release:

- oxygen & SO2 molecules diffuse into growing bubbles

- bubble ascension increases (vascension~R2)

- sulfate retention decreases

pSO2· pO21/2

K’ =[SO3]


Fining reaction: T > TFining onset

Na2SO4 ⇔ Na2O + SO2 (gas) +1/2 O2 (gas)

Fining (primary)

– Fining agents added to the batch to enhance the

rising velocity of bubbles

– Often used fining agent: Sodium sulphate

Dilution of N2 & CO2 in bubble by fining gases

SO2CO2

O2

N2

Stripping of CO2

and N2 from melt

Cm CO2

Cm N2

][SO

pOpSOK

3

22'⋅

=


Multicomponent diffusion of gases in bubbles

Shi = 1+ (1+ 2·v·R/Di )1/3

[ ] ( )

⋅⋅⋅

+⋅−⋅⋅⋅⋅Σ⋅=⋅⋅

tDShR

CCTRp

DShRTRpR

dt

d

ii

iisig

t

iigt

2

11

2 4)3/()4( i

23

ππππ

ππππππππ


Fining/Refining: degassing & removal of bubbles

• Mostly applied fining agents in glass industry: Na2SO4 & Sb2O5

– Na2SO4 (m) → SO2 (g) + 0.5 O2 (g) + Na2O (m)

– Sb2O5 (m) → Sb2O3 (m) + O2 (g)

• Na2SO4 added in concentrations 0.1 – 1 wt. % to batches of:

– Soda lime glass for container, float and tableware

– E-borosilicate glass for fibres

• Na2SO4 partly decomposes during batch melting & releasing SO2 in

early melting stages

• Dissociation temperature of Na2SO4 in melt:

– Between 1350 – 1480 ºC, depending on redox state

– Between 1100-1350 oC (reduced batches) Na2SO4+Na2S

reactions forming SO2 and or S2 gas.


0.0

0.1

0.2

0.3

0.4

0.5

0.6

-8 -7 -6 -5 -4 -3 -2 -1

Log pO2 in the melt at 1400°C (bar)

Sulfur retention (wt.%SO

3) Sulfur only in

form of S2-

Sulfur in

form of SO42-, S2-

(probably also SO32-?)

Sulfur only in

form of SO42-

-30 -20 -10 0 +10 +20

redox number

Fe2+/Fetotal 80 70 60 40 25 15 %

1400 oC

1500 oC


30 mm

Synthetic gas

Mass

Spectrometer


High temperature test facility



1. Primary fining

– Removal of bubbles by rising of bubbles to melt

surface

– Bubble growth under influence of fining agents

– Stripping of dissolved gases by growing of gas bubbles

(dilution)

Fining


Enhanced Sulfate Fining by

Dissolved Water in Melt

SO2

H2O

O2 In oxygen-fired glass furnace:

peH2O = 0.25-0.40 bar

Fining only if:

peSO2 + peO2 > 0.70 - 0.75 bar

In air-fired furnace:

peH2O = 0.10-0.15 bar

Fining only if :

peSO2 + peO2 > 0.9 barSO2

H2OO2

CO2

SO2

H2ON2

O2

SO2

CO2

Oxy-case

Air case

O2

N2


Gas evolution during sulfate fining of soda lime glass

melt - effect of water vapor level -

0

10

20

30

40

50

60

1300 1400 1500 1600

Temperature in oC

Volume of gas in

m3/batch

0 bar

0.20 bar

0.60 bar

water vapor pressure

Evolution of fining gas: water lean & rich melts


Stripping of dissolved gases from melt


Pressure in melt before and during fining & cooling

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1200 1300 1400 1500 1600

Temperature in oC

Total internal pressure in melt

bar

[S]initial= 0.3 mass% SO3 300 mgr water/kg [Fe2+]/ [Fetotal] = 20 %


1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1250 1350 1450 1550

Temperature in oC

Partial pressure in float glass m

elt

in bar

O2

SO2

H2O

N2

CO2

Partial pressure in float glass melt during heating

[S]initial = 0.3 mass% SO3 300 mgr water/kg [Fe2+]/ [Fetotal] = 20 %


CO2

O2fining gas

Modeling dissolved gas distribution in glass melt tank

mol/m3

mol/m3



2. Secondary fining (refining)

– Re-absorption of residual gases during controlled cooling

• Chemical solubility SO2 and O2 increases with

decreasing temperature: gases will be re-absorbed

during cooling.

• Physical solubility of dissolved gases increases slightly

with decreasing temperature: these gases will also be re-

absorbed during cooling

Refining


Fining at low pressure

- Same amount of gas needs large volume

- Low partial pressures in bubble will stimulate gas diffusion

from melt into bubble


6. Evaporation processes


Multi-component glasses

• Different oxides

• Oxides in glass with high chemical activity or vapour

pressure:

– React at glass melt surface with combustion gases

– Evaporate from glass melt surface

– Show depletion at surface layer

INCONGRUENT EVAPORATION


Evaporation mechanisms

• Direct evaporation of volatile glass components from the surface of the melt,

e.g. volatilization of PbO from lead crystal melts;

• Evaporation of components by reactions in the melt itself, forming volatile

compounds; generally such volatile compounds exhibit high activity coefficients

and weak bonding with other glass melt species.

– An example: formation of alkali borates in alkali borosilicate melts,

subsequently evaporation of alkali meta-borates/tetra-borates takes place,

Na2O(melt) + B2O3 (melt) ⇔ 2NaBO2 (melt) ⇒ 2 NaBO2 (vapor)

• Evaporation by reactions of certain glass melt components with gas

species at the surface of the melt.

The evaporation rate & vapor pressure depends on the composition of

the gas atmosphere above the melt.

B2O3 (glass melt) + H2O ⇒ 2HBO2 (vapor)

Na2O (glass melt) + H2O (gas) ⇒ 2NaOH (vapor)

Na2O(glass melt) + CO (gas) ⇒ 2Na (vapor) + CO2


Kinetics of evaporation

The volatilization rate is often determined by:

• mass transport of the relevant species from the

melt interior (bulk) to the surface;

• the vapor pressures of the volatile components at the

surface of the melt, dependent on the glass composition,

temperature and gas atmosphere;

• the mass transfer of evaporated species from the surface

of the melt into the main gas stream above the melt.


Reactive evaporation

For reactive evaporation of a component j in the melt reacting with

a gas k and forming gaseous species i with saturation pressure

pi*, according to reaction:

n·j (melt) + m·k (gas) � q·i (gas)

Reaction equilibrium: pi*q = K · aj

n · pkm

The values of K (equilibrium constant, assuming chemical

equilibrium at the glass melt surface) and aj (activity of component j

in the molten glass at the surface) can be determined

experimentally or by thermodynamic modeling


Static melt and static atmosphere above the

melt (interface x = 0)Diffusion in melt of reacting glass melt component j:

dCj/dt = Dm,j·δCj2/δx2

Dm,j is the inter-diffusion coefficient of the volatile component j in the melt.

at t = 0 -∞ < x < 0 Cj = Cjbulk

at t > 0 x �−∞ Cj = Cjbulk

at t > 0 x = 0 Cj = Cjsurface(t)

For the vapor i in a static gas phase with partial vapor pressure pi,

the diffusion process in the gas phase can be described in a similar way:

δ(pi/RgT)/δt = Dg,i ·δ2(pi/RgT) /δx2

Dg,i is the diffusion coefficient of the vapor I in the gas phase.

at t = 0 0 < x < ∞ pi = pi,gasbulk

at t > 0 x �∞ pi = pigasbulk

at t > 0 x = 0 pi = pi*(t)

Time dependency: Cjsurface(t).


4954

4956

4958

4960

4962

4964

4966

4968

4970

0 0.01 0.02 0.03 0.04 0.05 0.06

distance from surface [mm]

Na2O concentration [mol.m-3]

5 sec.

50 sec.

250 sec.

DNa2O=3.3 10-11 m2.s -1

Calculated time dependent- Na2O concentration profiles in static melt

Situation: static conditions in semi-infinite gas phase with 0.55 bar vapor pressure

and semi-infinite soda-lime-silica melt

(13 wt% Na2O, 10 wt% CaO, 5 wt% MgO, 72 wt% SiO2).

Dg,NaOH = 2.7 10-4 m2·s-1 , Dm,Na2O = 3.3 10-11 m2·s-1


Evaporation in gas flow above molten glass

glass melt surfaceC j-profile

pb,i

p*i

Transport of component

j in the , Dm,j

main gas stream

velocity, vg

surface reaction:

n·j (melt)+ m·k (gas) ⇒ q·i (gas)

diffusion of gas i in

gas boundary layer, Dgi

Example:

Na2O (m) + H2O(g) ⇔ 2NaOH (g)

melt


Evaporation in gas flow

Average evaporation rate (over length Lg of gas flow above

melt ) of component i (formed by reaction of glass

compound j) into (turbulent) gas phase:

Qm,j =(ni/qi)·A·vg0.8·ρg

0.47·µgas-0.47·Dg

0.667·Lg-0.2· Rg

-1·T-1·B·Cj,x=0(t)

The proportionality parameter B depends on the furnace

atmosphere composition and the chemical activity of the

volatile component in the melt.

For NaOH-evaporation, the B value depends on the water

vapor pressure in the furnace atmosphere, B ∼ pH2O0.5


Mass transfer equations

Average evaporation rate (rate of loss of glass component j)

over length Lg from leading edge:

Qm,j = -Dm,j·(δCj/δx)x=0 = α·Cj,x=0(t)

α = (ni/qi) · A· vg0.8·ρg 0.47·µgas

-0.47·Dg0.667·Lg

-0.2· Rg-1·T-1· B

Turbulent flow of gas

v = velocity, g refers to gas phase, Rg is universal gas constant, T in K,

B ratio between vapour pressure i and surface concentration component j

A = between 0.03 and 0.04 for turbulent gas flow (Re > 300000 or for disturbed flows)


Solution in flowing gas and static melt

For kd defined as α/DmNa2O the solution for a single component j

Evaporating from a static melt in flowing gas phase

Assuming complete depletion at surface for t �∞

MQm.j is the total evaporation mass loss per unit surface area between

time 0 and τ

MQm.j = (Cj,0/kd)·{exp(kd2·DmNa2O·τ)·erfc[kd·(DmNa2O·τ)

0.5] -1

+ 2kd·(DmNa2O·τ/π)0.5}

Cj,x=0(t) = Cj,0· exp(kd2·DmNa2O·τ)·erfc[kd·(DmNa2O·τ)

0.5]

Cj,0 = bulk concentration compound j at t=0


3000

3500

4000

4500

5000

5500

0 0.5 1 1.5 2 2.5

distance from surface [mm]

Na2O concentration in

melt [mol.m

-3]

stagnant gas

Lg= 2 m, v= 2 m.s-1

Lg= 2 m, v = 5 m.s-1

Lg= 0.5 m, v= 2 m.s-1

Local concentration profile in soda-lime silica melt after 7200 seconds exposure time,

calculated for NaOH-evaporation from static melt in static or flowing gas phases,

(Lg= downstream distance from leading edge ).

Temperature = 1500 oC, pH2O = 0.55 bar. Dm,Na2O = 3.3 10-11 m2·s-1

Glass composition (mass %): SiO2 =72, Na2O =13, MgO = 5, CaO = 10


Change in Na2O-surface concentration soda-lime-silica melt at different

temperatures in flowing gas (5 ms-1), 1 meters downstream.

pH2O in gas = 0.55 bar & Na2O in glass = 13 mass%.

Dm,Na2O= 8 10-10 exp(-5655/T) in upper graph

parameter is temperature:

0

1000

2000

3000

4000

5000

6000

0 5000 10000 15000 20000 25000 30000

time [s]

Na2O-surface concentration

[mol.m

-3]

1723K

1773 K

1823 K

1873 K


Experimental – Set up to study

(reactive) evaporation from molten glass

Thermocouples

Gases IN:

N2, H2O,

O2

Porous

plate

Platinum

coating (30 cm)Platinum boat

Platinu

m gas

samplin

g probemelt

Platinum funnel


Mass transfer in gas phase during

transpiration – evaporation test

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

0 100 200 300 400Reynolds number

Re (-)

Water evaporation rate

QH2O (m

oles s

-1 m

-2)

Measurerments

CFD model

Empirical equation (2.19)

( )31

5.1

3

5.0

21 Re221

2Re

⋅⋅⋅

⋅+

+⋅⋅+= ScCSc

ScCCSh ddiontranspirat

d

DShh

igiontranspirat

ig

,

,

⋅=

Vessel with

liquid of melt

x = 0

( )bulkii

ig

ig ptpTR

hQ −⋅

⋅= *,

, )(

pi*(t) (e.g. p*NaOH or p*NaBO2)

can be derived from evaporation

(transpiration experiments)

From measured Qg,i and Sherwood

relations derived with model liquids


y = 0.9823x

R2 = 0.9283

1.E-09

1.E-08

1.E-07

1.E-06

1.E-09 1.E-08 1.E-07 1.E-06

Measured aNa2O (-)

Modeled a

Na2O (-)

SiO2:Na2O:CaO = 74:16:10 mol

Na2O.2SiO2

Na2O activity at glass melt surface determined by transpiration test

measuring p*NaOH: Na2O + H2O � 2 NaOH


Derivation chemical activity of volatile glass

component at surface of melt

K = exp(-∆G/RT) = p*NaOH2/aNa2O.pH2O

From thermodynamic tables:

∆G = GfNa2O+GfH2O- 2GfNaOH(g)

p*NaOH is measured from QNaOH and pH2O is

controlled � aNa2O (surface) can be determined

K is calculated by standard Gibbs free energy values of

products & reactants of reaction


Non static melt & non static gas phase

free convection by density gradients

Float glass melt with Na2O concentration differences

High Na2O

Low Na2O

Mid Na2O

Gas flow


6. Homogeneity of glassMicro-mixing: transfer from high to low chemical activity by diffusion

Macro-mixing: elongation of in-homogeneities exposed to velocity gradient in melt

Lo

Slow diffusion processes

C(x,t)t = 0

t = t1

t = t2

dC

dtDd C

dx= ⋅

2

2

C

C

-

L

2

o

m

o

2A= exp

. .π D t

Co

Cm (t)


Macro-mixingReduction of diffusion distance, Lo

y

velocity v + dv

velocity v

In the case, t dv/dy >> 1:

For macro-mixing in combination with diffusion (by approximation):

A = proportionality factor dependent on the shape of the cord

C

C

m

o

A= −.exp. . .( / )π 2 3 2

0

2

D t dv dy

L

LL

tdv

dy

=⋅

0


Macro versus only Micro mixing

• Small velocity gradients (> 0.01 m/s per m) enhance

homogenisation process with factor 20 to 100

• Velocity gradients by:

– Stirring

– Bubbling

– Temperature gradients � free convection


Thank you for your attention

What does a number tell us without the proper unit?

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