20031176325

Thermal and chemical behavior

of glass forming batches

Thermal and chemical behavior

of glass forming batches

PROEFSCHRIFT

ter verkrijging van de graad van doctoraan de Technische Universiteit Eindhoven,

op gezag van de Rector Magnicus, prof.dr. R.A. van Santen,voor een commissie aangewezen door het College voor Promoties

in het openbaar te verdedigen op woensdag 25 juni 2003 om 16.00 uur

door

Oscar Silvester Verheijen

geboren te Arnhem

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr.ir. R.G.C. Beerkensen

prof.dr.rer.nat. R. Conradt

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Verheijen, Oscar S.

Thermal and chemical behavior of glass forming batches / by Oscar S. Verheijen. -Eindhoven : Technische Universiteit Eindhoven, 2003.Proefschrift. - ISBN 90-386-2555-3NUR 913Trefwoorden: glasfabricage ; glasovens / glassmelten / warmteoverdracht /fysisch-chemische simulatie en modellering / reactiekinetiekSubject headings: glass technology ; glass furnaces / glass melting / heattransfer / physicochemical simulation and modeling / reaction kinetics

Printed by: Universiteitsdrukkerij Technische Universiteit Eindhoven.

Voor Roelie

Summary

The quality of the glass melt produced in a glass furnace is to a large extent determined bythe temperature-time trajectory of the freshly molten glass melt in the melting tank of the glassfurnace. The residence time and the temperature of the glass melt need to be sufcient forcomplete dissolution of raw materials, the release of dissolved gases from the glass melt andthe homogenization of the glass melt. To understand, control and optimize glass melt qualityand to improve glass furnace design, since the early 1980s, mathematical simulation models,describing melting and heat transfer in glass furnaces, have been used. These mathematicalsimulation models show that thickness, length, reactivity and thermal properties of glass form-ing batches have a large impact on the temperature distribution and glass melt ow patterns ina glass furnace. Therefore, detailed models describing the thermal and chemical behavior ofglass forming batches are required in mathematical simulation models.

The melting of glass forming batches is a complex process involving different reaction typessuch as dehydration reactions, crystalline inversions, solid-state reactions between different rawmaterial grains, decomposition reactions, melt forming reactions and dissolution processes. Theheating of the three-phase (reacting) glass forming batch is determined by both heat transferfrom the combustion space above and the glass melt underneath the glass batch and by heattransport in the interior of the glass batch. Because of the complexity of the melting and heat-ing process of glass batches and due to the lack of sensors and accurate analyzing techniquesto measure and monitor the progress of glass batch melting, no quantitative description of thesimultaneous heating and reactive melting of glass forming batches is known so far.

The objective of this study is to obtain a quantitative description of the heating process ofa glass forming batches and the conversion rate of the glass forming batch into the glass melt.The heat transfer in the interior of a glass forming batch can be described by:

(m cp,m Tm)t = ( g cp,g vg,z Tg) (effTm)+

q r,eff +(1 ) Hchemt . (1)

The left-hand-side term in the energy equation describes the local accumulation of heat. Therst, second and third right-hand-side terms in the energy equation indicate convective, con-ductive and radiative heat transfer, respectively. The fourth right-hand-side term in the energyequation indicates the energy consumption by chemical reactions. A detailed description of theenergy equation of the glass forming batch requires values for the temperature dependent glassforming batch properties. In this study, the temperature dependent chemical energy demandand the heat conductivity of glass forming batches are determined. To describe the conversionrate of a glass forming batch into a glass melt, the dissolution rate of sand grains, which is con-sidered as the most signicant criterion for the conversion of glass forming batches, has beenstudied.

vii

viii

The glass forming batch properties have been determined by the following steps:

1. The identication of the main batch reactions in a typical oat and TV-panel glass batchduring heating by phase analysis on quenched samples of heat-treated glass batch mix-tures.

2. The development of both experimental and mathematical techniques to determine quanti-tatively the kinetics of batch reactions and the heat penetration in typical industrial glassbatches.

3. The measurement and modelling of the temperature dependent chemical energy demand,the effective heat conductivity and reaction kinetic parameters.

For a oat glass batch, containing silica sand, soda ash and dolomite, it was demonstratedthat the thermal calcination of dolomite and limestone and the reactive calcination of soda ashoccur (almost) independently from each other. The reactive calcination of soda ash with sanddetermines the onset for batch-to-melt conversion of the oat glass batch, which starts at about1070 K. The formation of this primary formed melt phase enhances the dissolution of sand,(at least part of) MgO and intermediately formed binary and ternary silicates. In contrast tothe oat glass batch, the rate of the calcination reactions in TV-panel glass batches are depen-dent on other batch reactions such as the dissolution of intermediate formed crystalline silicates.

The chemical energy demand of a glass forming batch is mainly dependent on the energyrequired for calcination reactions in the glass batch. Combination of measured kinetics of calci-nation reactions in a oat glass batch with the enthalpies for these calcination reactions, resultsin an expression for the chemical energy required for complete calcination of the oat glassbatch as function of time, temperature and partial CO2-pressure in the oat glass batch. Todetermine the chemical energy demand of a oat glass batch, the kinetics of the thermal decom-position of dolomite and limestone and the kinetics of the reactive calcination of soda ash havebeen measured.

The heat transport in the interior of a glass batch is determined by a combination of threemodes of heat transfer. To study the contribution of these three modes, viz. convection, con-duction and radiation, an experimental set-up was developed to measure the temperatures in aglass batch as function of time and position. A numerical-experimental technique was used toderive heat conductivity data from the measured time- and position dependent temperatures.

With the numerical-experimental technique, the temperature dependent heat conductivity ofsolid particle mixtures of individual glass batch components and mixtures of glass batch com-ponents were estimated. It is shown that the heat ow through a glass batch in the solid-stateregime can be regarded as a combination of a serial and parallel connection of thermal resis-tances.

The prediction of the effective heat conductivity of mixtures of glass batch componentsbased on the glass batch composition and the porosity of the glass batch, has become pos-sible by regarding the glass batch as only a parallel connection of thermal resistances usingapparent values for the thermal heat conductivity of the glass batch components instead of theintrinsic values for the thermal heat conductivity. Using this approach, the difference in es-timated and predicted effective heat conductivity of a three-component mixture was less than

ix

0.01 W m1 K1 for a value of the heat conductivity between 0.15 en 0.40 W m1 K1.The effect of the presence of cullet in a glass batch on the net effective heat conductivity

of the glass batch in the temperature range up to 1200 K has been studied with the numerical-experimental technique. The calculation of the contribution of radiative heat transport on thenet effective heat conductivity of a glass batch shows that the expected increase in effective heatconductivity for a cullet containing glass batch is only observed (in case of a cullet particle sizebetween 4 and 8 mm) in case the cullet fraction exceeds 50 %.

The heating of glass forming batch oating on top of a glass melt is not only determinedby the heat penetration through the glass forming batch, but also by the heat transfer from thecombustion space above the glass forming batch to the top layer of the glass forming batch. Itis shown that the heat transfer towards the glass batch is mainly determined by radiative heattransfer and less by free and forced convective ow of hot gasses over the glass forming batch.

In general, the degree of dissolution of sand grains during heating of glass forming batchesis considered as the most signicant criterion for glass batch conversion. The mathematicalformulation of this mainly diffusion governed process requires a description of phenomena atmicro scale, such as the wetting of single sand grains by low viscous melt phases, in combina-tion with complex time-dependent boundary conditions. For the use of glass tank simulationmodels as tool in the glass industry, it is desired to have a simple expression describing the time-and temperature dependent dissolution of sand grains in glass batches instead of using complexdissolution models on micro scale. A prerequisite of the use of such a simple expression is thatthis expression should reect the practical observed dissolution behavior of sand grains as func-tion of e.g. particle size, heating rate and cullet fraction in the glass batch. It is a widespreadpractice to use simple approximate theoretical models to describe complex processes similar tothe dissolution of sand grains.

It is shown that the best available approximate model describing the kinetics of a threedimensional diffusion governed process, such as the dissolution of sand grains embedded in aliquid reactive phase during heating of glass forming batches, is the Ginstling-Brounstein model(GB-model). The applicability of the GB-model for describing the dissolution of sand grainsduring the heating of glass batches was studied by comparing the results of the GB-model withresults of a more detailed rst principle numerical model. Under certain conditions, it appearedto be possible to predict the dissolution of sand grains as function of time and temperature witha modied GB-model. This is the case for large sand grains dissolving in a thick glass meltlayer surrounding the sand grain. For very thin layers, the prediction of the modied GB-modelappears to be rather inaccurate.

The use of the GB-model for the description of the dissolution of sand grains during heatingof glass batches has experimentally been validated by analysis of the conversion rate of sandgrains in oat glass batches. The degree of sand grain conversion as function of time and tem-perature has been analyzed by quantitative phase analysis using X-ray diffraction. For the oatglass batch, the GB-model parameters have been determined as function of sand grain size,heating rate and cullet fraction.

Contents

1 Introduction 11.1 Description of the industrial glass melting process . . . . . . . . . . . . . . . . 11.2 The chemical behavior of glass forming batches . . . . . . . . . . . . . . . . . 41.3 Modelling the thermal and chemical behavior of glass forming batches . . . . . 61.4 Objectives and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Energy demand of glass forming batches 132.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Energy demand during heating of glass forming batches . . . . . . . . . . . . . 152.3 Description of the kinetics of batch reactions . . . . . . . . . . . . . . . . . . . 21

2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2 Kinetics of homogeneous reactions . . . . . . . . . . . . . . . . . . . 212.3.3 Kinetics of heterogeneous reactions . . . . . . . . . . . . . . . . . . . 232.3.4 Heterogeneous reaction kinetics with participation of melt phases . . . 262.3.5 Characteristics of calcination reactions . . . . . . . . . . . . . . . . . 29

2.4 Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.1 Thermogravimetric analysis . . . . . . . . . . . . . . . . . . . . . . . 312.4.2 Differential thermal analysis . . . . . . . . . . . . . . . . . . . . . . . 342.4.3 Phase analysis on partly reacted glass batches . . . . . . . . . . . . . . 34

2.5 Calcination of a oat glass batch . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.1 Calcination of dolomite . . . . . . . . . . . . . . . . . . . . . . . . . 362.5.2 Calcination of limestone . . . . . . . . . . . . . . . . . . . . . . . . . 422.5.3 Calcination of soda ash . . . . . . . . . . . . . . . . . . . . . . . . . . 492.5.4 Calcination of a mixture of silica sand, soda ash and limestone . . . . . 622.5.5 Reaction mechanism of a oat glass batch . . . . . . . . . . . . . . . . 642.5.6 Chemical energy demand of a oat glass batch . . . . . . . . . . . . . 67

2.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712.7 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3 Dissolution of sand grains during heating of glass forming batches 773.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.2 Mathematical and experimental descriptions of the sand grain dissolution process 803.3 Evaluation of the application of the Ginstling-Brounstein model . . . . . . . . 92

xi

xii Contents

3.3.1 Derivation of the Ginstling-Brounstein model . . . . . . . . . . . . . . 923.3.2 Modelling of the dissolution of a single sand grain in a sodium silicate

melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.3.3 Applicability of the Ginstling-Brounstein model . . . . . . . . . . . . 103

3.4 Quantitative phase analysis with X-ray diffraction . . . . . . . . . . . . . . . . 1093.5 Experimental determination of the apparent GB-model parameters . . . . . . . 116

3.5.1 Apparent GB-model parameters as function of the sand grain particle size1163.5.2 Apparent GB-model parameters as function of the cullet fraction . . . . 120


4 Heat conductivity of glass forming batches 1294.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1294.2 Phonon and photon conductivity . . . . . . . . . . . . . . . . . . . . . . . . . 132

4.2.1 Intrinsic phonon conduction of solid species . . . . . . . . . . . . . . . 1324.2.2 Intrinsic photon conduction of solid species . . . . . . . . . . . . . . . 1334.2.3 Phonon conduction of mixtures of solid species . . . . . . . . . . . . . 1354.2.4 Photon conduction in mixtures of solid species . . . . . . . . . . . . . 137

4.3 Estimation of the heat conductivity from heat penetration experiments . . . . . 1394.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1394.3.2 Parameter estimation without a-priori knowledge of = f (T ) . . . . . 1414.3.3 Parameter estimation with a-priori knowledge of = f (T ) . . . . . . . 143

4.4 Experimental set-up for measuring the heat penetration in solid particle mixtures 1564.5 Experimental determination of heat conductivity in a particle bed . . . . . . . . 160

4.5.1 Heat conductivity of a silica sand batch . . . . . . . . . . . . . . . . . 1614.5.2 Heat conductivity for multi-component mixtures . . . . . . . . . . . . 1644.5.3 Heat conductivity of particle beds containing cullet . . . . . . . . . . . 166


5 Complete simulation model for the heating of glass forming batches 1775.1 Energy conservation equation and temperature dependent glass batch properties 1775.2 Heat transfer towards a batch blanket . . . . . . . . . . . . . . . . . . . . . . . 180

5.2.1 Forced convective heat transfer . . . . . . . . . . . . . . . . . . . . . . 1805.2.2 Free convective heat transfer coefcient . . . . . . . . . . . . . . . . . 1835.2.3 Radiative heat transfer coefcient . . . . . . . . . . . . . . . . . . . . 184

5.3 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1865.4 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

A Calcination of a TV-panel glass batch 189A.1 Description of the calcination mechanism of a TV-panel glass forming batch . . 189A.2 Calcination of SrCO3- and BaCO3-grains . . . . . . . . . . . . . . . . . . . . 192A.3 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Contents xiii

B Estimation of model parameters by a least squares approach 197B.1 Description of the least squares approach for parameter estimation . . . . . . . 197B.2 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

C Derivation of 2nd order derivative of position dependent temperature 201

Samenvatting 203

Dankwoord 207

Curriculum Vitae 209

xiv Contents

Chapter 1

Introduction

1.1 Description of the industrial glass melting process

Nowadays, glass is mainly produced in continuously operating glass melting furnaces. In gen-eral, the glass melt ows through three segments of the furnace, i.e. the melting tank, theworking end and the feeder section. Figure 1.1 shows a schematic view of the melting tank andthe superstructure of an industrial glass furnace with a so-called throat.

Batch blanket

Throat

SuperstructureCombustion room

Spring zone

First circulation loop

Short cut flow

Doghouse

Bac

k w

all

Fron

t wal

l

Glass melt

Second circulation loop

Burner

Figure 1.1: Scheme of the melting tank and the superstructure of an industrial glass furnace.

In the doghouse of the melting tank, a glass forming batch1 is charged on top of the hot glassmelt and forms the so-called batch blanket or batch rolls (see gure 1.2) oating on top of theglass melt. The batch blanket is mainly heated by radiative heat transport from the ames andsuperstructure in the combustion chamber above the batch blanket and by conductive and ra-

1The glass forming batch is the mixture of raw material components, which forms a glass melt during heating.Further in this thesis, a glass forming batch is denoted as glass batch.

1

2 Chapter 1. Introduction

diative2 heat transport from the hot glass melt underneath the batch blanket. During heating ofthe glass batch, up to temperatures of even 1850 K, a complex process of chemical reactionstakes place transforming the solid raw material batch components into a liquid melt phase. Thefreshly formed glass melt, still containing undissolved raw materials and gas bubbles, enters thebulk glass melt underneath the batch blanket and follows the ow pattern(s) through the meltingtank towards the throat.

Figure 1.2: Batch rolls floating on top of the glass melt in an end-port fired container glass furnace

The ow pattern of the glass melt in the melting tank is the result of both forced and freeconvection driven ow. Forced convective ow is imposed on the glass melt by the pull rate3of the furnace. Due to an unequal fuel distribution over the burners above the glass melt andthe cooling effect of the relative cold batch blanket in the doghouse, temperature gradients arepresent at the glass melt surface. These temperature gradients at the surface of the glass meltlead to temperature gradients deeper in the glass melt by conductive, convective and radiativeheat transport. Free convective ow of the glass melt is caused by density gradients in the glassmelt as a consequence of the temperature gradients in the glass melt.

The combination of furnace geometry, pull rate and fuel distribution over the burners, mayin the ideal case cause two glass melt circulation loops in the melting tank. In the rst and oftenlargest circulation loop, the glass melt ows from the spring zone4 in the direction of the batchblanket and returns via the back wall (at the doghouse side) towards the throat. In the second

2The contribution of radiative heat transport to the overall heat transport from the hot glass melt to the batchblanket is dependent on the emissivity of the glass that is produced.

3Here, the pull rate of the furnace is defined as the amount of glass melt per period of time withdrawn from thefurnace for producing glass products.

4The position at the surface of the glass melt at which the glass melt flow splits up in a forward (towards thethroat) and backward (towards the charging end) flow. In general, the spring zone is positioned close to the hotspot of the glass melt, at which the position with the highest glass melt temperature is located.

1.1. Description of the industrial glass melting process 3

loop, the glass melt ows from the spring zone to the front wall and then downwards towardsthe throat. A part of the glass melt enters the throat and a part follows the second circulationloop towards the spring zone. In case this return ow of glass melt reaches the bottom of themelting tank, a shortcut ow of glass melt from the batch blanket directly into the throat isprevented. Now, the glass melt is forced to ow over the glass melt surface at which the highestglass melt temperatures exist.

Next to the melting of the raw materials, also homogenization of the freshly formed non-homogeneous melt phases is required, and ning and rening of the glass melt should take placein the melting tank. During the ning process, bubbles which initially mainly contain CO2 andair, and dissolved gases, are removed from the glass melt. At elevated temperatures, deliber-ately added ning agents such as sodium sulfate and antimony oxide decompose, producingSO2 and/or O2. As an example, the thermal decomposition of chemically dissolved SO24 inoxidized glass melts is given by

SO24 (m)T SO2(g)+ 12O2(g)+O

2(m). (1.1)

By the formation of the ning gases, the existing gas bubbles expand resulting in an en-hanced rise of the bubbles towards the surface of the glass melt. At the surface of the glassmelt, the bubbles release their gases into the combustion space or may form a foam layer oat-ing on top of the glass melt. During the take up of the ning gases in the gas bubbles, the initialbatch gases, which are enclosed in the bubbles, are diluted by the ning gases. The decrease inthe partial pressure of these gases in the bubbles is followed by diffusion of the dissolved gasesfrom the glass melt into the gas bubbles. In this way, dissolved gases are stripped from the glassmelt.

During the subsequent rening process, residual small gas bubbles are resorbed in the glassmelt due the shift of reaction 1.1 towards the left-side-side as a consequence of the temperaturedecrease in later stages of the process. Via the throat of the melting tank, the glass melt entersthe working end and subsequently the feeder section(s), in which the glass melt is slowly cooleddown to the temperature required for the forming process of the nal glass products.

In order to understand, control and optimize the glass melting process, since the early1980s, mathematical simulation models, based on computational uid dynamics, have beenused. These models describe the physical and chemical processes in industrial glass meltingfurnaces [1]. The basic equations of these simulation models are the conservation laws for mass,energy and momentum. With these equations glass melt temperatures and velocity vectors inindustrial glass furnaces are calculated. For describing typical features of the glass meltingprocess, additional models are added to the conservation laws such as a separate batch blanketmodel. The batch blanket model describes the thermal, chemical and rheological behavior ofglass batches oating on top of a glass melt.

In industrial glass furnaces, the batch blanket has a direct impact on both the energy trans-port in the glass furnace and on the ow patterns of the glass melt in the melting tank. A batchblanket can be regarded as a layer with a low heat conductivity and high heat reecting proper-ties at the upper surface. Due to these properties, the batch blanket acts as an insulation layerblocking direct heat input from the combustion room into the glass melt. Consequently, thedirect energy input from the combustion room in the glass melt itself is mainly limited to thearea of the glass melt, which is not covered with the batch blanket. The energy input per amountof produced glass for given combustion conditions, is dependent on the batch blanket size and


shape.The batch blanket has also an impact on the ow pattern of the glass melt in the melting

tank. The intensity of the rst circulation loop in the melting tank is determined by the tem-perature difference between the hot spot of the glass melt and the temperatures under the batchblanket. An increase of this temperature difference results in a more intense circulation loop,i.e. higher glass melt velocities, intensifying the bottom ow of glass melt from the back walltowards the throat. In case the intensity of the second circulation loop is not sufcient, a shortcut ow of glass melt over the bottom from the rst circulation loop directly into the throat ispossible.

Despite the large impact of the batch blanket on the temperatures and glass melt ow in glassfurnaces, the current batch blanket models still represent a too much simplied description ofthe physical and chemical processes occurring during heating glass batches. Improvement of theglass tank simulation models requires a thorough investigation of the melting and heat transferprocesses in the glass batch layers, which is the main subject of the current study.

1.2 The chemical behavior of glass forming batchesThe composition of a glass batch is dependent on the glass type to be produced. A glassbatch producing oat glass5 typically contains silica sand (SiO2), soda ash (Na2CO3), dolomite(MgCO3 CaCO3) and/or limestone (CaCO3), sodium sulfate (Na2SO4) as ning agent and areducing agent such as carbon or the steel slag calumite. As mentioned by Hrma [2], the melt-ing of glass batches is a complex process involving different reaction types such as dehydrationreactions, crystalline inversions, solid-state reactions between the different raw material grains,decomposition reactions, melt forming reactions and dissolution processes. Below, a short de-scription of the characteristics of these different reaction types is given.

Dehydration reactions: In the glass batch, water may be present as either molecular wa-ter and chemically bonded water (e.g. Na2CO3 H2O or water bonded in clays). Molec-ular water is added to the glass batch to lower the dusting of ne batch particles duringtransport towards the glass furnace and to prevent extensive carry-over of loose batchparticles in the glass furnace. Molecular water, with a fraction of about 1.5-4 wt.%in the glass batch, is released at temperatures below 373 K. The temperature at whichchemically bonded water is released, is dependent on the bonding strength of the watermolecule(s) to the batch constituents and may last up to temperatures of 880 K. The im-pact of dehydration reactions on the melting process of the glass batches is mainly theconsumption of extra energy during water evaporation.

Crystalline inversions: During melting of glass batches, structural modications of somecrystalline batch constituents occur. An example of a crystalline inversion in sand con-taining glass batches is the transformation of the -modication of quartz into the -modication of quartz at 846 K. Crystalline inversions have no signicant impact on themelting process of the glass batch.

Decomposition reactions: The main decomposition reactions during melting are the cal-cination reactions. The typical weight loss for a oat batch, without the presence of

5Float glass is flat glass, e.g. window glass, that is produced via the so-called float process.

1.2. The chemical behavior of glass forming batches 5

cullet6, due to these calcination reactions equals about 15-20 wt.%. Alkaline (Na2CO3,K2CO3) and earth-alkaline carbonates (MgCO3, CaCO3, SrCO3 and BaCO3) either de-compose due to temperature increase, i.e. thermal calcination above a certain temperaturelevel, or via a reaction with other batch constituents, i.e. reactive calcination. As an ex-ample, the thermal calcination of limestone is given by

CaCO3(s) T CaO(s)+CO2(g). (1.2)

The calcination temperature7 for the earth-alkaline carbonates, which is described inchapter 2, is dependent on the bonding strength of CO2 with the earth-alkaline oxideand equals 687 K, 1173 K, 1513 K and 1646 K for MgCO3, CaCO3, SrCO3 and BaCO3,respectively.An example of reactive calcination of a carbonate is the calcination of soda ash via a solid-state reaction with silica sand resulting in the formation of a crystalline sodium silicatephase. The formation of sodium metasilicate (Na2O SiO2) due to reactive calcination ofsoda ash with silica sand is given by

Na2CO3(s)+SiO2(s) Na2O SiO2(s)+CO2(g). (1.3)

Although the formation of Na2O SiO2 is already thermodynamically favorable at tem-peratures below 620 K (see chapter 2), the kinetics of these solid-state reactions are loweven at temperatures of 1000 K. These low reaction kinetics are caused by slow solid-state diffusion of reacting species through the formed crystalline binary silicates towardsthe interface of the reacting grains. Enhanced reactive calcination is observed at the pres-ence of a melt phase [3] by which the transport of reactants and reactions products isacceleration due to the higher diffusion coefcient of the formed oxides in the liquid statecompared with the solid-state.

Melt forming reactions: Melt phases are either formed by the melting of pure substances(e.g. the melting of soda ash at 1129 K) or by eutectic melting of two solid species. Anexample of eutectic melting is the melting of a mixture of Na2O SiO2 and Na2O 2SiO2 at1110 K. The formation of these so-called primary melt phases is regarded as the measur-able onset for both reactive calcination of carbonates and the dissolution of solid oxidesin the glass batch such as e.g. silica (SiO2), zircon (ZrO2 SiO2) and alumina (Al2O3).

Dissolution reactions: According to Conradt et al. [4], the dissolution rate of the oxidessuch as silica is dependent on primary melt phase properties such as viscosity, surfacetension and composition. Next to these properties, the particle size of the oxide grainshas a large impact on the dissolution rate of the oxides in the glass melt [5]. Because themain fraction of commercial glass batches is occupied by silica, the dissolution processof silica is regarded as the most signicant criterion for the degree to which the meltingof a glass batch based on silica sand has advanced [6].

Concerning the melting of glass batches, two reaction paths are distinguished for soda-lime-silicate glass batches [2, 4], i.e. the carbonate route and the silicate route (see also chapter 2).

6Recycled glass which acts as alternative raw material for glass production7The temperature at which the thermodynamic equilibrium CO2-pressure of the carbonate equals 1 bar.


The carbonate route is characterized by reactive dissolution of silica sand with a binary meltphase of soda ash and limestone at temperatures below 1170 K. Soda ash and limestone mayform a double carbonate by a solid-state reactions according to

Na2CO3(s)+CaCO3(s) Na2Ca(CO3)2(s). (1.4)At 1090 K, the double carbonate forms a low viscous melt phase, with which silica grains mayform a sodium calcium silica melt:

Na2Ca(CO3)2(l)+ SiO2(s) NCS(m)8. (1.5)For the silicate route, the (eutectic) melting of crystalline sodium silicates is regarded as theonset for batch melting. The eutectic melting of soda disilicate with silica at 1072 K is given by

Na2O 2SiO2(s)+SiO2(s) NS(m) (1.6)The carbonate route is assumed to be predominant at rapid heating rates in the order of 200 Kmin1, whereas the silicate route is predominant at heating rates in the order of 10 K min1. Thepresence of different reaction mechanisms as function of heating rate was clearly demonstratedby Riedel [7], who studied the reactivity of mixtures of glass batch components with hot-stagemicroscopy. The mechanism of the conversion of a typical oat and TV-panel batch as functionof temperature is discussed in more detail in chapter 2.

1.3 Modelling the thermal and chemical behavior of glassforming batches

A glass batch is a mixture of a gas phase and solid particles. During heating of the glass batch,the two-phase mixture transforms into a three-phase mixture also containing the melt phases,which are formed by (reactive) melting of the glass batch. An accurate prediction of the energybalance of a reacting glass batch requires knowledge of intrinsic properties of the solid phase,the melt phase and the gas phase, such as e.g. heat capacity and heat conductivity. Also theheat exchange between the different phases in the glass batch has to be known. Ungan andViskanta [9] assumed that the solid phase and the melt phase are, locally, in thermal equilib-rium, which simplies the reacting glass batch to a two-phase mixture.

Wakao and Kaguei [8] presented different heat transfer models for gas-solid mixtures undertransient conditions. These heat transfer models, which could also be applied to glass batchescomposed of a condensed phase and a gas phase, consist of the fundamental energy equationsfor both phases in the two-phase mixture. The form of these idealized energy equations is de-pendent on the arrangement of the two phases in the two-phase mixture, the intrinsic propertiesof both phases and the ow conditions of the gas phase through the porous solid phase. How-ever, all energy equations used in these heat transfer models are approximations of the energyequation taking into account all modes of heat transfer (conductive, convective and radiativeheat transfer) in the individual phases and the heat exchange between the two phases. As (ex-perimental) discrimination between the temperature of both the gas phase and the condensedphase in glass batches is very difcult or even impossible at the moment, in general a mean

8NCS(l) denotes a glass melt containing the oxides Na2O (N), CaO (C) and SiO2 (S).

1.3. Modelling the thermal and chemical behavior of glass forming batches 7

temperature of the glass batch is obtained when measuring the temperature in the glass batch.The overall energy balance of a glass batch during heating, with respect to a xed frame ofreference, can be described by

t( cp T

)mn =

[(1 p) c cp,c vc Tc + p g cp,g vg Tg

] (eff Tmn)+ q r,eff +(1 p) Hchemt . (1.7)

in whicht( cp T

)mn =

t[(1 p) c cp,c Tc + p g cp,g Tg

]. (1.8)

The subscripts c and g denote the condensed phase and the gas phase, p is the porosity of theglass batch, is the intrinsic density, cp is the heat capacity, T is temperature, t is time, v is thethree-dimensional velocity, eff represents the effective heat conductivity of the glass batch witha mean temperature Tmn, q r,eff represents the effective three-dimensional radiative heat ux inthe glass batch and Hchem is the energy per unit volume of the glass batch required for batchreactions. Assuming that the horizontal velocity of the condensed phase and the gas phase aresimilar [9], the Lagrangian description of the energy balance of a glass batch is given by

t( cp T

)mn =

(p g cp,g vg,z Tg

) (effTmn)+ q r,eff +(1 p) Hchemt ,(1.9)in which vg,z is the vertical velocity of the gas phase relative to the condensed phase. The heattransport in the interior of the glass batch is determined by a combination of three modes ofheat transfer:

convective heat transport by the ascending gas phase (characterized by the rst right-hand-side term in equation 1.9),

conductive heat transport by mutual contact between solid particles and between solidparticles and liquid phases (characterized by the second right-hand-side term in equation1.9),

radiative heat transport through the transparent phases (characterized by the third right-hand-side term in equation 1.9).

The mean and effective properties of the glass batch are dependent on the time- and temperaturedependent composition of the glass batch. Therewith, these glass batch properties are also time-and temperature dependent.

The melting of the initial solid glass batch producing a particle free glass melt proceeds viaa series of serial and parallel batch reactions. To describe the complete chemical conversionprocess of a glass batch, for each reactant and (intermediate) reaction product, a single massconservation equation has to solved. In case accurate analyzing techniques and sensors wouldbe present to measure the kinetics of all individual batch reactions occurring simultaneouslyduring heating of a glass batch, still the complete description of the kinetics of all batch reactionsremains a very complex and time-consuming task. Therefore, rst the kinetics of the mostimportant batch reactions have to be determined. As mentioned in section 1.2, the dissolutionprocess of sand grains is regarded as the most signicant criterion for the degree to which themelting of a glass batch based on silica sand has advanced. In chapter 3, the dissolution of sandgrains during glass batch melting is studied.


1.4 Objectives and outlineThe objective of this study is to obtain a quantitative description of the heating process of a glassbatches and the conversion rate of the glass batch into the glass melt. To meet the objectives ofthis study, the following activities are distinguished:

1. The identication of the main batch reactions in a typical oat and TV-panel glass batchduring heating.

2. The development of both experimental and mathematical techniques to determine quanti-tatively the kinetics of batch reactions and the heat penetration in typical industrial glassbatches.

3. The measurement and modelling of the temperature dependent chemical energy demandHchem, the effective heat conductivity eff and reaction kinetic parameters using the in thisstudy developed techniques.

A better quantitative understanding of these glass batch properties may lead to the improvementof the performance of glass tank simulation models. The implementation of the glass batchproperties, which are determined during this study, in glass tank simulation models will resultin improved predictions of both the energy balance of the glass batch and the dimensions (sizeand shape) of the batch blanket. These two aspects have a large impact on both the glass quality,by inuencing the intensity of the rst circulation loop in the melting tank (see section 1.1), andthe energy consumption of the glass tank.

In this study, the experimental determination of the glass batch properties mentioned above,are conned to a glass batch with a typical composition for the production of oat glass. Beside,the conversion mechanism of a glass batch with a typical composition for the production of TV-panel glass is studied qualitatively. The melting experiments are performed with industrialraw materials and at conditions (i.e. temperatures and heating rates) that are typical for theindustrial glass melting process. However, not the full range of industrial conditions is covereddue to experimental limitations.

One of the glass batch parameters that is required for solving the energy equation of theglass batch is the source term Hchem representing the energy demand for chemical reactionsoccurring during glass batch heating. In chapter 2, the chemical energy demand of the glassbatch producing oat glass is studied. According to Madivate et al. [10], the main energyconsuming batch reactions are the decomposition reactions during which batch gases such asCO2 is released. Therefore, the major part of the activities described in chapter 2 focus on theexperimental determination of the calcination rate of the raw material carbonates present in theoat glass batch. These calcination reactions are studied by both:

thermogravimetric analysis of (mixtures of) glass batch components, and by identication of (intermediate formed) crystalline species in cooled samples of (mixtures

of) glass batch components, which have been imposed to a dened temperature program.Also in this chapter, a qualitative description of the conversion of a TV-panel batch is discussed.

Because the dissolution process of silica sand is regarded as the most signicant criterionfor the degree to which the melting of a glass batch based on silica sand has advanced, themechanism and the rate of the sand grain dissolution process in a glass batch is studied (chapter

1.4. Objectives and outline 9

3). To measure the degree of sand grain dissolution in a glass batch as function of time andtemperature, a quantitative analyzing technique is required. This technique should be able todetermine the residual amount of crystalline sand in the partly molten glass batches. In thisstudy, the method of quantitative phase analysis with X-ray diffraction is applied as analyz-ing technique for measuring the crystalline silica content in partly molten glass batches. Next,an approximate analytical model describing the sand grain dissolution during heating of glassbatches is proposed. The applicability of this approximate model is studied by comparing re-sults of this approximate model with the results obtained with a more detailed numerical model.Finally, the parameters required for this approximate model are determined for the oat glassbatch as function of the particle size of the sand grains and the cullet fraction in the oat glassbatch.

In chapter 4, the experimental determination of the effective heat conductivity of glassbatches is studied. To measure the heat penetration in a glass batch, an experimental set-upwas developed, with which at different positions in the glass batch the temperature as functionof time is monitored. Because the effective heat conductivity of a glass batch is temperaturedependent, the value for the effective heat conductivity of the glass batch cannot be derivedexplicitly from the heat penetration experiments. To calculate the effective heat conductivityfrom the measured heat penetration in a glass batch, a numerical-experimental technique is ap-plied. With this technique, for different glass batch mixtures, the effective heat conductivity isdetermined.

Finally, in chapter 5.1 the results of this study are summarized. To complete the descriptionof the heating process of glass batches, information of the heat transfer towards the boundariesof glass batches is required. In section 5.2, a description is given of the heat transfer process tothe top layer of the batch blanket and the major mode of heat transfer is identied.


1.5 NomenclatureLatin symbols

cp heat capacity [J kg1 K1]g gas phaseHchem chemical energy demand [J m3]l liquid phasem dissolved in the melt phaseq heat ux [W m2]s solid phaset time [s]T temperature [K]v velocity [m s1]

Greek symbols

p porosity [-] heat conductivity [W m1 K1] stoichiometric reaction coefcient density [kg m3]

Subscripts

c condensed phaseeff effectivemn mean

r radiativez vertical direction

1.6. Bibliography 11

1.6 Bibliography[1] R. Viskanta. Review of three-dimensional mathematical modeling of glass melting. J.

Non-Cryst. Sol., 177:347, 1994.

[2] P. Hrma. Complexities of batch melting. In: Proc. of the 1st International Conference onAdvances in the Fusion of Glass, pages 10.110.18, Alfred University, Alfred, New York,June 14-17, 1988.

[3] C. Kroger. Gemengereaktionen und Glasschmelze. Glastech. Ber., 25(10):307324, 1952.[4] R. Conradt, P. Suwannathada, and P. Pimkhaokham. Local temperature distribution and

primary melt formation in a melting batch heap. Glastech. Ber. Glass Sci. Technol.,67(5):103113, 1994.

[5] R.G.C. Beerkens, H.P.H. Muijsenberg, and Heijden van der T. Modelling of sand graindissolution in industrial glass melting tanks. Glastech. Ber. Glass Sci. Technol., 67(7):179188, 1994.

[6] L. Bodalbhai and P. Hrma. The dissolution of silica grains in isothermally heated batchesof sodium carbonate and silica sand. Glass Technology, 27(2):7278, 1986.

[7] L. Riedel. Die Benetzung von Kalk und Quarz durch schmelzende Soda - Eine phanome-nologische Studie. Glastechn. Ber., 35(1):5356, 1962.

[8] N. Wakao and S. Kaguei. Topics in chemical engineering: Vol. 1 - Heat and mass transferin packed beds. Gordon and Breach, Science Publishers, Inc., New York-London-Paris,1st edition, 1982.

[9] A. Ungan and R Viskanta. Melting behavior of continuously charged loose batch blanketsin glass melting furnaces. Glastech. Ber., 59(10):279291, 1986.

[10] C. Madivate, F. Muller, and W. Wilsmann. Thermochemistry of the glass melting process- energy requirement in melting soda-lime-silica glasses from cullet-containing batches.Glastech. Ber. Glass Sci. Technol., 69(6):167178, 1996.

12 Bibliography

Chapter 2

Energy demand of glass forming batches

2.1 IntroductionAs mentioned in chapter 1, a glass forming batch can be regarded as a mixture of a condensedphase, which encloses the solid batch particles and the formed melt phases, and a gas phase.The Lagrangian description of the energy equation of the two-phase glass batch is given by

t( cp T

)mn =

(p g cp,g vg,z Tg

) (effTmn)+ q r,eff +(1 p) Hchemt ,(2.1)in which

( cp T

)mn represents the mean value of the enthalpy of the glass batch, g and cp,g

are the density and heat capacity of the gas phase, Tmn is the mean temperature of the glassbatch, t is the time, p is the porosity of the glass batch, vg,z is the vertical velocity of the gasphase relative to the condensed phase1, eff is the effective heat conductivity of the glass batch,q r,eff is the effective radiative heat ux through the glass batch, and Hchem is the temperaturedependent energy per unit volume of the glass batch required for batch reactions. For a com-plete description of the heating of glass batches, values for the parameters p, g, cp,g, vg,z, eff,q r,eff, and Hchem are required.

In this chapter, the time- and temperature dependent glass batch property Hchem is deter-mined for a glass batch producing oat glass. Madivate et al. [2] dened the net chemicalenergy demand of a glass batch as the enthalpy difference of the glass batch at 298 K and theformed melt phase with the released gases after cooling from the batch melting temperaturedown to 298 K. For a cullet-free glass batch, the net chemical energy demand for commercialcontainer glass batches was estimated to be approximately 15 % of the total net energy requiredfor batch melting. The residual 85 % is used for heating of the unreacted glass batch, the formedmelt phase and the released gases. Next, Madivate et al. [2] distinguished two types of batchreactions:

1. Gas-releasing decomposition reactions, during which H2O, CO2, NOx, SOx and/or O2 isreleased and during which solid oxides are formed, such as the calcination of limestonegiven by CaCO3(s) CaO(s) + CO2(g).

2. Mixing and fusion reactions of the solid oxides forming a glass melt.1It is assumed that the horizontal velocity of the gas phase is similar to the horizontal velocity of the condensed

phase [1].

13

14 Chapter 2. Energy demand of glass forming batches

The rst type of batch reactions are endothermic reactions and require approximately 40 % ofthe total energy demand of a glass batch, whereas the latter type of batch reactions are exother-mic reactions, which compensate about 55 % of the energy required for the endothermic batchreactions. In practice, the batch reactions may already start at about 300 K and may range up toabout 1700 K for the dissolution of oxides. The chemical energy required for batch reactions istemperature dependent. A detailed description of the chemical energy demand of a glass batchcontaining silica sand, soda ash, limestone and dolomite is given in section 2.2.

The major part of the gas-releasing batch reactions are the calcination reactions duringwhich CO2 is released. Therefore, the temperature dependent net chemical energy demandduring melting of glass batches is to a large extent determined by the rate of the calcinationreactions. The net rate of consumption of chemical energy per unit volume of the glass batchfor all calcination reactions is given by

Hchemt =

nc

i=1

(Hr,i w0i c

Miit

), (2.2)

in which nc is the total number of carbonates in the glass batch, Hr,i is the enthalpy requiredfor the calcination of carbonate i expressed in J mole1, w0i is the initial weight fraction ofcarbonate i in the condensed phase, c is the density of the condensed phase, Mi is the molarmass of carbonate i, i is the degree of conversion2 of carbonate i, and t is the time. To determinethe time- and temperature dependent energy demand for the calcination reactions, the rate ofthe calcination reactions expressed by it has to be determined. In section 2.3, the generalapproach for describing the reaction rate of homogeneous and heterogeneous reactions withand without the presence of a non-ideal liquid phases such as glass melts is discussed. Based onthe equations presented in this section, the rate of the calcination reactions which occur duringheating of a typical oat glass batch is studied in section 2.5.

The identication of the calcination reactions in the oat glass batch and the determinationof the calcination rate of these decomposition reactions are studied by

analysis of the (intermediate formed) crystalline phases which are present in cooled heat-treated oat glass batch samples, and

thermogravimetric analysis.The backgrounds and procedure for these two experimental techniques is discussed in section2.4.

The calcination behavior of dolomite, limestone and soda ash is discussed in sections 2.5.1,2.5.2 and 2.5.3, respectively. The calcination behavior of the complete oat glass batch con-taining these batch components is discussed in section 2.5.4. In section 2.5.5, the conversionmechanism of the oat glass batch, based on literature data and on the results of the calcinationexperiments described in this chapter, is described. The temperature dependent energy demandof the oat glass batch, calculated from the measured rate of the calcination reactions and thecalcination enthalpies of these decomposition reactions, is presented in section 2.5.6. In section2.6 concluding remarks are presented concerning the reaction mechanism, the calcination rateand the chemical energy demand of the oat glass batch are given. Also a few comments aregiven to the calcination behavior of a TV-panel glass batch.

2The degree of conversion of a carbonate is defined as the ratio of the weight loss with respect to the totalweight loss when the carbonate has completely been dissociated.

2.2. Energy demand during heating of glass forming batches 15PSfrag replacements

T0 Tr,onset Tr,end Tfinal

H(T0)

H(Tr,onset)

H(Tr,end)H(Tfinal)

A

B

C

D

E

r2,1

r2,2r2,3

H1

H2

H3

r1

r2

r3

Figure 2.1: Schematic representation of the energy demand of a glass batch as function of temperature. Aindicates the enthalpy of the glass batch at the initial glass batch temperature T0. E indicatesthe enthalpy of the formed glass melt and gas phase after heating and melting the glass batchup to Tfinal. B, C and D are intermediate enthalpy states of the reacting glass batch. Tr,onsetand Tr,end are the onset and end temperature for the batch reactions. The routes along whichthe energy demand of a glass batch may run are indicated by r1, r2, r2,1 or r2,2 or r2,3 and r3.It is remarked that the energy required for evaporation of water, which is in general presentin glass batches, is not indicated in this figure.

2.2 Energy demand during heating of glass forming batchesIn this section, a general description is given of the energy demand of a glass batch duringheating. Next, the temperature dependent energy demand of a glass batch producing oat glassis calculated based on literature data. It is shown that for an accurate description of the tem-perature dependent energy demand of a glass batch, the onset temperature and the kinetics ofthe (mainly) energy consuming batch reactions is required.

The energy demand of a glass batch is determined by the energy required for heating the rawmaterials, the formed melt phases and the released gases, and the energy required for the en-dothermic and exothermic batch reactions. The melting of a glass batch can be described by

(1+)batch(T0) H 1 melt(Tfinal)+ gas(Tfinal), (2.3)


in which T0 is the initial temperature of the glass batch, Tfinal is the temperature to which theglass batch is heated3, H is the energy demand of heating and melting the glass batch, and is the mass of gas that is released during heating of a glass batch with mass (1+).

With respect to the energy demand during the melting process of glass batches, three tem-perature ranges (see gure 2.1) are distinguished:

1. The temperature range between the initial temperature of the glass batch T0 and the onsettemperature for the batch reactions Tr,onset. The reaction occurring in this temperaturerange is given by

(1+)batch(T0) H1 (1+)batch(Tr,onset). (2.4)During heating of the glass batch in this temperature range, the enthalpy of the glass batchruns via route r1 from A towards B in gure 2.1. The energy demand of this reaction,expressed in J per (1+) kg of batch, is given by

H1 = H(Tr,onset)H(T0) = Tr,onset

T0

nb

i=1

mi cp,i dT, (2.5)

in which nb is the number of batch components, mi is the mass of batch component iper (1 + ) kg of batch, and cp,i is the temperature dependent heat capacity of batchcomponent i.

2. The temperature range between the onset for batch reactions Tr,onset and Tr,end, duringwhich the endo- and exothermic batch reactions occur, as described by

(1+)batch(Tr,onset) H2 1 melt(Tr,end)+ gas(Tr,end). (2.6)

In case no batch reactions occur in this temperature regime, the enthalpy change of theglass batch runs via route r2 towards C. However, because of the occurrence of (mainly)energy consuming batch reactions, the enthalpy change runs via the arbitrarily drawnroutes r2,1, r2,2 or r2,3 from B towards D. The route that is followed is dependent onthe temperature and time dependent chemical energy consumption during batch melting.The enthalpy change in this temperature range, which is dependent on the kinetics of theenergy consuming and producing batch reactions, expressed in J per (1 + ) kg of batchis described by

H2 = Hr,endHr,onset = Hr + Tr,end

Tr,onset

nb

i=1

mi cp,i dT, (2.7)

in which Hr is the chemical energy demand for the batch reactions, nb is the number ofbatch components, mi is the temperature and time dependent mass of batch componenti per (1 + ) kg of batch and cp,i is the temperature dependent heat capacity of batchcomponent i, which is either a solid specie, a gaseous specie or a melt phase. The mixtureof all species i at temperature T and time t represents the composition of the reactingglass batch at temperature T and time t.

3Here it is assumed that the final heating temperature of the generated melt phase and the released gases isidentical.

2.2. Energy demand during heating of glass forming batches 17

3. The temperature range between Tr,end and the nal heating temperature Tfinal, duringwhich the formed melt phases and the released gases are heated as described by

1 melt(Tr,end)+ gas(Tr,end) H3 1 melt(Tfinal)+ gas(Tfinal). (2.8)

This equation describes the enthalpy change via route r3 from D towards E. The totalenergy demand of this reaction is given by

H3 = Tfinal

Tr,endmmelt cp,melt dT +

TfinalTr,end

ngc

g=1

mg cp,g dT, (2.9)

in which ngc is the number of gaseous components, mmelt is the mass of melt phase pro-duced during melting of (1 + ) kg of batch, cp,melt is the temperature dependent heatcapacity of the formed melt phase, mg is the temperature dependent mass of gaseousspecie g per (1 + ) kg of batch, and cp,g is the temperature dependent heat capacity ofgaseous component g. The rst right-hand-side term in equation 2.9 represents the dif-ference in sensible heat of the melt phase at T = Tfinal and T = Tr,end, whereas the secondright-hand-side term in equation 2.9 represents the difference in sensible heat of the gasphase at T = Tfinal and T = Tr,end.

According to equation 2.7, for the determination of the chemical energy demand of the glassbatch Hr, the value for H2 and information of the temperature dependent composition of thereacting glass batch are required. According to gure 2.1, the value for H2 can be estimatedfrom

H2 = (H(Tfinal)H(T0)) (H1 +H3) = Ht (H1 +H3) . (2.10)The value for H3 is deduced from

H3 = Hmelt + Hgas, (2.11)

in which is the mass of the gas phase released per unit mass of glass melt and Hmelt andHgas are the differences in sensible heat between Tr,end and Tfinal of the formed glass melt andthe released gases, respectively. Combining equations 2.7, 2.10 and 2.11 results in an expressionfor the chemical energy demand of the glass batch:

Hr = Ht(H1 +Hmelt + Hgas

) Tr,endTr,onset

nb

i=1

mi cp,i dT. (2.12)

For a given onset and end temperature for batch reactions, the values for H1 and Hgas canbe calculated from thermodynamic tables [3]. The value for Hmelt can either be derived froman empirical formula describing the temperature dependent heat capacity of melt phases [4] orby thermodynamic models [5]. Another possibility is to determine Hmelt from the measuredsensible heat of the glass melt as function of temperature [2]. The total energy demand forheating and melting of the glass batch Ht requires knowledge of the formation enthalpies

of the glass batch at T0, the formed melt phase at Tfinal, and


PSfrag replacements

T0 Tr,onset Tr,end Tfinal

H(T0)

H(Tr,onset)

H(Tr,end)

H(Tfinal)

A

B

C

D

E

Reaction zone

r2,1

r2,2

r2,3

r2,4

H1

H2

H3

Hr(Tonset)

Hr(Tend)

r1

r2

r3

Figure 2.2: Schematic representation of the energy demand of a glass batch as function of temperature.

the released gases at Tfinal.

The enthalpy of both the glass batch and the released gases can be derived from thermodynamictables [3]. The formation enthalpy of the glass melt can be estimated from models describingthe thermodynamic behavior of glass melts [58] or it can be measured directly. Now, the onlyremaining unknown parameter required for calculation of the chemical energy demand of aglass batch by equation 2.12 is the sensible heat of the glass batch components between Tonsetand Tend.

In gure 2.2, the temperature dependent heat capacity of the unreacted glass batch in thereaction zone is characterized by the slope of line r2,3, whereas the heat capacity of the formedglass melt and the released gases in the reaction zone is characterized by the slope of line r2,2. Incase these slopes are identical, the chemical energy demand of the glass batch is independent onthe reaction path followed in the reaction zone. This means that Hr(Tonset) equals Hr(Tend).However, since these heat capacities are in general not identical, the chemical energy demandof a glass batch depends on the temperature range during which the batch reactions occur. Thedependency of the chemical energy demand Hr on the temperature range in which the batchreactions take place is shown by the following example. For the ease of the calculation, itis assumed that the glass batch reacts at a distinct reaction temperature Tr and not during atemperature range. This simplies equation 2.12 because the last right-hand-side term becomeszero.

Madivate et al. [2] measured the total energy demand of a glass batch, with the compositionlisted in table 2.1. For this glass batch, the value for the mass of gas that is released duringheating of a glass batch with mass (1+) equals 0.212. The total energy demand of this glass

2.2. Energy demand during heating of glass forming batches 19

Table 2.1: Glass batch composition for which the chemical energy demand is calculated.

Batch component Concentration [wt. %]

SiO2 58.21Na2CO3 18.76CaCO3 5.24MgCO3 CaCO3 15.89

batch with respect to 298 K is given by

Ht =514.9+1.818 T, (2.13)

in which the total energy demand is expressed in kJ per kg of glass and the temperature isexpressed in K. The sensible heat of the glass melt is given by

Hmelt =614.0+1.373 T. (2.14)

Both H1 and Hgas are determined from thermodynamic tables [3]. Figure 2.3 shows thechemical energy demand of the glass batch expressed in J per kg of glass as function of thebatch reaction temperature. The chemical energy demand at 298 K, which equals 471 kJ kg1melt,is almost equal to the values presented by Conradt and Pimkhaokham [7] and Madivate et al. [2].

From this gure it is clearly seen that the chemical energy demand of the glass batch de-creases with increasing reaction temperature. The reason for this is the larger heat capacity ofthe unreacted glass batch components compared to the heat capacity of the mixture of the meltphase and the released gases. This means that the slope of line r2,3 in gure 2.2 is steeper thanthe slope of line r2,2.

Figure 2.4 shows the total energy demand during heating and melting of the glass batch forboth a reaction temperature of 1080 K (solid line) and a reaction temperature of 1400 K (dottedline). Line 1 indicates the total energy demand of the glass batch during heating from the initialtemperature up to 1080 K. Line 2 describes the instantaneous chemical energy consumption at1080 K, which is followed by line 3, which describes total energy demand during heating ofthe formed melt phase and the released gases. In case the reaction temperature equals 1400 Kinstead of 1080 K, the energy consumption during heating of the glass batch runs via line 1and followed by line 4. At 1400 K, the chemical energy is consumed instantaneously and theenthalpy change runs along line 5.

Resuming, an accurate prediction of the net chemical energy demand of a glass batch asfunction of time and temperature requires knowledge of the onset temperature and the kineticsof the energy consuming and producing batch reactions. As mentioned in the previous section,the main energy consuming batch reactions are the calcination reactions. In section 2.5, thekinetics of the calcination reactions occurring during heating of a oat glass batch is studied.The determination of the calcination rate of these batch reactions is based on kinetic equationswhich are discussed in the next section.


400 600 800 1000 1200 14000

1x105

2x105

3x105

4x105

5x105

PSfrag replacementsReaction temperature [K]

Che

mic

alen

ergy

dem

and

[Jkg

1 melt]

Figure 2.3: Chemical energy demand of the glass batch as function of the reaction temperature for thecomposition given in table 2.1 and with respect to 298 K.

200 400 600 800 1000 1200 1400 16000.0

5.0x105

1.0x106

1.5x106

2.0x106

2.5x106

PSfrag replacements

Temperature [K]

Tota

lene

rgy

dem

and

[Jkg

1 melt]

1

2

3

4

5

Hr(1080 K)

Hr(1400 K)

Figure 2.4: Total energy demand of the glass batch as function of temperature for both a batch reactiontemperature of 1080 K (solid line) and 1400 K (dotted line).

2.3. Description of the kinetics of batch reactions 21

2.3 Description of the kinetics of batch reactionsIn this section, the kinetics of both homogeneous and heterogeneous chemical reactions, withand without the presence of a non-ideal liquid phase such as a glass melt is discussed. Basedon the equations presented in this section, the kinetics of calcination reactions occurring in aoat glass batch are studied in section 2.5.

2.3.1 IntroductionDuring heating and melting of glass batches, different types of reactions occur such as solid-state reactions, gas-solid reactions, gas-liquid reactions and solid-liquid reactions. In general,the overall rate of each of these heterogeneous batch reactions is dependent on the rate of threeseparate process steps, viz.:

the transport of reactants to the reaction interface, the reaction rate at the reaction interface, and the transport of reaction products away from the reaction interface.

The overall rate of chemical reactions is governed by the process step with the lowest rate. Ingeneral, three reaction types are distinguished, i.e. reactions that are governed by mass transferprocesses, reactions that are governed by reaction kinetics and reactions that are governed bythermodynamic driving forces. To describe mass transfer governed processes knowledge is re-quired about the diffusive and convective transport of reactants and reaction products towardsand from the reaction interface. In general, for a mass transfer governed process, it is assumedthat the reaction rate is fast with respect to the rate of mass transfer. This means that for masstransfer governed processes it is assumed that at the reaction interface thermodynamic equilib-rium exists between the reactants and the reaction products.

Reaction kinetic governed processes require knowledge of reaction kinetic parameters. Forheterogeneous reactions, such as the main glass batches, these reaction kinetic parameters aredescribed in section 2.3.3. The description of kinetics of these heterogeneous reactions is basedon the description of reaction governed homogeneous reactions such as gas phase reactions.Although homogeneous batch reactions are not expected to contribute to a large extend to batchmelting, a description of homogenous reaction kinetics is given in section 2.3.2, because someaspects of the description of homogeneous reaction kinetics are applied for the description ofheterogeneous reaction kinetics. Section 2.3.4 describes the effect of the presence of non-idealliquid phases, such as glass melts, on the kinetic description of the rate of a chemical reaction.

2.3.2 Kinetics of homogeneous reactionsThe chemical conversion of reactants A and B into the reaction products C and D is given by

A A+B Bk f

kbC C +D D, (2.15)

in which k f and kb are the rate constants of the forward and the backward reaction, and A,B, C and D are the stoichiometric reaction coefcients. Assuming that reaction 2.15 is a


reversible and elementary reaction4, the overall reaction rate of reaction 2.15 is given by

r = r f rb = k f aAA aBB kb aCC aDD , (2.16)

in which aA, aB, aC and aD are the activities of the species A, B, C and D. The rates of theforward and the backward reaction are indicated by r f and rb, respectively. For pure condensedphases, such as solids and pure liquids, the activity is dened as unity. The activity of a com-ponent i in a gas phase mixture, which is known as the fugacity f of component i, is givenby

fi = i pi, (2.17)in which i is the activity (or fugacity) coefcient of component i and pi is the partial pressureof component i in the gas phase. For ideal gases, the fugacity or activity coefcient for eachspecie equals unity and the fugacity of component i equals the partial pressure of component i.

Similar to a gas phase, the activity of a component i in a liquid solution is given by

ai = i xi, (2.18)

in which i is the activity coefcient of component i and xi is the mole fraction of componenti in the liquid solution. For ideal liquid solutions, the activity coefcient of each specie equalsunity and the activity of component i equals the mole fraction of component i. However, fornon-ideal solutions such as glass melts, the activity coefcient deviates signicantly from unity.For example, the activity coefcient for Na2O in a binary melt phase with a mole fraction ofNa2O equal to 0.25 and a mole fraction of SiO2 equal to 0.75 equals 2.4 1011 at 1173 K [5].

Usually, a chemical reaction is the result of a number of successive elementary reactionsteps. In case reaction 2.15 is the overall reaction of the two successive elementary reactions,i.e.

A A+B Bk f

kbI I, (2.19)

and

I Ik f

kbC C +D D, (2.20)

in which I indicates an intermediate reaction product, two reaction rates, r2.19 and r2.20, areobtained, viz.

r2.19 = k f ,2.19 aAA aBB kb,2.19 aII , (2.21)

andr2.20 = k f ,2.20 aII kb,2.20 aCC aDD . (2.22)

The overall reaction rate of the reaction steps 2.19 and 2.20 is now governed by the rate of therate governing reaction step, which is either r2.19 or r2.20. Therefore, the determination of thekinetics of chemical reactions starts with the identication of the rate governing reaction step.

At thermodynamic equilibrium, the reaction rate of a chemical reaction equals zero, becausethe rate of the forward reaction equals the rate of the backward reaction. The ratio of the reaction

4A chemical reaction which proceeds exactly as expressed by the stoichiometric reaction equation [9]. How-ever, usually a chemical reaction is the result of a number of successive elementary reactions as will be described byequations 2.19 and 2.20. Than the chemical conversion proceeds via (a number of) intermediate reaction products.


rate constant of the backward and the forward reaction equals the reaction equilibrium constantKeq. The reaction equilibrium constant for reaction 2.15 is dened by

rb,2.15

r f ,2.15= 1 Keq,2.15 =

k f ,2.15kb,2.15

=a

CC a

DD

aAA a

BB

. (2.23)

Combining equations 2.16 and 2.23 results in a general expression for the reaction rate of areversible elementary chemical reaction as function of the rate constant of the forward reactionk f , the reaction equilibrium constant Keq, the activities of nr participating reactants and theactivities of nrp participating reaction products:

r = k f

(nr

i=1

aii

1Keq

nrp

j=1

a jj

). (2.24)

The reaction equilibrium constant Keq is obtained from the standard chemical potential 0 ofthe reactants and the reaction products according to

lnKeq = 1R T

(nrp

j=1

j 0j

nr

i=1

i 0i

)=G

0r

R T, (2.25)

in which R is the gas constant, T is the absolute temperature and G0r is the standard Gibbs freeenergy of reaction. The values for the standard standard chemical potential for a large numberof species are tabulated in thermodynamic tables [3].

For gas phase reactions, the rate constants k f and kb are temperature dependent accordingto the so-called Arrhenius equation, which is given by

k = A eEa

R T , (2.26)

in which A is the pre-exponential factor and Ea is the reaction activation energy. The exponentialtemperature dependency of the gas phase rate constants is based on the exponential energydistribution over the gas molecules in a system at a specic temperature, which is known as theBoltzmann-distribution.

Resuming, the rate of a reversible homogeneous chemical reaction is described by equation2.24, in which the rate constant is given by an Arrhenius equation. In the next section, thekinetics of heterogeneous reactions, which is the major reaction type occurring during meltingof glass batches, is discussed.

2.3.3 Kinetics of heterogeneous reactions

The description of heterogeneous reactions originates from the kinetic description of solid-statereactions, which are either diffusion or reaction governed processes. Both for diffusion and re-action kinetics governed solid-state reactions, the overall rate of the reaction is dependent on thegeometry of the reacting species. Dependent on the size and the shape of the reacting species,four different processes are generally distinguished, viz. a one-, two- or three-dimensional dif-fusion governed process or a reaction governed process. Therefore, for the description of the


kinetics of solid-state reactions, different geometrical models have been developed. In general,the rate of a heterogeneous reaction is described by

it = k f (i) , (2.27)

in which i is the conversion of specie i 5, k is the reaction rate constant, and f (i) is theso-called reaction mechanism function for specie i. Table 3.1 lists the main generally appliedreaction types and their function f () derived from the reaction mechanism.

Table 2.2: Code, reaction type and reaction mechanism function (see for an overview of these reactionmechanism functions [10]).

Code Reaction type f ()Fn nroth order reaction (1)nro

D1 One-dimensional diffusion 12

D2 Two-dimensional diffusion 1ln(1)

D3 Three-dimensional diffusion (Janders type) 1.5(1)2/3

1(1)1/3

D4 Three-dimensional diffusion (Ginstling-Brounstein type) 1.5(1)1/31

R2 Two-dimensional phase boundary reaction 2(1)1/2

R3 Three-dimensional phase boundary reaction 3(1)2/3

Similar to the homogeneous gas phase reaction kinetics, the reaction rate constant k is as-sumed to be temperature dependent according to the Arrhenius equation. In contrast to gasphase reactions, the energy distribution amongst the, in this case, immobilized constituents of(crystalline) species is not represented by the Boltzmann-distribution. For this reason, the ap-plicability of the Arrhenius equation, describing the exponential temperature dependency of therate constants for reactions at which solids participate, has been questioned for a long time byGalwey and Brown [11]. In solids, energy transfer is determined by either phonon or photontransfer. Recently, Galwey and Brown [11] reported that the energy distributions of these twoenergy transfer modes also show an exponential temperature dependency, which allows the useof the Arrhenius equation for describing the exponential temperature dependency of the rateconstants for solid-state reactions.

When applying equation 2.27, the reaction activation energy Ea and the pre-exponential fac-tor A for a chemical reaction can be derived by plotting the left-hand-side term of equation 2.28

5The conversion i of a specie i is defined as the ratio of the actual amount of specie i with respect to the initialamount of specie i.


versus the reciprocal absolute temperature.

ln(

t

) ln f () = lnA Ea

R T(2.28)

The intercept and the slope of this plot provide the values for lnA and Ea/R, respectively. Ingeneral, the selection of the reaction mechanism function f () for a specic reaction is basedon the correlation coefcient describing the accuracy of t of the reaction mechanism functionwith the measured conversion data. The reaction mechanism function f () providing the largestvalue for the correlation coefcient is identied as the reaction mechanism function describingthe conversion mechanism for the reaction that is investigated. According to Opfermann [12],the selection of the reaction mechanism function based on the correlation coefcient does notalways seem to be statistically well-founded. The difference in correlation coefcients for thedifferent reaction mechanism functions is often insignicant. It is also mentioned that the re-action mechanism based on this selection approach is likely to provide no accurate informationabout the real reaction mechanism. For this reason, the reaction kinetic parameters are not ex-pected to have a physical meaning. Therefore, the reaction activation energy determined by thisapproach will be denoted throughout this chapter as an apparent reaction activation energy.

Equation 2.27 can be regarded as a kinetic equation describing the reaction rate of a het-erogeneous reaction which occurs far from thermodynamic equilibrium. In order to predict thekinetic behavior of a heterogeneous reaction close to thermodynamic equilibrium, the reactionequilibrium has to be taken into account in equation 2.27. Pokol [13] discussed different ap-proaches to take thermodynamic equilibrium into account. Similar to homogeneous reactions,the reaction rate of a heterogeneous reaction can be described by an equation similar to equa-tion 2.24. Equation 2.29 describes the rate of a heterogeneous reaction both far and close tothermodynamic equilibrium in which Keq is the reaction equilibrium constant and Ka, givenby equation 2.30, describes the ratio of the actual activities of the reactants and the reactionproducts.

r = k f f ()nr

i=1

aii

(1 Ka

Keq

)(2.29)

Ka =nrpj=1 a

jj

nri=1 aii(2.30)

The forward reaction of a reversible reaction is favored in case Ka < Keq, whereas the backwardreaction is favored in case Ka > Keq. For example, for the reversible calcination of limestone,which is given by CaCO3(s) CaO(s) + CO2(g), equation 2.29 simplies to equation 2.31,because the activities of solid species equal unity by denition. The partial CO2-pressure inthe atmosphere surrounding the limestone particle is given by pCO2,a, whereas the tempera-ture dependent equilibrium partial CO2-pressure during limestone decomposition is given bypCO2,eq.

r = k f f ()(

1 pCO2,apCO2,eq

)(2.31)

In case the actual partial CO2-pressure in the atmosphere surrounding the limestone particlesexceeds the thermodynamic equilibrium partial CO2-pressure, the carbonization reaction, i.e.CaO(s) + CO2(g) CaCO3(s), is favored, whereas in case pCO2,a is lower than pCO2,eq, thecalcination reaction, CaCO3(s) CaO(s) + CO2(g), is favored.


Resuming, the kinetics of reversible heterogeneous reactions is described by equation 2.29.Up to now, the kinetics of chemical reactions at which reactants participate with a xed stoi-chiometry are discussed. However, melt phases formed during heating of glass batches have noxed composition. In the next section, the effect of melt phases on the kinetics of heterogeneousreactions is discussed.

2.3.4 Heterogeneous reaction kinetics with participation of melt phasesThe reactive decomposition of soda ash at the presence of a binary sodium silicate melt is givenby

y Na2CO3(s)+xNa2O (1-x)SiO2(l) (1+ y)

[ (x+ y1+ y

)Na2O

(1 x1+ y

)SiO2

](l)+ y CO2(g) (2.32)

Similar to equation 2.29, the kinetics of the soda ash calcination can be described by

r = k f f () amelt1(l)(

1 KaKeq

), (2.33)

with:Keq = e

G0rR T , (2.34)

and

Ka =a

1+ymelt2 p

yCO2(g)

amelt1, (2.35)

in which amelt1 is the activity of the reacting melt phase and amelt2 is the activity of theformed melt phase. The calculation of the activity of the reacting and formed melt phases is nottrivial. In order to explain the effect of melt phases on the thermodynamics of batch reactions,the approach for describing the thermodynamics of molten oxide systems, such as glass meltsystems, presented by Shakhmatkin et al. [8] is discussed.

In general, the energy state of a solid, liquid or gas phase mixture is given by the Gibbs freeenergy of the mixture according to

G =nms

i=1

xi 0i +R T

nms

i=1

xi lnxi +GE , (2.36)

in which G is the molar Gibbs free energy of the mixture, nms is the number of species in themixture, xi is the mole fraction of specie i in the mixture, 0i is the standard chemical potential ofspecie i, R is the universal gas constant, T is the absolute temperature and GE is the excess Gibbsfree energy. For ideal mixtures, such as gas phase mixtures, the excess Gibbs free energy equalszero and the Gibbs free energy of the mixture can be calculated from the tabulated values of thestandard chemical potential of the mixture components and their mole fraction in the mixture asgiven by equation 2.36. However, glass melts do not behave as an ideal mixture of the individualoxides. The Gibbs free energy of a glass melt is given by

G =nms

i=1

xi 0i +R T

nms

i=1

xi lnxi +R Tnms

i=1

xi lni, (2.37)


in which i is the activity coefcient of oxide i in the glass melt. For species in an ideal mixture,the activity coefcient equals unity. The activity coefcient of Na2O in the non-ideal binarymelt phase with a mole fraction of Na2O equal to 0.25 and a mole fraction of SiO2 equal to 0.75equals 2.4 1011 at 1473 K [5].

To describe the thermodynamics of glass melts, an expression for the activity coefcient ofall species in the glass melt as function of glass melt composition and temperature is required,i.e. lni = f (x1, ..,xi, ..,xn,T ). The main problem with non-ideal solutions is that setting-up amodel describing the interaction between solution components and the determination of theseinteraction parameters is a complex and laborious task. In general, thermodynamic modelsdescribing the deviation from ideal behavior of a solution formulate expressions for the ac-tivity coefcients of each specie i in the non-ideal solution as function of the composition ofthe non-ideal solution and the temperature, i.e. lni = f (x1, ..,xi, ..,xn,T ). For a glass melt,these expressions are based on assumed structural models of the glass melt, such as the quasi-chemical model [5]. The parameters of these models describing the interaction between theoxides in the glass melt are derived from phase diagrams of (subsystems of) the complete glassmelt and from measured thermodynamic properties of the glass melt such as for example partialvapor pressures of the glass melt oxides.

Shakhmatkin et al. [8] developed a thermodynamic model, with which the activity coef-cients of glass melt oxides can be predicted based on thermodynamic properties of purecomponents, which are tabulated in several references such as Knacke et al. [3]. According toShakhmatkin et al. [8], a glass melt can be considered as an ideal solution of so-called stoichio-metric compounds in the vitreous state. These stoichiometric compounds have a stoichiometry,which is similar to the crystalline compounds existing in the phase diagrams of the subsys-tems of the glass melt. For example, for a binary melt phase containing the oxides SiO2 andNa2O, the main important stoichiometric compounds of the melt phase are SiO2, Na2O 2SiO2,Na2O SiO2, 2Na2O SiO2 and Na2O (see gure 2.5). The Gibbs free energy of a glass melt isnow described by

G =nms

i=1

xsc,i 0sc,i +R T

nms

sc,i=1

xsc,i lnxsc,i, (2.38)

in which sc denotes the stoichiometric compound in the vitreous state6. Minimization of theGibbs free energy with respect to the mole fractions of the stoichiometric compounds and takinginto account the element balances of the oxides in the glass melt, results in the thermodynamicmost stable composition of the glass melt expressed in the mole fractions of the stoichiometriccompounds.

Conradt proposed a similar model [15], in which the composition of a glass melt can be ap-proximated by an ideal mixture of the so-called nearest stoichiometric compounds7, which arein thermodynamic equilibrium with the pure oxides of the glass melt. For example, for a sodiumsilicate melt phase with a molar SiO2 fraction of 0.75, the glass melt mainly contains the near-est stoichiometric compounds SiO2 (in which xSiO2=1) and Na2O 2SiO2 (in which xSiO2=0.67).Now, the glass melt in thermodynamic equilibrium can be described by an equilibrium between

6In general, Shakhmatkin et al. use the crystalline state of the stoichiometric compounds as reference stateinstead of the vitreous state.

7Conradt uses the vitreous state of the stoichiometric compounds as reference state. Below the liquidus tem-perature of a glass melt, Conradt estimates the Gibbs free energy of the vitreous state.


Figure 2.5: Binary phase diagram of SiO2 and Na2O [14]. The temperature is expressed in C.

the stoichiometric compounds according to

Na2O(l)+2 SiO2(l) Na2O 2SiO2(l), (2.39)in which Na2O(l), SiO2(l) and Na2O 2SiO2(l) represent the stoichiometric compounds in thevitreous state. The reactive calcination of solid soda ash with a binary melt phase in which themole fraction of SiO2 equals 0.75 can now be described by

Na2CO3(s)+2SiO2(l) Na2O 2SiO2(l)+CO2(g). (2.40)Using equation 2.29, the calcination rate of soda ash is given by

r = k f f () x2SiO2(

1 KaKeq

), (2.41)

in whichKa =

xNa2O 2SiO2 pCO2x2SiO2

, (2.42)


and xSiO2 and xNa2O 2SiO2 are the mole fractions of the stoichiometric compounds SiO2 andNa2O 2SiO2 in the reacting glass melt. Resuming, using the approach for modelling the ther-mochemistry of glass melts proposed by Conradt and Shakhmatkin et al., the kinetics of ther-modynamic driving force governed batch reactions at which melt phases participate can bedescribed.

Next to the presence of oxides in a glass melt, also dissolved gases can be present. A gaseousspecie can either be physically or chemically dissolved in the glass melt [16, 17]. The physicaldissolution of gases in a glass melt concerns the settling of gas atoms or molecules in holes inthe network of the glass melt matrix. On the other hand, gases can dissolve in the glass melt viaa reaction with glass melt components. For example, CO2 may react with free oxygen presentin the glass melt according to

CO2(g)+O2(m) CO23 (m). (2.43)The thermodynamic model presented by Shakhmatkin et al. and Conradt, incorporate the chem-ically dissolved CO2 by allowing the stoichiometric compound Na2CO3 to be present in theglass melt. The description of reactive dissolution of Na2O in the binary glass melt accordingto equation 2.32, requires both the thermodynamic equilibrium data of equation 2.40 and of

Na2CO3(s) Na2CO3(m), (2.44)and

Na2CO3(m) Na2O(m)+CO2(g), (2.45)in which Na2CO3(m) is the stoichiometric compound Na2CO3 in the melt phase, which repre-sents the chemical dissolved CO2. Now, the calcination rate of soda ash is not only given byequation 2.41, which describes the reactive calcination of soda ash with the melt phase, but alsoby

r = k f f () xNa2CO3(

1 KaKeq

), (2.46)

which describes the thermal calcination of chemically dissolved Na2CO3 in the glass melt. Thechemically solubility of Na2CO3 is given by xNa2CO3 and Ka is given by

Ka =xNa2O(m) pCO2(g)

xNa2CO3(m). (2.47)

2.3.5 Characteristics of calcination reactionsCalcination reaction

Date post:	14-Oct-2015
Category:	Documents
Upload:	catherine-cooke
View:	28 times
Download:	0 times

20031176325

Documents