thermochemistry of salts 0703

ÅBO AKADEMI

TEKNISKA FAKULTETEN Processkemiska Centret

FACULTY OF TECHNOLOGY

Process Chemistry Centre

REPORT 07-03

Thermochemistry and melting properties of alkali salt mixtures

in black liquor conversion processes

Daniel Lindberg

Academic Dissertation

Laboratory of Inorganic Chemistry

Thermochemistry and melting properties of alkali salt mixtures in black liquor

conversion processes

Daniel Lindberg

Academic dissertation

Åbo Akademi University Faculty of Technology

Process Chemistry Centre

Laboratory of Inorganic Chemistry

Preface

Preface The work described in this thesis was carried out at the Process Chemistry Centre at Åbo

Akademi University from 2002 to 2007 and at CRCT, École Polytechnique de Montréal

during a six month stay in 2004. Funding for the work has been received from several

sources: Nordic Graduate School of Biofuel Science and Technology, part of the Nordic

Energy Research, the Fondation de l’École Polytechnique de Montréal, U.S. Borax Inc.,

Andritz Oy, Foster Wheeler Energia Oy, International Paper Inc., Kvaerner Power Oy,

Oy Metsä Botnia Ab, Vattenfall Utveckling AB and the National Technology Agency of

Finland (TEKES). All financial support is gratefully acknowledged.

Professor Rainer Backman has been the main supervisor of the work presented in this

thesis. I wish to express my deepest gratitude to Rainer for giving me the opportunity to

do research on interesting topics in the field of high-temperature inorganic chemistry.

The endless hours we have spent discussing thermodynamics, chemistry, and science in

general have always kept me inspired to push forward in my research. I especially

appreciate that he has always been available to help and support me in my work.

The thermodynamic modeling presented in publications III-VI was performed together

with Professor Patrice Chartrand at CRCT, École Polytechnique, in Montréal, Canada.

The modeling work was planned in cooperation with Professor Chartrand, and he

functioned as my supervisor during my visits to Montréal. I wish to thank Patrice for

giving me the opportunity to visit CRCT, Montréal and for his supervision during my

stays there. Patrice’s dedication to my work has helped me tremendously, and for that I

am greatly thankful. I also want to acknowledge all the people at CRCT for making my

stays in Canada enjoyable.

I want to express my gratitude to Professor Mikko Hupa for giving me the opportunity to

do my doctoral studies at the Laboratory of Inorganic Chemistry. His competence and his

positive attitude have been a source of inspiration and it has given me a great platform for

my doctoral studies.

Special thanks go to Mr. Linus Perander for performing the experimental work for

Publication II, as well as being a co-author of the paper. In addition, Linus’ comments on

i

Preface

Publications III-VI were valuable. His contribution to the doctoral study has been

important, and his cooperation and friendship are greatly appreciated.

I thank Dr. Saied Kochesfahani and Dr. Helen Rickards for their support on the borate

autocausticizing work, and for their contributions as co-authors to Publication II. Dr.

Nikolai DeMartini and Professor Chris Bale are acknowledged for their comments on

publications related to the thesis, and in addition Mrs. Debby Repka for her comments on

the thesis.

Mr. Peter Backman performed the experimental work for Publications I and VI. I wish to

thank him for his diligence and accuracy in the experimental work.

I want to thank all my colleagues, both past and present, at the Laboratory of Inorganic

Chemistry who have ensured that my doctoral studies have been a tremendously

rewarding time. I especially want to acknowledge Dr. Mischa Theis and Mr. Johan

Werkelin, with whom I have shared the joy and agony of making a doctoral thesis the last

couple of years.

Finally, I want to thank all my friends and my family, whose love and support have kept

my spirits up high during the whole process of making a doctoral thesis. I am especially

grateful to my parents, whose support and encouragement have made it possible for me to

to pursue a career in the field of science.

Åbo, February 2007

Daniel Lindberg

ii

Abstract

Abstract Alkali salt mixtures play an important role in the chemical processes in a kraft recovery

boiler burning black liquor. The smelt, a liquid phase containing mainly Na2CO3 and

Na2S, is the main chemical product from the recovery boiler and is utilized for producing

the pulping chemicals. Several reactions occur in the smelt, such as the sulfur reduction,

which is a reaction between the smelt and the char carbon. Alkali compounds, such as

alkali chlorides and various sulfur-containing species, play an important role in the

formation of deposits on heat exchanger surfaces in the boiler. Molten alkali salts can

also cause corrosion problems in the boiler.

The thermochemistry and melting properties of alkali salt mixtures involved in

black liquor and biomass combustion have been studied by evaluating and optimizing the

thermodynamic data for all known phases in the Na+,K+/CO32-,SO4

2-,S2-,S2O72-,Sx

2-,Cl-,

Va- system using experimental data as input. Additional experimental data for melting

temperatures in the ternary NaCl-Na2CO3-Na2SO4 and KCl-K2CO3-K2SO4 systems were

obtained by simultaneous differential thermal analysis and thermogravimetry and the

results were used as input for the thermodynamic optimization. The thermodynamic

properties of the liquid phase were modeled using the Modified Quasichemical Model in

the Quadruplet Approximation, which is a thermodynamic model developed especially

for molten salts. The obtained thermodynamic database reproduces the solid-liquid

equilibrium of the binary, ternary and quaternary systems within the experimental

uncertainties. The database of thermodynamic data for all phases can be used in Gibbs

energy minimization software for calculating the phase equilibria and all thermodynamic

properties of multicomponent alkaline salt mixtures. The alkali salts are of great

importance for ash-related problems in biomass combustion and for processes in black

liquor combustion. Predictions of the melting behavior of the alkali salts are useful for

understanding the behavior of the smelt bed and the formation of harmful deposits in the

kraft recovery boiler.

Borate autocausticizing is a concept for reducing the lime consumption at pulp

mills by adding boron to the pulping process. The amount of Na2CO3 that needs to be

causticized for the production of white liquor can be reduced by the borate reactions in

iii

Abstract

the kraft recovery boiler. The autocausticizing reactions mainly occur in the smelt or in

burning black liquor droplets.

The effects of chemical and physical variations on the borate autocausticizing

reactions in mixtures of alkali carbonates and alkali borates were studied by simultaneous

differential thermal analysis and thermogravimetry. The results showed that the borate

autocausticizing reactions are reversible, and that high temperatures and low borate

contents enhance the conversion of borates to the preferred orthoborate form. High

potassium contents and high partial pressures of CO2 inhibit the autocausticizing reaction.

High conversion of the autocausticizing reaction can be attained at the conditions

prevalent in the char bed of a kraft recovery boiler. The experimental results can be used

as input for future thermodynamic evaluations of borate-containing alkali salt systems

involved in combustion of boron-containing black liquors.

iv

Svensk sammanfattning

Svensk sammanfattning Alkalisaltblandningar spelar en viktig roll i de kemiska processerna i en sodapanna.

Sodapannesmältan, som huvudsakligen består av Na2CO3 och Na2S, tappas ut ur

sodapannan och används till att producera vitlut. Flera viktiga kemiska reaktioner sker i

smältan. Svavelreduktionen sker huvudsakligen genom en reaktion mellan smälta och

koks. Alkaliföreningar, till exempel alkaliklorider och olika alkali-svavel föreningar, kan

leda till uppkomsten av beläggningar på värmeväxlarytor. Alkalisaltsmältor kan förorsaka

korrosionsproblem i sodapannan.

I denna studie har de termokemiska egenskaperna och smältbeteendet för

alkalisaltblandningar relevanta för svartluts- och biomasseförbränning undersökts genom

en evaluering av experimentella termodynamiska data och fasjämviktsdata för alla kända

faser i det kemiska systemet Na+,K+/CO32-,SO4

2-,S2-,S2O72-,Sx

2-,Cl-,Va-. En

termodynamisk optimering av de termodynamiska funktionerna för dessa faser utfördes

på basen av evalueringen. Smälttemperaturerna för de ternära systemen NaCl-Na2CO3-

Na2SO4 och KCl-K2CO3-K2SO4 undersöktes med simultan differentiell termisk analys

och termogravimetri och resultaten utnyttjades som ingångsdata för den termodynamiska

evalueringen. Smältfasens termodynamiska egenskaper modellerades med den

modifierade kvasikemiska modellen, en termodynamisk modell utvecklad för jonsmältor.

Jämviktsberäkningar med den erhållna termodynamiska databasen återger fastfas-

vätskefasjämvikten för de undersökta binära, ternära och kvaternära systemen inom den

experimentella osäkerheten. Databasen kan utnyttjas i program för kemiska

jämviktsberäkningar baserade på minimering av Gibbs energi för att bestämma

fasjämvikter och termodynamiska egenskaper för system av alkalisalter viktiga för

askrelaterade problem i biomass- och svartlutsförbränning. Smältbeteendet hos

alkalisalter ger information om förhållanden i smältbädden och om hur skadliga

beläggningar uppkommer i sodapannan.

Boratautokausticering är en metod ämnad att reducera kalkförbrukningen vid

pappersmassabruk genom att tillsätta grundämnet bor i massaprocessen. Mängden

Na2CO3 som bör kausticeras för produktionen av vitlut kan minskas genom boratets

v

Svensk sammanfattning

reaktioner i sodapannan. Autokausticeringsreaktionerna sker huvudsakligen i smältan

eller i brinnande svartlutsdroppar.

Effekten av olika kemiska komponenter och fysikaliska förhållanden på

autokausticeringsreaktionerna i blandningar av alkalikarbonater och alkaliborater

undersöktes med simultan differentiell termisk analys och termogravimetri. Resultaten

visade att boratautokausticeringsreaktionerna är reversibla och att höga temperaturer och

låga boratkoncentrationer gynnar omvandlingen av boraterna till ortoborat, som är

gynnsamt för autokausticeringen. Höga kaliumkoncentrationer och högt partialtryck av

CO2 hämmar autokausticeringsreaktionen. En hög omvandlingsgrad av boraterna kan

uppnås vid förhållanden som råder i koksbädden i en sodapanna. De erhållna

experimentella resultaten kan användas som ingångsdata för framtida termodynamisk

evalueringar av alkaliboratblandningars kemi vid användning av bor för att befrämja

autokausticering vid svartlutsförbränning.

vi

Table of contents

Table of contents

Preface.................................................................................................................................. i

Abstract .............................................................................................................................. iii

Svensk sammanfattning ...................................................................................................... v

Table of contents............................................................................................................... vii

List of publications ............................................................................................................. x

1. Introduction..................................................................................................................... 1

1.1 Objective of the study ............................................................................................... 4

2. Alkali salts in the recovery boiler ................................................................................... 5

3. Thermodynamic modeling of alkali salt mixtures involved in black liquor combustion 9

3.1 Overview of the properties of ionic compounds and solutions................................. 9

3.2 Thermodynamic equilibrium modeling .................................................................. 10

3.3 Optimization of phase diagrams and thermodynamic data..................................... 12

3.4 Thermodynamic models of ionic solutions............................................................. 13

3.4.1 Ideal solutions .................................................................................................. 13

3.4.2 Nonideal solutions ........................................................................................... 14

3.4.3 Sublattice models ............................................................................................. 16

3.4.4 Compound Energy Formalism......................................................................... 18

3.4.5 Modified Quasichemical Model in the Quadruplet Approximation ................ 19

3.4.6 Extrapolation of excess Gibbs energy in multicomponent solutions............... 25

3.5 Thermodynamic evaluation and optimization of the Na+, K+/CO32-, SO4

2-, S2-, S2O7

2-, Sx2-, Cl-, Va- system .......................................................................................... 27

3.5.1 The Na-K-S system.......................................................................................... 29

3.5.1.1 Na-S .......................................................................................................... 31

3.5.1.2 K-S ............................................................................................................ 33

3.5.1.3 Na-K.......................................................................................................... 33

3.5.1.4 Na2S-K2S................................................................................................... 34

3.5.1.5 Na2S-K2S-S............................................................................................... 34

vii

Table of contents

3.5.2 The Na+,K+/CO32-,SO4

2-,Cl-,S2-,S2O72- system................................................. 36

3.5.2.1 Binary systems.......................................................................................... 36

3.5.2.2 Na2CO3-Na2SO4........................................................................................ 38

3.5.2.3 Na2CO3-Na2S ............................................................................................ 38

3.5.2.4 Na2SO4-Na2S............................................................................................. 38

3.5.2.5 Na2SO4-Na2S2O7 ....................................................................................... 39

3.5.2.6 NaCl-Na2SO4 ............................................................................................ 41

3.5.2.7 NaCl-Na2CO3............................................................................................ 41

3.5.2.8 NaCl-Na2S................................................................................................. 42

3.5.2.9 K2CO3-K2SO4 ........................................................................................... 43

3.5.2.10 K2CO3-K2S.............................................................................................. 44

3.5.2.11 K2SO4-K2S .............................................................................................. 45

3.5.2.12 K2SO4-K2S2O7......................................................................................... 46

3.5.2.13 KCl-K2SO4.............................................................................................. 47

3.5.2.14 KCl-K2CO3 ............................................................................................. 47

3.5.2.15 Na2CO3-K2CO3 ....................................................................................... 49

3.5.2.16 Na2SO4-K2SO4 ........................................................................................ 50

3.5.2.17 Na2S2O7-K2S2O7 ..................................................................................... 50

3.5.2.18 NaCl-KCl ................................................................................................ 51

3.5.2.19 Ternary systems ...................................................................................... 52

3.5.2.20 Na2CO3-Na2SO4-Na2S ............................................................................ 53

3.5.2.21 NaCl-Na2CO3-Na2S ................................................................................ 54

3.5.2.22 NaCl-Na2CO3-Na2SO4 ............................................................................ 55

3.5.2.23 KCl-K2SO4-K2CO3 ................................................................................. 57

3.5.2.24 Na2SO4-K2SO4-Na2S2O7-K2S2O7............................................................ 59

3.5.2.25 Na2CO3-Na2SO4-K2CO3-K2SO4 ............................................................. 61

3.5.2.26 NaCl-Na2SO4-KCl-K2SO4 ...................................................................... 63

3.5.2.27 NaCl-Na2CO3-KCl-K2CO3 .................................................................... 64

viii

Table of contents

3.5.3.28 Multicomponent systems: NaCl-Na2SO4-Na2CO3-KCl-K2SO4-K2CO3 . 66

3.6 Discussion ............................................................................................................... 68

3.7 Conclusions............................................................................................................. 68

4. Alkali borates in the kraft recovery boiler .................................................................... 69

4.1 Definitions of nonconventional causticizing concepts ........................................... 70

4.2 Borate autocausticizing........................................................................................... 71

4.2.1 Partial borate autocausticizing ......................................................................... 74

4.3 Objective of the experimental study of borate autocausticizing............................. 76

4.4.1 Borates in the recovery boiler .......................................................................... 76

4.4.1.1 Alkali orthoborates.................................................................................... 78

4.4.1.2 Alkali diborates......................................................................................... 78

4.4.1.3 Alkali metaborates .................................................................................... 79

4.4.1.4 Molten alkali borates................................................................................. 79

4.5 Experimental setup.................................................................................................. 82

4.6 Results..................................................................................................................... 84

4.7 Discussion ............................................................................................................... 90

4.8 Conclusions............................................................................................................. 92

5. Conclusions and implications ....................................................................................... 93

References......................................................................................................................... 95

Appendix A: Thermodynamic data of pure compounds

Appendix B: Thermodynamic functions of solid solutions

Appendix C: Interaction parameters of the liquid phase

ix

List of publications

List of publications

I. Lindberg, D., Backman, R. (2004) Effect of temperature and boron contents on the

autocausticizing reactions in sodium carbonate/borate mixtures. Industrial and Engineering Chemistry Research, 2004, 43, 6285-6291.

II. Lindberg, D., Perander, L., Backman, R., Hupa, M., Kochesfahani, S., Rickards, H.

(2005) Borate autocausticizing equilibria in recovery boiler smelt. Nordic Pulp and Paper Research Journal, 2005, 20(2), 232-236.

III. Lindberg, D., Backman, R., Hupa, M., Chartrand, P. (2006) Thermodynamic

evaluation and optimization of the (Na+K+S) system. The Journal of Chemical Thermodynamics, 2006, 38(7), 900-915.

IV. Lindberg, D., Backman, R., Chartrand, P. (2006) Thermodynamic evaluation and

optimization of the (Na2SO4+K2SO4+Na2S2O7+K2S2O7) system. The Journal of Chemical Thermodynamics, 2006, 38(12), 1568-1583

V. Lindberg, D., Backman, R., Chartrand, P. Thermodynamic evaluation and

optimization of the (Na2CO3+Na2SO4+Na2S+K2CO3+K2SO4+K2S) system. The Journal of Chemical Thermodynamics, In Press

VI. Lindberg, D., Backman, R., Chartrand, P. Thermodynamic evaluation and

optimization of the (NaCl+ Na2SO4+Na2CO3+KCl+K2SO4+K2CO3) system. The Journal of Chemical Thermodynamics, In Press

x

Chapter 1- Introduction

1. Introduction

The kraft pulping process is the main chemical pulping process in the world today. In

contrast to the mechanical pulping processes, chemical pulping processes separate the

cellulose from wood chips by chemical means,. In the kraft pulping process, the wood

chips are cooked in an alkaline solution containing dissolved Na2S and NaOH. Lignin

and some carbohydrate material are dissolved from the wood chips during cooking. The

resulting pulp, which is made up mainly of wood fibers, is separated from the cooking

solution and used for the production of different pulp and paper products. The spent

cooking solution, which is called black liquor, contains the dissolved organic matter, the

inorganic material from the wood, and the spent cooking chemicals. The processing of

the black liquor is an integral part of pulp mill operations. Much of the water has to be

evaporated from the black liquor so that it can be burned. The concentrated black liquor

is combusted in the kraft recovery boiler to produce heat and power and to convert the

inorganic substances into regenerable forms. Sodium and sulfur compounds are

converted under reducing conditions into a liquid phase called the smelt, consisting of

Na2CO3 and Na2S. The smelt flows from the furnace floor to a dissolving tank for further

processing where the alkaline cooking solution is recovered. A schematic diagram of the

processes and streams in the chemical recovery cycle of a typical kraft pulp mill is shown

in Figure 1.1.

1


PULP FIBRES

CHIPS Pulping

WHITE LIQUOR

Weak black liquor

Washing

H2O

H2O

Black liquor

Evaporators

Smelt

Recovery boiler

Paper mill

Green liquor

Dissolver

Causticising Lime kilnLime

Lime mud

Flue gases

Flue gasesSteam

Electricity

Figure 1.1. Schematic diagram of chemical recovery in the kraft pulping process

The dual role of the kraft recovery boiler as both a chemical reactor and a

heat/power boiler presents unique challenges compared to traditional heat and power

boilers. Not only should the heat be recovered and emissions kept low, but also a

chemical product of the desired quality should be produced. The fuel, black liquor, adds

to the complexity of the processes in the kraft recovery boiler, because it contains large

amounts of sodium and sulfur originating from the cooking chemicals. This gives it

unusual combustion properties compared to other fuels, which can lead to serious

problems with fouling, plugging, and corrosion in the recovery boiler.

In many of the processes in the kraft recovery boiler, the role of inorganic alkali

compounds is central. The main reaction related to chemical recovery in the boiler, the

reduction of sulfur to the preferred sulfide species S2-, involves reactions between char

carbon and molten sodium compounds containing sulfurous anions [1]. In addition,

organically associated sodium plays an important catalytic role in the conversion of the

2


char carbon [2-4]. In some of the more problematic aspects of operations in the recovery

boiler, like fouling, plugging, and corrosion, the role of molten salts is significant. The

behavior of molten salts is also of great interest when developing new technologies or

concepts for chemical recovery from black liquor. In the direct causticizing or

autocausticizing concepts, chemicals are added to or are present in the chemical recovery

cycle in order to decrease the load on the causticizing units of the pulp mill. Many of the

important reactions involved occur in the liquid phase in the recovery boiler [5].

The chemical behavior of the various alkali compounds and their mixtures is of

utmost importance for processes occurring in the kraft recovery boiler and other similar

devices. Several approaches are required to investigate the behavior of the alkali

compounds and their mixtures in the kraft recovery boiler, and to predict how they affect

the processes. Experimental studies are the basis for understanding the chemical

processes in the recovery boiler. Data on the chemical equilibrium of reactions, rates of

reactions, and mass transfer of the different phases and species are needed to understand

the chemical reactions in the kraft recovery boiler. However, in the study of complex

chemical processes, such as the combustion of black liquor and the reactions related to

chemical recovery occurring on such a large scale, the need for proper modeling tools

arises. Thermodynamic modeling gives the equilibrium composition of phases and

species under specified conditions, while chemical kinetics modeling takes into account

the temporal variation of the chemical reactions. Additional models for diffusion in

particles and for fluid flow are essential, as thermodynamic modeling does not consider

how particles come into contact with each other, which is important when chemical

reactions involve two or more reactants. To obtain a comprehensive understanding of the

chemistry in the kraft recovery boiler requires all the above-mentioned modeling

approaches plus other models. Computational fluid dynamics (CFD) can be used to

construct comprehensive models of the processes in the kraft recovery boiler, but the

validity of such simulations is dependent on the various submodels that are used.

Thermodynamic modeling is often used to predict the melting properties of the

inorganic condensed phases in the boiler; it is based on Gibbs energy minimization

techniques, assuming that the Gibbs energy of all phases is known. For the

thermodynamic modeling to be a useful and accurate tool, it is essential to have a

3


consistent set of thermodynamic data for all phases. The thermodynamic data for solution

phases must also be modeled, which requires the choice of appropriate solution models.

The Calphad method is a procedure to evaluate the phase equilibrium and thermodynamic

data and to optimize the Gibbs energy functions of the phases involved. With an

appropriate description of the thermodynamic properties of the alkali salt mixtures,

several important phenomena in the kraft recovery boiler can be modeled and understood,

such as melting of the recovery boiler smelt and superheater deposits, sulfur reduction

reactions, autocaustizing reactions, and volatilization of alkali compounds.

1.1 Objective of the study

The objective of the present study was to gain a better understanding of the reactions and

phase relations of alkali salts in the kraft recovery process. The thermodynamic

properties of the alkali salt mixtures typically found in the kraft recovery boiler, mainly

sodium and sulfur-containing salts, were evaluated and optimized based on experimental

data from the literature to obtain a consistent thermodynamic database. The database can

be used to model and shed light on phenomena occurring in the kraft recovery boiler,

such as smelt bed behavior, deposit formation and corrosion. The main emphasis was on

the solid-liquid equilibrium of alkali salt mixtures, but the solid phase equilibrium and the

solid-liquid-gas equilibrium were also studied. Additional experiments were conducted

for ternary systems to produce new input data for the thermodynamic evaluation. In

addition, an experimental study was carried out on the reactions of borates in alkali salt

mixtures to understand the effect of chemical components and physical conditions on the

borate autocausticizing concept. The results can be used as input for future

thermodynamic evaluations of alkali borate mixtures, which play an important role in the

combustion of boron-containing black liquors.

4

Chapter 2-Alkali salts in the recovery boiler

2. Alkali salts in the recovery boiler

Black liquor is a complex material consisting of water, organic residues from pulping,

and dissolved or solid inorganic compounds. The specific properties and composition of

black liquor are dependent on the raw material and the processes used by the pulp mill.

The primary organic compounds are lignin, polysaccharides, carboxylic acids and

extractives. The inorganic compounds are alkali salts such as Na2CO3, Na2S, Na2S2O3,

Na2SO3, Na2SO4, NaCl, NaOH, NaHS, Na2Sx, and corresponding potassium compounds

[6]. These salts may be solid or dissolved, depending on the water content of the black

liquor. A large part of the sodium and sulfur that forms inorganic salts in the recovery

boiler exists in organic compounds in the black liquor. The speciation of the elements in

the black liquor is dependent on the pulp mill processes and can vary considerably within

a pulp mill and between different mills. The elemental composition of typical

Scandinavian and North American virgin black liquors is given in Table 2.1. The main

difference between the elemental composition of black liquor and that of solid fuels such

as coal, wood, and straw, is the higher concentration of sodium and sulfur. Black liquor

has unique characteristics as a fuel due to its high water content and the high inorganic

material content, which give it low heating values compared to other fuels.

Table 2.1. Typical elemental composition (in wt-%) of black liquor from softwood and hardwood black liquors from Scandinavia and North America on a dry solid basis [6]. Scandinavian wood North American wood

Element Softwood (pine) Hardwood (birch) Softwood (pine) Hardwood

Typical Range Typical Range Typical Range Typical Range

Carbon, % 35.0 32-37 32.5 31-35 35.0 32-37.5 34.0 31-36.5

Hydrogen, % 3.6 3.2-3.7 3.3 3.2-3.5 3.5 3.4-4.3 3.4 2.9-3.8

Nitrogen, % 0.1 0.06-0.12 0.2 0.14-0.2 0.1 0.06-0.12 0.2 0.14-0.2

Oxygen, % 33.9 33-36 35.5 33-37 35.4 32-38 35.0 33-39

Sodium, % 19.0 18-22 19.8 18-22 19.4 17.3-22.4 20.0 18-23

Potassium, % 2.2 1.5-2.5 2.0 1.5-2.5 1.6 0.3-3.7 2.0 1-4.7

Sulfur, % 5.5 4-7 6.0 4-7 4.2 2.9-5.2 4.3 3.2-5.2

Chlorine, % 0.5 0.1-0.8 0.5 0.1-0.8 0.6 0.1-3.3 0.6 0.1-3.3

Others, % 0.2 0.1-0.3 0.2 0.1-0.3 0.2 0.1-2.0 0.5 0.1-2.0

5


The main purpose of the combustion of black liquor is to produce heat, which can

be recovered and utilized for other processes; it also provides energy for the conversion

of inorganic compounds into the smelt, which is recovered and processed into the

cooking chemicals for the pulping process. Black liquor, which has been dried to a dry

solid content of 70-85%, is sprayed as droplets into the recovery boiler furnace.

Combustion occurs in several stages: As black liquor droplets enter the furnace, they are

dried and water vapor is released. Next, they are heated and gas components with low

molecular weights, such as CO, CO2, CH4, H2 and H2S, are released in the pyrolysis or

devolatilization stage [7]. The devolatilization stage is usually associated with a

considerable increase in the black liquor droplet volume. The combustible gases are

burned when they come into contact with oxygen. Finally, the solid char matrix begins

reacting with oxygen. Much of the inorganic matter remains in the char, and during the

char carbon conversion, the important sulfur reduction reactions occur. The overall

reduction reaction can be described by the following equation:

Na2SO4(l) + 2(1+X) C(s) ⇌ Na2S(l) + 2(1-X) CO2(g) + 4X CO(g), [0 ≤ X ≤1]. [Eq. 2.1]

The reduction of sulfate to sulfide is an endothermic process, and the energy required for

the reaction is provided by the heat released when the char carbon burns. Organically

associated sodium plays an important catalytic role in the conversion of the char carbon

[2-4]. As the char carbon burns away, the remaining molten salt coalesces and forms the

smelt. If the smelt comes into contact with oxygen, the sulfide can be re-oxidized

according to the following reaction:

Na2S(l) + 2 O2(g) ⇌ Na2SO4(l) [Eq. 2.2]

In reality all the different stages of black liquor droplet combustion overlap [8, 9].

Ideally, in the recovery boiler, the drying and the devolatilization steps take place

in flight before the droplets reach the char bed at the bottom of the furnace. Char

6


combustion and sulfur reduction take place on the char bed, and the smelt containing

Na2S and Na2CO3, is removed from the recovery boiler before re-oxidation occurs.

In addition to the combustion of black liquor and the sulfur reduction, there are

other processes involving alkali compounds that are important for the operations of the

recovery boiler. The volatilization and condensation of alkali salts play an important role

in the formation of so-called fume, which can cause unwanted deposit buildup on heat

exchangers. Also, Na2CO3 can react with carbon, producing sodium vapor, CO, and CO2

in the recovery boiler [10]. The overall reaction is given by Equation 2.3:

Na2CO3(s,l) + X C(s) ⇌ 2 Na(g) + (2X-1) CO(g) + (2-X) CO2(g) [0.5≤X≤2]. [Eq. 2.3]

The formation of gaseous Na-compounds is enhanced by the higher furnace temperatures

achieved by lowering the water content of the black liquor. The condensation of the alkali

vapors is related to fume formation in the boiler, which can cause deposit buildup on heat

exchangers. The fume particles generally have a diameter of about 0.1 to 1 μm [11]. In

modern boilers, which burn black liquor with a high dry solids content, SO2 emissions are

very low because SO2 reacts with gaseous Na-compounds to form condensed Na2SO4,

which makes up a large part of the fume particles. Moreover, NaCl and KCl are also

enriched in the fume because the chlorides have higher volatility than the other alkali

compounds in the boiler.

The formation of alkali salt deposits on heat exchanger surfaces is also related to

the formation of carryover particles. Carryover particles are black liquor droplets or

fragments of burning droplets that are mechanically entrained by the furnace gases. The

size of carryover particles varies between 20 μm and 3 mm [11]. Their composition is

similar to that of oxidized smelt, as the particles originate from entrained smelt or black

liquor particles. However, mature carryover deposits generally have higher sulfate

concentration due to sulfation of carbonates and/or chlorides. The deposits in the kraft

recovery boiler are mixtures of fume particles and carryover particles in a ratio which

varies in different parts of the boiler.

Corrosion in the recovery boiler is often related to the presence of molten alkali

salts. The existence of low-melting sodium polysulfides (Na2Sn, n>1) in the char bed has

7


been suggested by Backman et al. [12] as a source of furnace floor corrosion. The alkali

polysulfides melt at considerably lower temperatures than a mixture of Na2CO3, Na2SO4,

and Na2S. Generally, the floor temperatures are kept below the melting temperatures of

the smelt. However, the existence of a liquid phase in contact with the furnace floor may

cause corrosion of the floor material at low temperatures. Corrosion of superheaters is

often attributed to molten salt corrosion [13]; a liquid phase in the deposits is the

corrosive agent. High concentrations of chlorides in the deposits usually give low first-

melting temperatures and are often related to increased corrosion of the superheaters.

However, the mechanisms of chlorine-induced corrosion are not fully understood.

Formation of low-melting acidic sulfates, such as alkali disulfates (Na2S2O7, K2S2O7) and

alkali hydrogen sulfates (NaHSO4, KHSO4), are also related to corrosion in recovery

boilers burning black liquors with high sulfur contents [14].

Alkali borate compounds also play an important role in the autocaustizing concept

in recovery boilers firing borate-containing liquors. The behavior of alkali borates is

discussed in detail in Section 4.

8

Chapter 3-Thermodynamic modeling

3. Thermodynamic modeling of alkali salt mixtures involved in black

liquor combustion

3.1 Overview of the properties of ionic compounds and solutions

The solid and liquid alkali compounds in a kraft recovery boiler are ionic compounds.

The solid sodium and potassium compounds, such as Na2SO4, Na2CO3 and KCl, are often

called salts. The term “salt” has traditionally been used for table salt or rock salt (NaCl)

and for the ionic solid product that is formed when a metal hydroxide or oxide (base)

reacts with an acid. The term “molten salt” is commonly used both in industry and in the

scientific community to describe high-temperature ionic liquid phases. The term “ionic

liquid” is mainly used for low or room temperature liquids of an ionic nature.

Ionic compounds consist of electrically charged components, anions and cations,

which are attracted to or repelled by each other due to Coulomb forces. The result is that

ionic crystals have strong ordering, in which anions are surrounded by cations and cations

are surrounded by anions in the crystal lattice. The anions reside on an anionic sublattice,

with cations as the nearest neighboring ions, and vice versa for the cations. Ionic

compounds usually have low volatility and high melting temperatures (except for room

temperature ionic liquids), and in the liquid state, they are electrically conductive due to

the mobility of the ions. In the liquid state, the ions are also arranged with anions

surrounded by cations, and vice versa. Due to their mobility in the liquid state, the ions

are not restricted to fixed lattice sites, but for modeling purposes quasi-sublattices for the

anions and cations are used to describe the thermodynamic properties of ionic liquid

phases [15-18].

Ionic melts have great importance in many industrial fields. In the manufacture of

aluminum, molten cryolite (Na3AlF6) is the base solvent for Al2O3 in Hall-Héroult

electrolysis cells [19]. Molten alkali and alkaline earth chloride mixtures are used as

electrolytes in the production of metallic sodium and magnesium, where the

corresponding chloride is electrolyzed to the metallic form, and the other chloride salts

act as fluxes to lower the melting temperature of the mixture [19]. In the molten

9


carbonate fuel cell (MCFC) and the sodium-sulfur battery [20], which have been

developed for medium-scale electricity production, ionic melts play an important role in

the electrochemical reactions. The molten salt reactor (MSR) [21] is considered to be a

promising type of nuclear reactor belonging to the class known as generation IV reactors.

In this type of reactor, the fuel is uranium or plutonium fluorides dissolved in a molten

mixture of NaF and ZrF4. Silicate melts, which consist of polymeric ionic species, are

used for example in glass manufacturing.

Ionic melts play an important role in chemical reaction engineering. In the

production of sulfuric acid, a molten mixture of alkali disulfates and V2O5 is the catalyst

for the oxidation reaction of SO2 to SO3 in the contact process [19]. Low temperature or

room temperature ionic liquids, which are molten organic salts, are becoming

increasingly important as solvents and catalysts in chemical reaction engineering because

of their thermal stability, low volatility, and ability to dissolve different types of chemical

substances. The ionic species in ionic liquids are usually much more complicated than

those in many inorganic salts, and the ionic liquids can be tailor-made for the specific

purposes.

The production of smelt in kraft pulping is one of the largest molten salt

producing chemical processes today. About 200 million tons of black liquor dry solids

are produced annually worldwide [22], and roughly one third of the mass is transformed

into smelt, which is used for the production of pulping chemicals

3.2 Thermodynamic equilibrium modeling

In order to predict the chemical behavior of multicomponent multiphase systems,

computational methods are needed to calculate the chemical equilibrium, the reaction

kinetics, and the transport properties of the species of interest. This becomes very

complicated for systems involving solid phases, a liquid phase, and a gas phase,

especially if the chemical composition of the phases varies. The mathematical models

need experimental data as input for the model parameters. Unfortunately for many

10


complex systems, these data do not exist or experimental results are too complicated to

use for extracting model parameters. Therefore, a good description of the chemical

behavior in simplified systems is essential for making predictions in more complicated

systems.

Thermodynamic modeling is a commonly used tool for predicting the chemical

behavior of complex systems. It is often based on minimization of the Gibbs energy of

the system, which can be calculated using modern software if thermodynamic data exist

for all the phases considered. Thermodynamic data for multicomponent solution phases

are based on the thermodynamic data of the end-member components and on the

interaction parameters of the solution model describing the Gibbs energy of the solution

phase. Thermodynamic modeling is also important in kinetic modeling [23] and in

modeling diffusion in alloys [24].

The computational methods involved in calculating multiphase multicomponent

thermodynamic chemical equilibrium revolve around Gibbs energy minimization [23].

The classical method of calculating the phase equilibrium from equilibrium constants is

not suitable for large multicomponent multiphase systems.

The true chemical equilibrium can be calculated by considering the Gibbs energy

of all phases and minimizing the total Gibbs energy of the system (G). Here, G can be

calculated either from the knowledge of the chemical potential ( iG , μi) of component i,

by

∑=i

ii GnG , [Eq. 3.1]

where ni is the amount of component i, or alternatively by

∑=φ

φφmGNG , [Eq. 3.2]

where Nφ is the amount of the phase and is the Gibbs energy of the phase. φmG

For a given set of constraints, such as fixed P, T, and overall composition, the

Gibbs energy minimization algorithms find the amounts of the various phases and the

composition of the solution phases which give a global minimum in the total Gibbs

energy of the system. One of the best-known Gibbs energy minimization programs is

11


SOLGASMIX by Eriksson [25]. This program has evolved over the years and is currently

an integral part of the thermochemical software package FactSage [26]. In the present

study, all thermodynamic calculations were performed using FactSage. Several other

programs have also been developed for thermochemical calculations. An entire issue of

the Calphad Journal is dedicated to reviews of many existing programs (Volume 26, issue

2, 2002).

3.3 Optimization of phase diagrams and thermodynamic data

Phase diagrams and phase equilibria can be calculated if the Gibbs energy functions of all

phases involved are known. If the Gibbs energy functions for a phase are not known but

experimental data for phase equilibrium or thermodynamic properties exist, it is possible

to obtain a thermodynamic description of the phase through an optimization procedure,

often called the Calphad method. The principle underlying the Calphad method is to

obtain a set of consistent Gibbs energy functions for all phases in the system of interest

by using experimental thermochemical and phase equilibrium data as input [27]. In many

cases, the main emphasis is on optimizing the Gibbs energy functions of the solution

phases, which in reality means optimizing the interaction parameters of various solution

models. The Gibbs energy functions are obtained by weighted nonlinear optimization of

the thermochemical and phase equilibrium data. Several of the commercially available

thermodynamic software packages include programs for these optimization. The Optisage

module in FactSage [26] was used in the present study. The optimization algorithm in the

program is a nonlinear Bayesian least squares technique [28-30]. The general procedures

for optimizing phase diagrams and thermodynamic data with the Calphad method are

described by Hari Kumar and Wollants [27] and Schimd-Fetzer et al. [31].

12


3.4 Thermodynamic models of ionic solutions

The thermodynamic properties of solution phases as function of composition must be

known to calculate phase equilibrium involving the solutions. For this purpose, different

thermodynamic models have been developed to describe the thermodynamic properties of

solutions. Solution phases are the gas phase, liquid phases and solid solutions. The gas

phase is a solution phase, which shows complete miscibility of all gas species. The non-

ideal behavior of the gas phase can be modeled by several different approaches. The van

der Waals equation was one of the first steps to introduce nonideality to the behavior of

real gases, taking into account the interaction between gas molecules. At the high

temperatures and the atmospheric pressure in a kraft recovery boiler, the non-ideality of

gases is usually not very pronounced; therefore, models for the nonideality of gases is not

treated further in this work. The solution models that are treated in more detail have been

developed for solid solutions or liquid solutions. Several of these models are often used

for both solids and liquids.

For all solution phases, the Gibbs energy is given by the general formula excessmix

idealmix GGGG +Δ+°= , [Eq. 3.3]

where G° is the contribution of the pure components of the phase to the Gibbs energy,

is the ideal mixing contribution, and is the excess Gibbs energy of mixing,

which is the contribution involving the non-ideal interactions between the components.

idealmixGΔ excess

mixG

3.4.1 Ideal solutions

The simplest solution model is an ideal substitutional solution or the Raoultian solution.

This approach is valid for an ideal gas phase and may be valid for simple metallic liquid

or solid solutions, where the components show very similar behavior. The ideal

substitutional solution is characterized by random distribution of components on one

lattice with an interchange energy equal to zero. For the gas phase and liquids, no actual

lattice exists as the crystallographic structure is lost, but for modeling purposes a quasi-

13


lattice or defined spatial positions are used to model the mixing of particles. For an ideal

substitutional solution, the excess Gibbs energy of mixing ( ) is zero, and as it is

assumed that there is no change in bonding energy or volume upon mixing, the enthalpy

of mixing is also zero:

excessmixG

idealmixHΔ =0. [Eq. 3.4]

The Gibbs energy of mixing is therefore given by the following expression: idealmix

idealmix STG Δ−=Δ . [Eq. 3.5]

The term is related to the Boltzmann equation for configurational entropy, which

deals with the entropy associated with random distribution of particles over a given

number of positions, and is given by the following expression:

idealmixSΔ

idealmixSΔ

∑−=Δi

iiidealmix xxRS ln . [Eq. 3.6]

The molar Gibbs energy of an ideal solution is

∑∑ +=i

iii

oiim xxRTGxG ln , [Eq. 3.7]

where is the Gibbs energy of the phase containing the pure component i. Ideal

solutions are uncommon for condensed phases as there usually is some interaction

between the components of the solution.

oiG

3.4.2 Nonideal solutions

The regular solution model is the simplest thermodynamic model for nonideal solutions.

The regular solution model considers that the magnitude and sign of the interactions

between components in a phase are independent of composition. If the total energy of the

solution (E0) originates from only nearest-neighbor bond energies in a system A-B then

E0=ωAAEAA+ωBBEBB+ωABEAB, [Eq. 3.8]

14


where ωAA, ωBB, ωAB are the number of bonds and EAA, EBB, EAB are energies associated

with the formation of different bond types AA, BB and AB. If there are N atoms in the

solution and the coordination number for nearest-neighbors is Z, the number of different

bond types formed in a random solution will be

2

21

AAA NZx=ω , [Eq. 3.9.1]

2

21

BBB NZx=ω , [Eq. 3.9.2]

BAAB xNZx=ω , [Eq. 3.9.3]

where xA and xB are the mole fractions of A and B. By substituting Equations 3.9.1-3.9.3

into Equation 3.8, the total energy of the solution will be given by the expression

B

))2((20 BBAAABBABBBAAA EEExxExExNZE −−++= . [Eq. 3.10]

By subtracting the energy of pure A and pure B from Equation 3.10, the energy change

for mixing A and B to an A-B solution will be

))2((2 BBAAABBA EEExxNZE −−=Δ . [Eq. 3.11]

One can approximate that ΔE≈ ΔHmix, where ΔHmix is the enthalpy of mixing. If the bond

energies are temperature-dependent, there will also be a term for excess entropy of

mixing, which can be derived in a similar fashion as for ΔHmix. The excess Gibbs energy

of mixing for the regular solution model is given by

Ω=Δ−Δ= BAexcessmixmix

excessmix xxSTHG , [Eq. 3.12]

where Ω is a composition-independent, temperature-dependent interaction parameter.

The general expression for the Gibbs energy of a regular solution is as follows:

∑∑∑∑>

Ω++=i ij

ijjii

iii

oiim xxxxRTGxG ln . [Eq. 3.13]

However, it has been realized that the assumption of composition-independent

parameters for the excess Gibbs energy is too simple for many systems. The approach

where the interaction terms change linearly with composition is called a subregular

15


solution model. Even more complex compositional dependencies can be adopted. The

Redlich-Kister form, (xA-xB) , where n is a positive integer, is a common form of

expressing composition-dependent terms of the excess Gibbs energy. The Gibbs energy

of the solution with the excess Gibbs energy expressed in Redlich-Kister form is

B

n

∑∑ ∑∑∑>

−Ω++=i ij n

nji

nijji

iii

i

oiim xxxxxxRTGxG )(ln , [Eq. 3.14]

where the term is a binary interaction parameter dependent on the value of n.

Equation 3.14 will reduce to Equation 3.13 if n=0. According to Saunders and

Miodownik [23], the value of n does not usually go above 2. If higher power expansions

are needed to describe G

nijΩ

excess, an incorrect model has probably been chosen to model the

solution. Other equivalent polynomial expansions, such as a simple power series or

Legendre expansions are also used [32].

3.4.3 Sublattice models

Simple nonpolar molecular solutions and ionic solutions, such as molten salts, often

exhibit approximately regular solution behavior according to Pelton [33]. Sangster and

Pelton [34] showed that the liquid phase and solid solutions in many of the binary

common-anion or common-cation systems of alkali halides can be modeled with regular

or subregular solution models. However, substitutional solution models are not suitable

for more complex ionic solutions with several cations and anions, or where there is a

strong ordering of the components in the liquid phase, which is the case for some alkali

halide-alkaline earth halide systems.

In a review of thermodynamic models for molten salts and slags, Pelton [35]

showed that an associate model will not predict the phase equilibrium satisfactorily for

ionic solutions, such as K+, Li+//Cl-, F-, where LiF, LiCl, KF and KCl are the solution

components. Instead, models that take into account physical properties of the ionic

16


solutions are needed. Temkin [16] was one of the first to propose a thermodynamic

model of ionic solutions, in which two sublattices are considered. The cations reside on

one sublattice and the anions reside on the other sublattice. The configurational entropy is

governed by the site occupation of the various cations and anions on their respective

sublattices. For a simple reciprocal ionic solution A, B/X, Y, where the cations A and B,

and the anions X and Y have the same absolute value of their ionic charge, the Gibbs

energy of the solution is given by the following expression:

.))ln()ln(())ln(

)ln((Eanion

YanionY

anionX

anionX

cationB

cationB

cationA

cationABY

anionY

cationBBX

anionX

cationBAY

anionY

cationAAX

anionX

cationAm

GxxxxRTxx

xxRTGxxGxxGxxGxxG

++++

++++= oooo

[Eq. 3.15]

The term is the site fraction of a sublattice component i on the sublattice, and

is the Gibbs energy of the pure component AX. If the valence of the cations and

anions varies, the modeling will become more complex. Pelton [36] developed a

sublattice model for molten salts, in which equivalent cationic and anionic fractions are

used instead of site fractions. The equivalent fractions are defined as

sublatticeix

oAXG

∑=i

iiiii nqnqY / . [Eq. 3.16]

The term qi is the absolute charge of the ion i, and ni is the number of moles of i on the

sublattice. The Gibbs energy of the solution is given by the expression

E

AAAAXXXXA X

AXXAm GxxxqxxxqRTGYYG +++= ∑∑∑∑∑∑ −− ))ln()()ln()(( 11o .

[Eq. 3.17]

A thermodynamic database for the Li+, Na+, K+//F-, Cl-, OH-, CO32-, SO4

2- system has

been developed using the sublattice model for molten salts [36], which gives good

estimates of the thermodynamic properties of multicomponent liquids.

Hillert et al. [18] also developed a sublattice model for ionic solutions, which is

known as the ionic two-sublattice model for liquids. The model can accommodate

hypothetical charged vacancies and neutral species on the anionic sublattice, meaning

17


that the solution composition can vary between a metallic state and a fully ionized state.

More in-depth descriptions of the sublattice models are given by Pelton [36] and Hillert

et al. [18].

3.4.4 Compound Energy Formalism

The Compound Energy Formalism is a mathematical formalism, which is commonly

used for describing the thermodynamic properties of solutions that are modeled with

sublattice solution models. In the present work, the thermodynamic properties of all

multicomponent solid solutions are described using the Compound Energy Formalism

[37, 38].

Sodium and potassium salts, such as sulfates, disulfates, carbonates, and

chlorides, tend to form complex solid solutions. In general, these solid salt solutions can

be considered to consist of sublattices, which contain the ionic components. In the

simplest case with two sublattices, one sublattice contains the cations, such as K+ and

Na+, and the other sublattice contains the anions, such as SO42- and CO3

2-. More

complicated sublattice configurations may be considered. The solid solution might have

several cationic crystal sites, where one cation is preferred on one site, and another cation

is preferred on another site. A classical example is the spinel phase, AB2O4, where A2+

resides on sites with tetrahedral coordination, and B3+ resides on sites with octahedral

coordination. The phase can be considered to consist of three sublattices, as O2- resides

on a third, anionic sublattice.

For the reciprocal solution phase (A,B)m(C,D)n, where the species A and B reside

on the sublattice S, and the species C and D reside on a second sublattice T, the molar

Gibbs energy of the solution is given by the following expression:

.))lnln()lnln((::::

ETD

TD

TC

TC

SB

SB

SA

SA

DBTD

SBCB

TC

SBDA

TD

SACA

TC

SAm

GyyyynRTyyyymRT

GyyGyyGyyGyyG

+++++

+++= oooo

[Eq. 3.18]

18


The first four terms give the reference Gibbs energy of the solution, where is the site

fraction of species A on sublattice S, is the standard molar Gibbs energy of the end-

member component A

SAy

oCAG :

mCn, and correspondingly for the other sublattice species and end-

member components. The two following terms give the ideal entropy of mixing (Temkin

type [16]), assuming a random distribution of the sublattice species on their respective

sublattices, and the final term is the molar excess Gibbs energy. The excess Gibbs energy

is given by the following expression:

DCBATD

TC

SB

SADCB

TD

TC

SBDCA

TD

TC

SADBA

TD

SB

SACBA

TC

SB

SA

E LyyyyLyyyLyyyLyyyLyyyG ,:,,:,::,:, ++++=

[Eq. 3.19]

The four first terms are interaction parameters of the four binary subsystems, and the last

term is a reciprocal interaction parameter. The L factors can be temperature- and

composition-dependent, commonly given as Redlich-Kister terms as function of the site

fraction.

3.4.5 Modified Quasichemical Model in the Quadruplet Approximation

The regular solution model and modifications of it, together with sublattice models

mentioned above, assume that the mixing of particles is random, even when the excess

Gibbs energy is not zero. However, several systems show considerable short-range

ordering in the liquid phase, especially oxide systems where polymeric units are present.

Examples are silicate, borate and phosphate liquids. Similar strong short-range ordering

can be found in many binary liquids consisting of alkali halides together with divalent or

trivalent metal halides. The Quasichemical Model was developed by Guggenheim [39]

and Fowler and Guggenheim [40] to take into account non-random short-range ordering

in solutions. Pelton and Blander [41] and Blander and Pelton [42] modified the model,

with further developments made by Pelton and Chartrand [43], Chartrand and Pelton

[44], and Pelton et al. [17, 45], by making the model more flexible and by merging the

19


quasichemical model with sublattice models. The article by Pelton et al. [17] on the

Modified Quasichemical Model in the Two-Sublattice Quadruplet Approximation is the

latest development of the Modified Quasichemical Model, permitting the treatment of

both first-nearest-neighbor and second-nearest-neighbor short-range ordering

simultaneously in molten salt solutions.

For the liquid solution, the thermodynamic model must take into account cations

and anions being distributed on a cationic and an anionic quasi-sublattice. If there are two

or more cations and two or more anions in the solution, the phase will be a

multicomponent reciprocal solution. Large deviations from ideal mixing can occur in

reciprocal molten salt solutions due to the strong first-nearest-neighbor (cation-anion)

interactions. Simultaneously, strong second-nearest-neighbor (cation-cation, or anion-

anion) interactions can occur, making modeling of such systems difficult.

The Modified Quasichemical Model in the Two-Sublattice Quadruplet

Approximation [17] was used in the present work to model the Gibbs energy of the liquid

phase. This model was developed particularly for molten salt solutions that exhibit

strong short-range ordering (SRO) between ions of opposite charges (first-nearest-

neighbours, FNN) and between ions of the same charge (second-nearest-neighbors,

SNN). The Modified Quasichemical Model in the Two-Sublattice Quadruplet

Approximation simultaneously evaluates the impact of all FNN exchange pair reactions

(similar to Eq. 3.20) and all reactions involving SNN pairs (similar to Eq. 3.21.1 and

3.21.2) on the configurational entropy:

[ ] [ ] [ ] [ ]pairpairpairpair CONaClKClNaCOK 33 −+−=−+− ClCONaKg ,/, 3Δ . [Eq. 3.20]

[ ] [ ] [ ]pairpairpair KSONaKSOKNaSONa −−=−−+−− 444 2 4/, SOKNagΔ , [Eq. 3.21.1]

[ ] [ ] [ ]pairpairpair SONaCOSONaSOCONaCO 434433 2 −−=−−+−− 43 ,/ SOCONagΔ .

[Eq. 3.21.2]

If the standard Gibbs energies of Eq. 3.20 and Eq. 3.21 are negative, the equilibrium will

be shifted to the right and FNN and SNN pair concentrations will be affected accordingly

(resulting in FNN SRO and SNN SRO). If the values of the standard Gibbs energies of

Eq. 3.20 and Eq. 3.21 are close to zero, the model will be reduced to a random mixing

20


model. In the model, each quadruplet consists of 2 cations and 2 anions forming a

configurational unit that includes 4 FNN pairs and 4 SNN pairs. Each quadruplet has

Gibbs energy, and the parameters of the model are the energies of the quadruplet-

formation reactions. The quadruplets mix randomly and are constrained by an elemental

mass balance. Overlapping of sites and pairs is considered in the configurational entropy.

The Gibbs energy of the quadruplets is defined as follows: The Gibbs energy of a

unary quadruplet consisting of two cations A and two anions X is

ooo

XqAqXqAq XAXXA

XXAA

XA

AXA g

Zqg

Zqg

/1/1

22

/1/1

22

22//

/22

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛= , [Eq. 3.22]

where qA and qX are the absolute charges for the ions A and X, is the second-

nearest neighbor coordination number of A when all A exist in A

AXAZ

22 /

2X2 quadruplets, and

is the standard Gibbs energy of the related pure component per charge

equivalent. The term is the standard Gibbs energy of per mole of A

o

XqAq XAg/1/1

o

22 / XAgAX qq XA 2X2

quadruplets. For binary common-anion quadruplets, such as ABX2, and similarly for

binary common-cation quadruplets, such as A2XY, the following reaction between unary

quadruplets can be considered:

[A2X2]quad + [B2X2]quad = 2[ABX2]quad. [Eq. 3.23]

The Gibbs energy change of the reaction is 2/ XABgΔ . The term

2/ XABgΔ is an empirical

parameter of the model and can be expressed as

)(2222 ////

ooXABXABXABXAB gggg Δ−Δ+Δ=Δ , [Eq. 3.24]

where is a function of temperature only, independent of composition, and

is expanded as an empirical polynomial in the quadruplet mole

fraction, . The Gibbs energy of the binary quadruplet ABX

o

2/ XABgΔ

)(22 //

oXABXAB gg Δ−Δ

klijx / 2 is given by the

following expression:

oooo

222

2

22

22

2

22

2 ///

//

/

//2 XABXBB

XAB

BXB

XAAXAB

AXA

XAB ggZZ

gZZ

g Δ+⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛= . [Eq. 3.25]

If = 0, the binary AX-BX liquid solution will be reduced to an ideal solution. For

the Gibbs energy of the reciprocal quadruplet ABXY, , the formation of the

2/ XABgΔ

oXYABg /

21


reciprocal quadruplet from the unary and binary quadruplets is considered. For the

quadruplet formation reaction

½ (ABX2 + ABY2+A2XY+B2XY) = 2(ABXY), [Eq. 3.26]

the Gibbs energy change is . The term

is an empirical parameter of the model, where is a function of temperature only,

and is expanded as an empirical polynomial in the quadruplet mole

fraction, . The Gibbs energy of the reciprocal quadruplets is given by the following

expression [17]:

XYABg /Δ )( ////oo

XYABXYABXYABXYAB gggg Δ−Δ+Δ=Δ

oXYABg /Δ

)( //o

XYABXYAB gg Δ−Δ

klijx /

ooo

oooo

ooo

XYABXYBBXYAB

BXYB

XYAAXYAB

AXYA

YABYXYAB

YYAB

XABXXYAB

XXAB

YBYXYAB

BXYAB

BYBY

YAYXYAB

AXYAB

AYAY

XBXXYAB

BXYAB

BXBX

XAXXYAB

AXYAB

AXAX

YXYAB

YX

XYAB

XXYAB

ggZZ

gZZ

gZZ

gZZ

gZZ

Zqg

ZZZq

gZZ

Zqg

ZZZq

Zq

Zqg

///

//

/

/

//

//

/

//

//

//

//

/

///

//

//

/1

///

2

2

2

2

2

2

2

2

22

22

22

22

22

22

22

22

41

22

22

Δ+⎟⎟⎠

⎞Δ⋅+Δ⋅+

⎜⎜⎝

⎛Δ⋅+Δ⋅+⎟

⎟⎠

⎞⋅+⋅+

⎜⎜⎝

⎛⋅+⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

−

[Eq. 3.27]

The parameters , , 2/ XABgΔ

2/YABgΔ XYAg /2Δ and XYBg /2

Δ are obtained from optimization

of thermodynamic and phase diagram data that involve the liquid phase in the binary

common-ion subsystems. The parameter XYABg /Δ is obtained from optimization of

thermodynamic and phase diagram data in the ternary reciprocal system.

Empirical ternary parameters may also be added to common-ion ternary systems

of the type AX-BX-CX. The ternary parameter gives the effect of a third component, CX,

on the quadruplet-formation energy of the binary AB/X2 quadruplet, . As

described by Pelton and Chartrand [43] and Pelton et al. [17], this is done by introducing

the empirical ternary parameter . The parameter is obtained from

optimization of thermodynamic and phase diagram data in the common-ion ternary

system. The functions of the binary interaction parameters of the type and

, taking into account the effect of the ternary interaction parameters are given by

Pelton et al. [17] (Equations 46-48 in reference [17]).

2/ XABgΔ

ijkXCABg

2/)(ijk

XCABg2/)(

2/ XABgΔ

XYAg /2Δ

22


The Modified Quasichemical Model takes into account non-random mixing of

particles in the solution. Therefore, an expression for the configurational entropy of

mixing, ΔSconfig, similar to Equation 3.6 cannot be used, as Equation 3.6 is an expression

for random distribution of particles. An exact expression for the distribution of all

quadruplets over “quadruplet positions” is not known, but Pelton et al. [17] proposed an

approximate expression for the configurational entropy, which is given by Equation 3.28

for a solution in the A,B/X,Y system:

))/(4

ln

)/(2ln

)/(2ln

)/(2ln

)/(2ln

)/(ln

)/(ln

)/(ln

)/(ln()lnln

lnln()lnlnlnln()/(

////

//

22/

2/

//22

/2

/

//22

/2

/

//

22/

2/

//224

/

//224

/

//

224/

//224

/

//

//

//

//

//

2

2

2

2

2

2

2

2

22

22

22

22

22

22

22

22

YXBAYBXAXBXA

XYABXYAB

YXBYBXB

XYBXYB

YXAYAXA

XYAXYA

YBAYBYA

YABYAB

XBAXBXA

XABXAB

YBYB

YBYB

YAYA

YAYA

XBXB

XBXA

XAXA

XAXA

YB

YBYB

YA

YAYA

XB

XBXB

XA

XAXAYYXXBBAA

config

YYYYxxxxxn

YYYxxx

nYYYxx

xn

YYYxxx

n

YYYxxx

nYYx

xn

YYxx

n

YYxx

nYYx

xn

YYxn

YYxn

YYxn

YYxnxnxnxnxnRS

+

++

+++

+++++

+++++=Δ−

[Eq. 3.28]

The term ni gives the number of moles of a species i, ni/k is the number of moles of first-

nearest-neighbor pairs and nij/kl denotes the number of moles of unary, binary and

reciprocal quadruplets. The term xi denotes the site fractions, xi/k is the FNN pair fraction

and xij/kl is the quadruplet fraction.

The Modified Quasichemical Model in the Quadruplet Approximation requires

the assignment of coordination numbers of a quadruplet species in the unary, binary and

reciprocal quadruplets. The first-nearest-neighbor coordination number is denoted by zi,

and gives the number of first-nearest-neighbor pairs emanating from a species i. The

second-nearest-neighbor coordination number is denoted by Zi, and gives the number of

second-nearest-neighbors pairs emanating from species i. Pelton et al. [17] made the

assumption that the ratio between SNN and FNN coordination numbers for a species i is

constant and is given by the expression:

Zi/zi=ζ/2. [Eq. 3.29]

23


Chartrand and Pelton [46] set the parameter ζ to 2.4 for liquid alkali-alkaline earth halide

systems, and in the present study it was set to the same value. For the quadruplet

approximation, gives the SNN coordination number of a species A when

(hypothetically) all of A exist in ABXY quadruplets. In the present work the SNN

coordination numbers for the quadruplets are as follows:

AXYABZ /

−−

−−−−

++

=

−==

=

====

==

====

========

====

====

VaClWZ

nSOSCOSOYXKNaBA

ZZZZ

ZZ

ZZZZ

ZZZZZZZZ

ZZZZ

ZZZZ

n

XXVaAB

XXVaA

VaXVaAB

VaXVaA

XXClAB

XXClA

ClXClAB

ClXClA

AXZAB

AXZA

ZZWAB

ZZWA

ZZAB

ZZA

AZWAB

AZWA

AZAB

AZA

XXYAB

XXYA

XXAB

XXA

AXYAB

AXYA

AXAB

AXA

,,

)81(,,,,,,

6

8

4

6

6

3

2272

23

24

////

//

////

////////

////

////

22

2

22

22222222

2222

2222

The coordination numbers for quadruplets containing both the charged vacancy (Va-) and

a divalent anion are given erroneously in Publication III. The correct coordination

numbers are given in the list above.

The binary composition variables XYA /2χ , YXA /2

χ , 22 / XABχ and

2/ XBAχ are defined

as previously [17, 43] as follows:

)/(22222222 ///// YAXYAXAXAXYA xxxx ++=χ , [Eq. 3.30.1]

)/(22222222 ///// YAXYAXAYAYXA xxxx ++=χ , [Eq. 3.30.2]

)/(22222222 ///// XBXABXAXAXAB xxxx ++=χ , [Eq. 3.30.3]

)/(22222222 ///// XBXABXAXBXBA xxxx ++=χ . [Eq. 3.30.4]

klijx / denotes the unary, binary and reciprocal quadruplet fractions as defined by Pelton et

al [17].

The Gibbs energy of the solution is given by the model as config

klijklij STgnG Δ−= ∑ // , [Eq. 3.31]

24


where nij/kl denotes the number of moles of the unary, binary and reciprocal quadruplets,

gij/kl denotes the Gibbs energy of the quadruplets, and ΔSconfig is the configurational

entropy of mixing. ΔSconfig is calculated from a distribution of all the quadruplets over

“quadruplet positions” by Equation 3.28.

3.4.6 Extrapolation of excess Gibbs energy in multicomponent solutions

Several methods have been proposed for extrapolating the thermodynamic properties of a

ternary solution from optimized data of its three binary subsystems. The equations of the

extrapolations are based on various geometrical weightings of the mole fractions [47].

The main extrapolation methods are either symmetric or asymmetric. Symmetric methods

treat all three binary systems in the same manner, while asymmetric methods treat one of

the binaries differently from the two others. Asymmetric extrapolation methods are

recommended for ternary systems if two of the components are chemically similar, while

the third is chemically different [48]. Examples of such systems are CaO-MgO-SiO2 and

NaCl-KCl-AlCl3 where SiO2 and AlCl3 are chemically much different than the other

components. The main symmetric extrapolation methods are the Kohler approximation

[49] and the Muggianu approximation [50]. The main asymmetric methods are the

Kohler/Toop approximation [51] and the Muggianu/Toop approximation [47]. For a

ternary A-B-C system, where all binary systems are modeled as subregular solutions with

the subregular terms given in Redlich-Kister formalism, the different extrapolation

equations are given by Equations 3.32-3.35 (Component A is the asymmetric component

in the asymmetric approximations):

Kohler approximation:

))(())(())(( 101010

CB

CBBCBCCB

CA

CAACACCA

BA

BAABABBA

E

xxxxLLxx

xxxxLLxx

xxxxLLxxG

+−

+++−

+++−

+=

[Eq. 3.32]

25


Muggianu approximation: ))(())(()(( 101010

CBBCBCCBCAACACCABAABABBAE xxLLxxxxLLxxxxLLxxG −++−++−+=

[Eq. 3.33]

Kohler/Toop approximation:

))((

))(()((

10

1010

CB

CBBCBCCB

BCAACACCACBAABABBAE

xxxxLLxx

xxxLLxxxxxLLxxG

+−

++

−−++−−+=

[Eq. 3.34]

Muggianu/Toop approximation:

))((

))(()((10

1010

CBBCBCCB

BCAACACCACBAABABBAE

xxLLxx

xxxLLxxxxxLLxxG

−++

−−++−−+=

[Eq. 3.35]

If all binary systems are regular solutions, Equations 3.32-3.35 will become identical

expressions [46, 48]. For additional equations of various approximation models for

multicomponent systems, see Hillert [47], Chartrand and Pelton [46] and Pelton [48].

Figure 3.1 shows the geometrical considerations for the symmetric and asymmetric

models.

26


Figure 3.1. Geometrical constructions of the Kohler, Kohler/Toop, Muggianu and Muggianu/Toop extrapolation models

3.5 Thermodynamic evaluation and optimization of the Na+, K+/CO32-,

SO42-, S2-, S2O7

2-, Sx2-, Cl-, Va- system

The thermodynamic properties of the phases in the multicomponent Na+, K+/CO32-, SO4

2-,

S2-, S2O72-, Sx

2-, Cl-, Va- system were evaluated and optimized in this work. The Modified

Quasichemical Model in the Two-Sublattice Quadruplet Approximation [17], was used to

model the Gibbs energy function of the liquid phase. The Compound Energy Formalism

27


was used for the complex solid solutions, such as the reciprocal (Na,K)2(CO3,SO4,S)

hexagonal phase, while simpler solid solutions, such as solid (Na,K)Cl and solid (Na,K),

have previously been modeled with simple substitutional models. The simpler solid

solution models can also be presented in the Compound Energy Formalism.

The phase equilibrium has not been studied experimentally for all possible binary,

ternary or higher-order subsystems. The evaluation has been separated into four parts,

which represent multicomponent subsystems containing sulfurous ions, whose every

binary subsystem has been studied experimentally previously and has been evaluated and

optimized in the present study. The multicomponent subsystems are Na-K-S, Na2SO4-

K2SO4-Na2S2O7-K2S2O7, Na2CO3-Na2SO4-Na2S-K2CO3-K2SO4-K2S and NaCl-Na2CO3-

Na2SO4-KCl-K2CO3-K2SO4. All thermodynamic data from unary components to

multicomponent systems are internally consistent. The thermodynamic data for the

stoichiometric solid phases, liquid phase components and gaseous compounds studied in

all the above-mentioned subsystems are given in Appendix A. The solution parameters of

the solid solutions are given in Appendix B, and the solution parameters of the liquid

phase are given in Appendix C. The phases that have been considered in this study are

the gas phase, several stoichiometric solid compounds, several solid solutions, an ionic

liquid phase and liquid elemental sulfur. The solid solutions are the hexagonal solid

solution of (Na,K)2(CO3,SO4,S), five low-temperature solid solutions of

(Na,K)2(CO3,SO4), the glaserite phase (non-stoichiometric K3Na(SO4)2), the cubic

(Na,K)Cl solid solution, the cubic (Na,K)2S solid solution, the (Na,K)2S2 solid solution,

two (Na,K)2S2O7 solid solutions and the metallic (Na,K) solid solution. The

thermodynamic data of the pure compounds were either evaluated and optimized in this

study or were taken from thermodynamic data compilations [52-60].

The evaluation and optimization of the Na-K-S system is treated separately from

the other “simple” ionic systems due to the more complex behavior of the Na-K-S

system.

28


3.5.1 The Na-K-S system

The chemical behavior of the solid and liquid phases in the Na-K-S system shows a great

variation over compositional range. The elements Na and K are low melting, reactive

metals, while elemental S shows covalent behavior, forming various polymerized units in

the gas, liquid and solid phases. The alkali sulfides and polysulfides are ionic compounds.

Na2S and K2S are high-melting compounds compared to the other compounds in the

alkali-sulfur systems. Na2S and K2S consist of the ions Na+ or K+ and S2-, while the

polysulfides are more complex. Liquid alkali polysulfides form an ionic melt that is a

mixture of unbranched Sn2- chains of varying length with the charges at both ends of the

chain [61]. The liquid phase shows a great tendency for supercooling and glass formation

due to the existence of the long polysulfide chains. The behavior of metal alloys

containing small amounts of sulfur is to a large extent unknown, and the behavior of

molten sulfur is quite complex [62].

The phase equilibria between gas, solid and liquid, and the thermodynamic

properties of the liquid phase in the Na-S system have been widely investigated [60, 63-

74]. The K-S system is not as widely studied [64, 75-80], and no gas phase/condensed

phase equilibrium has been reported. The phase relations and the thermodynamic

properties of the Na-K system have been reported in references [81-86]. Reviews of the

physicochemical properties of the liquid and solids in the K-S and Na-S systems have

been made by Sangster and Pelton [87, 88], Morachevskii [73, 89] and Borgstedt and

Guminski [90]. The Na-K system has previously been evaluated by Bale [91].

The thermodynamic properties for all known phases in the Na-K-S system were

evaluated and optimized. The binary systems Na-K, Na-S and K-S and the quasi-binary

system Na2S-K2S were optimized based on existing experimental data, and the phase

relations for the ternary Na-K-S system were predicted based on the thermodynamic

properties in binary systems. The liquid model considers two cations, Na+ and K+, and

nine anions, S2-, S22-, S3

2-, S42-, S5

2-, S62-, S7

2-, S82- and Va- (charged vacancies as F-

centers for metal solubility). To decrease the amount of independent parameters, the

thermodynamic data for the different polysulfide species were fitted as a function of the

Gibbs energy of the reaction between liquid alkali sulfide (Na2S or K2S) and liquid

29


sulfur. No reliable thermodynamic data for pure (“stoichiometric”) polysulfide species

exist as molten alkali polysulfides are mixtures of many polysulfide species. The largest

polysulfide species in the model is S82-, as molten sulfur, which mainly exists as S8-rings

or smaller ring- or chain units, is expected to be depolymerized and broken to ionic

polysulfide chains by the addition of alkali metals [61]. The model is not restricted to

polysulfides up to S82, but the concentration of possible higher polysulfide units is

expected to be very low and was therefore omitted from the present work. Possible

branched polysulfide units could exist, but experimental data have shown that the

polysulfide ions are predominantly unbranched chains, and therefore branched

polysulfide isomers are not taken into consideration here. The existence of polysulfide

radical anions has been shown (S2-, S3

-, S4-, S6

-) [61] but they were not considered in the

present assessment.

The thermodynamic data for the pure liquid alkali polysulfide components were

optimized and fitted as ΔG(M2S1+n) = A(n)+B(n)⋅T (n=1-7) for the reaction

M2S(l) + n S(l) ⇌ M2S1+n(l), M=Na, K. [Eq. 3.36]

The thermodynamic data for M2S(l) and S(l) are given in Appendix A and the

thermodynamic data for the polysulfide species were optimized. It was shown that

ΔG(M2S1+n) for both Na and K could be represented by the empirical equation

[ ] TBnkAAn

GnGGGn

k

kn

olS

olSM

olSMSM nn

⋅⋅+−⋅⋅+⋅

=⋅−−=Δ

∑=

−

++

110

)()()(

)1(22

21212

.

[Eq. 3.37]

As can be seen from Equation 3.37, the liquid model parameters are the three values of

A0, A1 and B for the Na-S system, the three similar parameters for the K-S system, the

excess Gibbs energy parameters of the Na-K system and the S2--Va- interaction

parameters for the Na-Na2S and K-K2S liquid regions. A parameter for Na2S-Na2S2

interactions was also included for a better agreement of the Na2S-liquidus line with the

experimental data.

The thermodynamic properties of three solid solutions were also modeled, the Na-

K alloy with body-centred cubic structure, cubic Na2S-K2S, and Na2S2-K2S2. The

thermodynamic properties for the Na-K alloy were based on a previous assessment by

30


Bale [91]. Very limited experimental data exist for the alkali sulfide and alkali disulfide

solid solutions, and only tentative thermodynamic properties were modeled in the present

work.

3.5.1.1 Na-S

The phase diagram has been measured by visual-polythermal methods [66], thermal

analysis [63-66], differential thermal analysis [60, 66, 68], quenching techniques [66] and

EMF-studies [67, 69]. Due to experimental difficulties, a notable scatter exists for

different experimental investigations. The main uncertainties stem from difficulties in

synthesizing pure samples of sodium sulfide and polysulfides, as hydration or oxidation

of the samples easily occur, and due to the fact that sodium polysulfide melts can easily

be supercooled and are glass-forming. Tegman [70, 71] and Cleaver and Davies [72] used

transpiration techniques to investigate the equilibrium between sulfur gas and sodium

polysulfide melt. Maiorova et al. [69], Cleaver and Davies [72] and Gupta and Tischer

[67] used EMF-techniques to measure the activity of liquid sulfur in sodium polysulfide

melts. Gupta and Tischer [67], Maiorova et al. [69], Morachevskii [73] and

Morachevskii et al. [74] measured the activity of liquid sodium in sodium polysulfide

melts up to the region of two liquid phases (Sodium polysulfide/sulfur) with EMF-

techniques.

Based on the recommendations by Sangster and Pelton [87], the most weight was

put on the measurements by Rosén and Tegman [66], which is the most complete study

of the phase diagram. Rosén and Tegman mainly used high-temperature microscopy, but

complementary experiments using thermal analysis, differential thermal analysis and

quenching techniques showed good agreement with the high-temperature microscopy. No

solid solubility has been reported in the system and no measurements have been made for

x(Na) > ⅔. Based on the experiments by Dworkin and Bredig [76] on the phase relations

of K-K2S, which show the existence of liquid-liquid immiscibility, a miscibility gap

might be expected to exist at compositions with x(Na) > ⅔. At high sulfur compositions

31


liquid-liquid immiscibility occurs between liquid polysulfide and almost pure liquid

sulfur [60, 64, 66, 67].

The Gibbs energy of the liquid sodium polysulfide components from Na2S2 to

Na2S8 was optimized and the thermodynamic data of the reaction

Na2S(l) + n S(l) ⇌Na2S1+n(l) [Eq. 3.38]

were fitted to the following empirical equation:

[ ] )/(184.4)1(225104248116

)/()/()/()/(

1

1)(

1)(

1)(

121212

KTnkn

molJGnmolJGmolJGmolJGn

k

kn

olS

olSNa

olSNaSNa nn

⋅⋅+−⋅⋅+⋅−

=⋅⋅−⋅−⋅=⋅Δ

∑=

−

−−−−++

.

[Eq. 3.39]

The terms and are found in Appendix A by integrating the ColSNaG )(2

olSG )( p expression for

H and S using and . According to Eq. 3.39, it is assumed that ΔCofH 298,Δ oS298 p of

formation of liquid polysulfides from liquid S and liquid Na2S is zero. One small

additional parameter was added to refine the fit of the Na2S liquidus.

According to Sangster and Pelton [87], it is likely that a miscibility gap will be

present for liquid Na-Na2S close to the melting point of Na2S. A mixing model parameter

was estimated to obtain a miscibility gap of reasonable size. Miscibility gaps in K-KX

(X=Cl, Br, I, F, H) systems were observed to generally be smaller than the corresponding

Na-NaX gaps [92, 93]. Hence the proposed calculated miscibility gap is larger than the

one calculated for the K-K2S system. The proposed miscibility gap is reproduced by

using a binary excess parameter, which is given in Appendix C.

The calculated phase diagram of Na-S is shown in Figure 3.2. The calculated

reverse solubility of liquid S in the polysulfide melt is probably a model artifact due to a

limited number of polysulfide species (n=8 is maximum for Na2Sn). The simple

temperature dependence of the Gibbs energy of formation of the polysulfides (Eq. 3.39),

which was introduced for reasons of simplicity, might also be a cause for the calculated

reverse solubility.

32


3.5.1.2 K-S

The phase diagram has been measured by thermal analysis [64, 75, 76], differential

scanning calorimetry (DSC) [77, 78] and EMF methods [79, 80]. No solid solubility has

been reported for any compounds in the system. Crosbie [79] and Morachevskii et al.

[80] used EMF-techniques to measure the activity of liquid potassium in potassium

polysulfide melt up to the region of two liquid phases (potassium polysulfide/sulfur). The

experimental difficulties for potassium sulfide and polysulfides are similar as in the

sodium systems.

The phase diagram has been investigated in the whole compositional range and

there exists liquid-liquid immiscibility both at the sulfur-rich end with molten sulfur in

equilibrium with a potassium polysulfide melt [79, 80], and at the potassium-rich end at

compositions with x(K) > ⅔ [76].

The Gibbs energy of the liquid potassium polysulfide components from K2S2 to

K2S8 was optimized and the thermodynamic data of the reaction

K2S(l) + n S(l) ⇌K2S1+n(l) [Eq. 3.40]

were fitted to the following empirical equation:

[ ] )/(6736.1)1(241840279496

)/()/()/()/(

1

1)(

1)(

1)(

121212

KTnkn

molJGnmolJGmolJGmolJGn

k

kn

olS

olSK

olSKSK nn

⋅⋅+−⋅⋅⋅+⋅−

=⋅⋅−⋅−⋅=⋅Δ

∑=

−

−−−−++

.

[Eq. 3.41]

To reproduce the liquidus in the compositional range of K-K2S, the interaction between

metallic potassium (nominally K(+)Va(-)) and K2S was optimized. The interaction

parameters are given in Appendix C. The calculated phase diagram of the K-S system is

shown in Figure 3.2.

3.5.1.3 Na-K

The phase diagram of Na-K has been assessed previously by Bale [91]. In his assessment,

Bale [91] used the experimental phase diagram points from Ott et al. [81]; hence the same

33


experimental points were used in the present evaluation. The activity of K in the liquid

has been measured by Lantratov [82] at 450°C and 500°C and by Cafasso et al. [83] at

111°C. The enthalpy of mixing of the liquid has been measured calorimetrically by

Yokokawa and Kleppa [84] at 111°C, and by McKisson and Bromley [85]. Other

calorimetric measurements have been done by Douglas et al. [86]: HT-H273.15K for pure K

and for a Na-K alloy with 78.26 wt-% K; HT-H323.15K for a Na-K alloy with 53.64 wt-% K

and for a Na-K alloy with 44.80 wt.% K. The parameters for the liquid phase and the Na-

K solid solution (bcc structure) were directly taken from Bale [91].

The calculated phase diagram of Na-K is shown in Figure 3.2.

3.5.1.4 Na2S-K2S

The quasibinary Na2S-K2S system has been studied with DTA by Mäkipää & Backman

[94] and a tentative phase diagram was constructed. They assumed solid solubility for the

whole composition range with a minimum solidus temperature at x(K2S)≈0.65 and

736°C. Extensive solid solubility is to be expected as both Na2S and K2S have the same

cubic anti-fluorite structure and complete solid solutions in common-anion Na-K salt

systems are very common. However, due to the fact that the potassium ion has

considerably larger radius than the sodium ion, low temperature miscibility gaps or

intermediate phases might occur. Sabrowsky et al. [95] have synthesized the compound

KNaS at 600°C, and determined the structure of the compound to be hexagonal of PbCl2-

type, showing the existence of an intermediate phase in the Na2S-K2S system.

With no further experimental data existing, ideal behavior was assumed for the

liquid phase and the solid solution was modeled as a regular solution with the Compound

Energy Formalism (which gives a symmetrical solid-solid miscibility gap). The

calculated phase diagram of Na2S-K2S is shown in Figure 3.2.

34


Liquid

Na 2

S

Na 2

S 2

Na 2

S 4N

a 2S 5

284 °C

98 °C

475 °C

244 °C

1172 °C

Liquid

Liquid + S(l)

Na(s) + Na2S(s)

Liquid + Na2S(s)

Gas + Na2S(s)

Na2S5(s) + S(l)

Liquid + S(l)

Na - S

x(S)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

800

1000

1200

K(s) + K2S(s)

K2S

K2S

2

K2S

3

K2S

4

K2S

563 °C

948°C

491°C

272°C

255°C

Liquid Liquid

Liquid + K2S(s)Liquid + S(l)

K2S(s) + Gas

466°C

K2S

6

Liquid + Gas

K2S6(s) + S(l)

Liquid + Gas

127°C

209°C

K - S

x(S)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

800

1000

Liquid

bcc

bcc

bcc + liq.

bcc + liq.

Na2K + bccbcc + Na2K

Liq. + Na2K

6.9°C

-12.6°C

63.2°C

97.2°C

Na - K

x(Na)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0-20

0

20

40

60

80

100

120

734 °C

Liquid

(Na,K)2S(s.s.)

Na2S - K2S

x(Na2S)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0600

700

800

900

1000

1100

1200

Figure 3.2. Calculated phase diagrams of Na-S, K-S, Na-K and Na2S-K2S at a pressure of 1 bar shown together with experimental data. References to the experimental data are given in reference [96] (Publication III).

3.5.1.5 Na2S-K2S-S

The phase diagram for the Na-K-S system has not been reported. The only existing phase

diagram data in the ternary system is the Na2S-K2S section. The calculated liquidus

projection of Na2S-K2S-S is shown in Figure 3.3. No ternary liquid parameters were used

for the liquid and no stoichiometric ternary compound was considered in the calculations.

Solid Na2S2 and K2S2 have the same crystal structure, and it was assumed that a solid

solution is formed. No experimental data exist, and therefore an interaction parameter

identical to the parameter of the alkali sulfide solid solution was used. Apart from the

(Na,K)2S and the (Na,K)2S2 solid solutions, no solid solubility in higher polysulfides was

35


assumed for the calculation of the liquidus projection shown in Figure 3.3. As Na-K salt

solid solutions very often exhibit some solubility, it is possible that at least limited

solubility exists. However, due to the low melting point of the compounds and the

estimated positive mixing parameter for the solid solutions, this assumption is probably

reasonable. The lowest eutectic temperature is 73°C at x(S)=0.733, x(Na2S)=0.062 and

x(K2S)=0.205.

0.

10.

20.

30.

40.

50.

60.

70.

80.

9

0.10.20.30.40.50.60.70.80.9

0.10.2

0.30.4

0.50.6

0.70.8

0.9

S

Na2S K2Smole fraction

1100

1000

900

800

700

400

300

500

600

200

Na2S2 K2S2

K2S3

K2S4

K2S5

K2S6

Na2S4

Na2S5

Twoliquids

1050

950

850

750

350

450

250

150

650

350

400

300

650

700

750

800

850

900

450

Figure 3.3. Calculated liquidus projection of Na2S-K2S-S. Isothermal lines are calculated at 50°C intervals.

3.5.2 The Na+,K+/CO32-,SO4

2-,Cl-,S2-,S2O72- system

3.5.2.1 Binary systems

All common-cation and common-anion binary systems of the multicomponent

Na+,K+/CO32-,SO4

2-,Cl-,S2-,S2O72- system that were evaluated and optimized in this study

36


are briefly discussed in the following sections. The Na2S-NaCl system has not been

reported in the publications, which the present study is based on, but the system is

discussed in this section. All optimized interaction parameters for the solid solutions and

liquid phase are given in Appendices B and C.

3.5.2.2 Na2CO3-Na2SO4

The phase relations in the Na2CO3-Na2SO4 system has been measured by thermal

analysis [97-99], visual-polythermal methods [100] and electrical conductivity

measurements [97]. The solid-liquid equilibrium is shown to have a minimum in the

solidus and liquidus, with a single solid solution in equilibrium with the liquid phase [97-

101]. The reported subsolidus phase relations are very complex [98, 99, 102], with the

existence of several solid solutions and intermediate phases.

The activity of Na2CO3 in the high-temperature hexagonal solid solution was

measured by Mukhopadhyay and Jacob [103] with EMF-techniques in the temperature

range of 600 to 800°C. Flood et al. [104] measured the oxygen activity in liquid Na2CO3-

Na2SO4 with a controlled level of CO2 in the gas phase. The liquid contains a very small

amount of O2- that stems from decomposition of Na2CO3. The study showed that the

liquid phase has ideal, or close to ideal, mixing behavior.

Based on the measurements, Mukhopadhyay and Jacob [103] derived the excess

Gibbs energy of the solid solution using a subregular solution model. In the present study

the solution properties of the hexagonal solid solution were taken from the work of

Mukhopadhyay and Jacob [103]. A full assessment of the low-temperature phase

equilibrium was not performed as the lack of thermodynamic data of the intermediate

phases, together with the complex and diverging phase relations reported by Khlapova

[98], Kurnakov and Makarov [99] and Makarov and Krasnikov [102], do not allow for a

reliable description of the thermodynamic properties for all the low-temperature phases.

Only tentative thermodynamic parameters for the Na2SO4-rich and Na2CO3-rich low-

temperature solid solutions are given in Appendix B. The Gibbs energy for the formation

of the binary quadruplet in the liquid phase was optimized based on the reported liquidus

37


and solidus data [97, 100, 101] with the most emphasis on the work of Gitlesen and

Motzfeldt [97]. The calculated minimum melting point is at x(Na2CO3)=0.63 and 826°C.

The calculated phase diagram of Na2CO3-Na2SO4 is shown in Figure 3.4.

3.5.2.3 Na2CO3-Na2S

The phase diagram of Na2CO3-Na2S has been measured with thermal analysis [105-108],

visual-polythermal methods [107, 109] and high-temperature X-ray powder diffraction

[109]. Courtois [108], Tammann and Oelsen [105], and Ovechkin et al. [106] described

the system as a simple eutectic system, while Tegman and Warnqvist [107], and Råberg

et al. [109] showed the existence of a Na2CO3-rich solid solution in equilibrium with the

liquid phase. The experimental scatter in the studies is probably due to impurities in the

sodium sulfide, oxidation of the sodium sulfide during the experiments and

decomposition of the sodium carbonate.

For the optimization in the current study, the most weight was put on the works

by Ovechkin et al. [106], Tegman and Warnqvist [107], and Råberg et al. [109]. The

thermodynamic data of pure Na2S in the metastable hexagonal structure was modeled

based on the subsolidus equilibrium between the hexagonal solid solution and solid Na2S

measured by Råberg et al. [109]. No binary interaction parameters for the hexagonal solid

solution in the Na2CO3-Na2S system were required to reproduce the experimental data

(Henrian ideal mixing was assumed). The calculated eutectic point is at x(Na2S)=0.39

and 761°C. The calculated phase diagram of Na2CO3-Na2S is shown in Figure 3.4.

3.5.2.4 Na2SO4-Na2S

The phase diagram of the Na2SO4-Na2S system has been investigated by thermal analysis

[105, 110-112], thermogravimetry [112], differential thermal analysis [113] and visual-

polythermal methods [113, 114]. EMF-studies have also been conducted for measuring

the activity of O2 in equilibrium with solid Na2S and Na2SO4 [115]. The studies indicate

that the system is eutectic, with a close agreement of the eutectic temperature at 740-

38


750°C in the different studies, but with highly varying eutectic compositions and liquidus

temperatures. The notable scatter in the experimental results is most likely due to

difficulties in synthesizing Na2S of high purity and also due to the possible oxidation of

Na2S during the experiments. Tran and Barham [112] argued for the existence of partial

solid solubility of Na2SO4 in Na2S. However, the method used by Tran and Barham [112]

should be considered unreliable due to possible contamination of hydrogenated species,

as H2 was used in the experiments.

An intermediate solid phase, Na2SO3 (sodium sulfite), has been shown to exist.

However, this phase is metastable and decomposes to Na2SO4 and Na2S. Foerster and

Kubel [116] and Råberg [114] studied the decomposition of Na2SO3 at high temperatures

and both showed that the decomposition is sluggish up to about 600-700°C. Råberg [114]

also measured the metastable phase diagram for Na2SO4-Na2S with Na2SO3 in the

starting material. Solid Na2SO3 was never formed when the sample was cooled from a

completely liquid phase. The thermodynamic data of both Na2SO3 and K2SO3 measured

by O’Hare et al. [117] also suggest that the alkali sulfites should decompose to their

corresponding alkali sulfates and sulfides.

No solid solubility of Na2S in Na2SO4 has been recorded, but the limiting slope of

the Na2SO4-liquidus indicates that a solid solution might exist. Na2S is partially soluble in

the hexagonal, high-temperature Na2CO3 [109], and the hexagonal, high-temperature

forms of Na2CO3 and Na2SO4 show complete solid solution [97, 103]. K2S is also

partially soluble in hexagonal K2SO4. This indicates that partial solubility of Na2S in

Na2SO4 is plausible. It was therefore assumed that Na2S is soluble in solid hexagonal

Na2SO4. The thermodynamic data of pure Na2S in the metastable hexagonal structure is

based on the optimization of the Na2S-Na2CO3 system, assuming no additional binary

interaction parameters for the Na2S-Na2SO4 system (Henrian ideal mixing is assumed).

Due to the large scatter of the experimental phase diagram data, the liquid phase

parameter was optimized as a composition- and temperature-independent parameter. The

main emphasis was to reproduce the eutectic temperature, which is similar in most of the

experimental work. The calculated eutectic point is at x(Na2S)=0.38 and 741°C. The

calculated phase diagram of Na2SO4-Na2S is shown in Figure 3.4.

39


Liquid

Na2(CO3,SO4) (hexagonal ss)

Na2CO3 - Na2SO4

x(Na2CO3)

T /(°

C)

0.0 0.2 0.4 0.6 0.8 1.0800

820

840

860

880

900

Liquid

Na 2(

CO

3,S) (

hexa

gona

l ss)

Na2(CO3,S)(hexagonal ss) + Na2S(s)

Liquid + Na2S(s)

Na2S - Na2CO3

x(Na2S)

T/(°

C)

0.0 0.2 0.4 0.6 0.8 1.0400

600

800

1000

1200

Liquid

Na 2

(SO

4,S)(

hexa

ss)

Na2(SO4,S)(hexagonal ss)+Na2S(s)

Liquid+Na2S(s)

Na2S - Na2SO4

x(Na2S)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0500

700

900

1100

Na2SO4(s,1) + Na2S2O7(s)

Na2SO4(s,1) + LiquidLiquid

Liquid + Gas

Na2SO4(s,1) + Gas

Na2SO4 - Na2S2O7

x(Na2SO4)

T /(°

C)

0.0 0.2 0.4 0.6 0.8 1.0300

400

500

600

700

Figure 3.4. Calculated phase diagrams of Na2CO3-Na2SO4, Na2S-Na2CO3, Na2S-Na2SO4 and Na2SO4-Na2S2O7 at a pressure of 1 bar shown together with experimental data. References to the experimental data of the Na2SO4-Na2S2O7 system are given in reference [118] (Publication IV), and for the other systems in reference [119] (Publication V).

3.5.2.5 Na2SO4-Na2S2O7

The phase diagram of the Na2SO4-Na2S2O7 system has been measured by

thermogravimetric and visual polythermal studies [120, 121] and thermal/chemical

analysis [122]. The equilibrium between a molten mixture of Na2SO4 and Na2S2O7 and

gaseous SO3 (including SO2 and O2) has been studied by thermogravimetry [120, 121,

123] and vapor pressure measurements [124]. Additional studies on the high-temperature

stability of Na2S2O7 have been made using thermogravimetry [125-127].

40


Tran et al. [125] and Kostin et al. [126, 127] suggested the existence of

intermediate solid phases in the system, but this has not been corroborated by other

studies. Additionally, both Tran et al. [125] and Kostin et al. [126, 127] used Na2S2O7

containing considerable amounts of impurities, which renders their results unreliable. No

solid solutions have been reported in the system.

The calculated eutectic point is at x(Na2SO4)=0.09 and 395°C. The calculated

phase diagram of Na2SO4-Na2S2O7 is shown in Figure 3.4.

3.5.2.6 NaCl-Na2SO4

The phase diagram of the NaCl-Na2SO4 system has been measured by thermal analysis

[128-132] and visual-polythermal methods [100, 133-138]. It is a simple binary eutectic

system with no solid solution or intermediate phases. No measurements of the

thermodynamic properties of the liquid phase have been reported. The measured liquidus

and solidus temperatures from the experimental studies are in good agreement with each

other. The liquid phase parameter was modeled based on the experimental liquidus and

solidus data. The calculated eutectic point is at x(Na2SO4)=0.47 and T=626°C. The

calculated phase diagram of NaCl-Na2SO4 is shown in Figure 3.5.

3.5.2.7 NaCl-Na2CO3

The phase diagram of the NaCl-Na2CO3 system has been measured by thermal analysis

[129, 139-141], visual-polythermal methods [100, 142] and hot filament techniques [143,

144]. It is a simple binary eutectic system with no solid solution or intermediate phases.

The activity of Na2CO3 in the molten or partially molten NaCl-Na2CO3 mixtures has been

measured by Iwasawa et al. [144] using EMF-techniques. The measured liquidus

temperatures shows some scatter, but measured or extrapolated eutectic points from the

studies are in good agreement. The calculated eutectic point is at x(Na2CO3)=0.45 and

T=632°C. The calculated phase diagram of NaCl-Na2CO3 is shown in Figure 3.5.

41


3.5.2.8 NaCl-Na2S

The phase diagram of the NaCl-Na2S system has been studied by Shivgulam et al. [145]

using thermal analysis. Magnusson and Warnqvist [146] also reported the eutectic

temperature of the same system. The system is a simple binary eutectic system.

Shivgulam et al. [145] reported a eutectic point at x(Na2S)=0.24 and 712°C, and

Magnusson and Warnqvist reported a eutectic temperature of 690°C. According to

Shivgulam et al. [145], the NaCl-Na2S system shows a tendency for liquid immiscibility

in the Na2S-rich region. However, a considerable compositional uncertainty is probable

for the measured liquidus points due to the volatilization of NaCl at high temperatures, as

pure Na2S melts at almost 400°C higher temperature than NaCl.

A set of optimized liquid phase parameters could not be attained in this work

without the use of a large number of parameters or giving the liquid phase unrealistic

mixing properties. Assuming an ideal liquid solution will give reasonable predictions of

the solidus temperature, eutectic point and of the liquidus temperatures at NaCl-rich

compositions measured by Shivgulam et al. [145]. Further experimental studies are

needed for a more detailed evaluation of the liquid phase properties in the binary NaCl-

Na2S system.

The calculated eutectic point is at x(Na2S)=0.25 and T=709°C. The calculated

phase diagram of NaCl-Na2S is shown in Figure 3.5.

42


NaCl(s) + Na2SO4(s,hexagonal)

Liquid

Na2SO4(s,hexagonal)Liquid+Liquid+

NaCl(s)

Na2SO4 - NaCl

x(Na2SO4)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0600

700

800

900

Liquid

NaCl(s) + Na2CO3(s, hexagonal)

Na2CO3(s, hexagonal)Liquid+

Liquid+NaCl(s)

Na2CO3 - NaCl

x(Na2CO3)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0600

700

800

900

Na2S(s)+NaCl(s)

Liquid

Liquid+Na2S(s)

Na2S-NaCl

x(Na2S)

T/ (°

C)

0.0 0.2 0.4 0.6 0.8 1.0600

800

1000

1200

Figure 3.5. Calculated phase diagrams of Na2SO4-NaCl, Na2CO3-NaCl and Na2S-NaCl at a pressure of 1 bar shown together with experimental data. References to the experimental data of the Na2SO4-NaCl and Na2CO3-NaCl systems are given in reference [147] (Publication VI). The experimental data of the Na2S-NaCl system is from reference [145].

3.5.2.9 K2CO3-K2SO4

The phase relations of the K2CO3-K2SO4 system have been studied with thermal analysis

[101, 148, 149], visual-polythermal methods [100] and high-temperature XRD [148]. At

high temperatures a solid solution with hexagonal crystal structure exists over the whole

compositional range of K2CO3-K2SO4. The equilibrium between the hexagonal solid

solution and the liquid phase has a minimum at pure K2CO3. The low-temperature form

of K2CO3 has monoclinic crystal structure and forms a partial solid solution with K2SO4

at temperatures below 422°C and x(K2SO4)<0.2 [148]. The low-temperature,

43


orthorhombic K2SO4 forms an extensive solid solution with K2CO3 with a maximum

thermal stability at around x(K2SO4)=0.5 and 635°C [101, 148].

The activity of K2CO3 in the high-temperature hexagonal solid solution was

measured by Mukhopadhyay and Jacob [150] with EMF-techniques in the temperature

range of 652 to 892°C.

Based on the measurements, Mukhopadhyay and Jacob [150] derived the excess

Gibbs energy of the solid solution using a subregular solution model. No experimental

data on the thermodynamic properties of the liquid phase has been reported.

In the present work the solution properties of the hexagonal solid solution were

taken from the work of Mukhopadhyay and Jacob [150], and the thermodynamic data for

the liquid phase and the monoclinic and orthorhombic solid solutions were derived from

the thermodynamic optimization. The study by Barde et al. [149] was considered the

most reliable on the solid-liquid equilibrium as they performed the experiments in CO2,

thus minimizing the possible decomposition of K2CO3. Therefore, the most weight was

put on the work by Barde et al. [149] for the optimization of the liquid phase parameters.

The calculated phase diagram of K2CO3-K2SO4 is shown in Figure 3.6.

3.5.2.10 K2CO3-K2S

The phase diagram of K2CO3–K2S has been measured by visual-polythermal methods

[151], thermal analysis [152] and X-ray diffraction [152]. Ovechkin et al. [152] suggested

that the system exhibits full solid-solid miscibility, while the liquidus measurements by

Babcock and Winnick [151] indicates that the K2CO3-K2S system is a eutectic system.

The two experimental determinations are highly divergent, and both reported melting

temperatures of K2S lower than the value used in this work (948°C), which is based on

the study by Dworkin and Bredig [153]. Babcock and Winnick [151] reported that the

K2S used in their experiments contained polysulfides as impurities. The assumption of a

complete solid solution reported by Ovechkin et al. [152] is most likely incorrect as K2S

and the high-temperature form of K2CO3 have different crystal structures. K2S has cubic

crystal structure, while high-temperature K2CO3 has a hexagonal crystal structure. Due to

44


the two strongly diverging experimental determinations of the K2CO3-K2S phase

diagram, only tentative thermodynamic parameters were optimized for the liquid phase

and solid solutions. Based on the fact that K2S is also partially soluble in hexagonal

K2SO4 and Na2S in hexagonal Na2CO3, it was assumed that K2S is partially soluble in

hexagonal K2CO3. The thermodynamic data of pure K2S in the metastable hexagonal

structure is based on the optimization of the K2SO4-K2S system, assuming no additional

binary interaction parameters for the K2CO3-K2S system (Henrian ideal mixing was

assumed). Due to highly diverging experimental data, only a tentative composition- and

temperature-independent parameter for the liquid was optimized. The most weight was

put on the experimental data at K2CO3-rich compositions.

The calculated eutectic point is at x(K2S)=0.53 and 641°C. The calculated phase

diagram of K2CO3-K2S is shown in Figure 3.6.

3.5.2.11 K2SO4-K2S

The phase diagram of K2SO4-K2S has been measured by thermal analysis [154] and by

thermogravimetry [155]. Goubeau et al. [154] reported solid solubility of K2S in K2SO4

and the presence of an intermediate phase K2SO (=K2SO4⋅3K2S). Winbo [156] confirmed

the existence of the intermediate phase by XRD, and also identified the solid solution.

However, the crystal structure of the solid solution was found to be orthorhombic, similar

to low-temperature, orthorhombic K2SO4(s,α), instead of the high-temperature, hexagonal

K2SO4(s,β), which would be expected from the measured phase diagram of Goubeau et

al. [154]. Winbo [156] made the crystallographic determinations on quenched samples

from the EMF-experiments. So and Barham [155] reported terminal solid solubility in

both K2S and K2SO4, but they found no intermediate phase. However, their study should

be considered unreliable due to the possible contamination of hydrogenated species as H2

was used for reducing K2SO4. Winbo [156] measured the activity of O2 in the K2SO4-K2S

system using EMF-techniques. The experiments were performed with the K2SO4-rich

solid solution at x(K2SO4)=0.75 and with a mixture of K2S and K2SO. The thermo-

45


dynamic properties for solid K2SO3 have been measured by O’Hare et al. [117], but the

phase is a metastable phase which decomposes to K2S and K2SO4.

The experimental phase equilibrium data and the existing thermodynamic data are

highly contradicting, and reasonable convergence of all existing data could not be

obtained in this study. The method used by So and Barham [155] is not a standard

method, and the results are considered to be unreliable. The K2S used in the study by

Goubeau et al. [154] had up to 3-4% of impurities, mainly in the form of K2SO4, K2SO3

and K2S2O3. Therefore, the mixtures in the experiments by Goubeau et al. [154] have

compositional uncertainties, especially in the K2S-rich region. The melting point of K2S

in the study by Goubeau et al. [154] was reported to be 912°C, compared to 948°C

reported by Dworkin and Bredig [153], which is the value reported in the NIST-JANAF

compilations [52]. This also indicates the existence of impurities in the K2S. The

existence of the intermediate phase K2SO has been corroborated, but the experimental

data [154, 156] are highly contradicting regarding equilibrium involving the intermediate

phase K2SO. A consistent set of thermodynamic data where K2SO was included could not

be produced. Only a tentative optimization was made of the K2SO4-K2S system, mainly

based on the solidus and liquidus of the K2SO4-rich solid solution from Goubeau et al.

[154] and on the EMF-measurements by Winbo [156]. The intermediate phase K2SO was

not included in the optimization, and the K2SO4-rich solid solution was considered to

have the hexagonal crystal structure.

The calculated eutectic point is at x(K2S)=0.63 and 645°C. The calculated phase

diagram of K2SO4-K2S is shown in Figure 3.6.

3.5.2.12 K2SO4-K2S2O7

The phase diagram of K2SO4-K2S2O7 has been measured by thermal analysis/chemical

analysis [122, 157], visual polythermal/thermogravimetric studies [120], EMF-studies

[158, 159], and cryoscopy [158]. The equilibrium between a molten mixture of K2SO4

and K2S2O7 and gaseous SO3 (+ SO2 and O2) has been studied by thermogravimetry

[120, 121, 160] and EMF-techniques [157, 161]. Kostin et al. [126, 127] reported the

46


existence of the intermediate phases K2SO4⋅2K2S2O7 and 2K2SO4⋅K2S2O7 based on

thermogravimetric experiments of the decomposition of K2S2O7. No solid solutions have

been reported in the system.

Kostin et al. [122, 126, 127, 160] used K2S2O7 containing considerable amounts

of impurities, which renders their results unreliable. The two reported intermediate

phases, K2SO4⋅2K2S2O7 and 2K2SO4⋅K2S2O7, were not included in the present

optimization due to the lack of any thermodynamic data of these phases and due to the

probable impurities in the K2S2O7 in the experiments by Kostin et al. [162].

The calculated eutectic point is at x(K2SO4)=0.07 and 406°C. The calculated

phase diagram of K2SO4-K2S2O7 is shown in Figure 3.6.

3.5.2.13 KCl-K2SO4

The phase diagram of the KCl-K2SO4 system has been measured by thermal analysis

[128, 129, 163] and visual-polythermal methods [100, 135, 136, 142, 164-166]. It is a

simple binary eutectic system with no solid solution or intermediate phases. No

measurements of the thermodynamic properties of the liquid phase have been reported.

The experimental studies are in good agreement with each other for the liquidus

temperatures for KCl-rich compositions and for the measured or extrapolated eutectic

point. The variations in the measured liquidus temperature are larger at K2SO4-rich

compositions, possibly due to volatilization of KCl during the experiments. The

calculated eutectic point is at x(K2SO4)=0.26 and 690°C. The calculated phase diagram

of KCl-K2SO4 is shown in Figure 3.6.

3.5.2.14 KCl-K2CO3

The phase diagram of the KCl-K2CO3 has been measured by thermal analysis [129, 140,

141, 167] and visual-polythermal methods [100, 142]. It is a simple binary eutectic

system with no solid solution or intermediate phases. No measurements of the

thermodynamic properties of the liquid phase have been reported. The calculated eutectic

47


point is at x(K2CO3)=0.38 and 631°C. The calculated phase diagram of KCl-K2CO3 is

shown in Figure 3.6.

Liquid

K2(CO3,SO4)(hexagonal ss)

K2CO3 - K2SO4

x(K2CO3)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0850

900

950

1000

1050

1100

Liquid

K 2(C

O3,S

)(hex

agon

al s

s)

K2(CO3,S)(hexagonal ss) + K2S(s)

Liquid+K2S(s)

K2S - K2CO3

x(K2S)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0500

600

700

800

900

1000

Liquid

K 2(S

O4,S

)(hex

agon

al s

s)

K2(SO4,S)(hexagonal ss) + K2S

Liquid+K2S(s)

K2S - K2SO4

x(K2S)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0500

600

700

800

900

1000

1100

Liquid + K2SO4(s,hexagonal)

Liquid + K2SO4(s,orthorhombic)

K2SO4(s,orthrhombic) + K2S2O7(s,high)

K2SO4(s,orthorhombic) + K2S2O7(s,low)

Liquid

Liquid + GasK2SO4(s,hexagonal) + Gas

K2SO4 - K2S2O7

x(K2SO4)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0200

300

400

500

600

700

800

Liquid

KCl(s) + K2SO4(s, hexagonal)

KCl(s) + K2SO4(s,orthorhombic)

Liquid+K2SO4(s, hexagonal)

K2SO4 - KCl

x(K2SO4)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0500

600

700

800

900

1000

1100

KCl(s) + K2CO3(s, hexagonal)

Liquid

Liquid+K2CO3(s, hexagonal)Liquid+KCl(s)

K2CO3 - KCl

x(K2CO3)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0600

700

800

900

Figure 3.6. Calculated phase diagrams of K2CO3-K2SO4, K2CO3-K2S, K2SO4-K2S, K2SO4-K2S2O7, K2SO4-KCl and K2CO3-KCl at a pressure of 1 bar shown together with experimental data. References to the experimental data of the K2SO4-K2S2O7 system are given in reference [118] (Publication IV), for the K2CO3-K2SO4, K2CO3-K2S and K2SO4-K2S systems in reference [119] (Publication V) and for the K2SO4-KCl and K2CO3-KCl systems in reference [147] (Publication VI).

48


3.5.2.15 Na2CO3-K2CO3

The phase equilibrium of the Na2CO3-K2CO3 system has been studied using thermal

analysis [139, 140, 168-171], visual-polythermal methods [172, 173] and XRD-analysis

[168]. The system has several solid solutions and displays a minimum in the solidus and

the liquidus. Andersen and Kleppa [174] measured the enthalpy of mixing of liquid

Na2CO3 and liquid K2CO3 at 905°C. Niggli [139], Reisman [168], and Andersen and

Kleppa [174] performed their experiments in CO2, and therefore they minimized possible

decomposition of the carbonates.

Makarov and Shulgina [170] and Reisman [168] reported several solid solutions,

both K2CO3-rich and Na2CO3-rich partial solid solutions at low temperature and complete

solid solubility of the high-temperature, hexagonal Na2CO3 and K2CO3. Both also

reported the existence of an intermediate phase with varying composition around

x(Na2CO3)=0.5. Dessureault et al. [175] pointed out that the measured phase equilibrium

at intermediate compositions between 400 and 600°C is not thermodynamically

consistent with either the existence of an intermediate phase or a possible miscibility gap.

No thermodynamic or crystallographic data of the intermediate phase have been reported,

which could aid in the modeling of the phase.

Only a tentative optimization was made in this study of the thermodynamic

properties of the low-temperature solid solutions. The intermediate phase was not

considered due to the lack of reliable data.

The interaction parameter of the liquid phase was optimized based on the

measured enthalpy of mixing by Andersen and Kleppa [174]. A small composition-

dependent parameter was included in the optimization for better agreement with the

experimental enthalpy data. For the solid-liquid equilibrium and the subsolidus

equilibrium, the most weight was put on the study by Reisman [168] in the present

optimization. The experiments were performed in CO2, and both the solidus and the

liquidus were measured. However, the other solid-liquid equilibrium determinations are

in good agreement with the study of Reisman [168]. The calculated minimum melting

point of the system is at x(Na2CO3)=0.59 and 709°C. The calculated phase diagram of

Na2CO3-K2CO3 is shown in Figure 3.7.

49


3.5.2.16 Na2SO4-K2SO4

The phase equilibrium in the Na2SO4-K2SO4 system has been studied using thermal

analysis [128, 129, 176-179], visual-polythermal methods [135, 180] and XRD-analysis

[177, 178, 181]. The system has several solid solutions and has a minimum in the solidus

and the liquidus. The experimental data for the solidus and liquidus were determined by

thermal analysis [128, 129, 176, 177] and by visual-polythermal methods [135, 180]. The

phase equilibrium in the subsolidus region has been determined by thermal analysis [128,

176-179] and XRD-analysis [177, 178, 181]. Østvold and Kleppa [182] measured the

enthalpy of mixing of liquid Na2SO4 and liquid K2SO4 at 1080°C with x(Na2SO4)=0.5.

The hexagonal solid solution is stable over the whole compositional range at elevated

temperatures. Two low-temperature solid solutions with orthorhombic crystal structure

exist at the terminal compositions, and the intermediate phase glaserite, K3Na(SO4)2

dissolves considerable amounts of Na2SO4 at elevated temperatures. The orthorhombic

and hexagonal solid solutions were modeled with two sublattices, while the glaserite was

modeled with three sublattices, where two sublattices represent two different

crystallographic sites occupied by the cations.

The liquid phase interaction parameter was fitted to the measured enthalpy of

mixing by Østvold and Kleppa [182]. The calculated minimum melting point of the

system is at x(Na2SO4)=0.74 and 834°C. The calculated phase diagram of Na2SO4-K2SO4

is shown in Figure 3.7.

3.5.2.17 Na2S2O7-K2S2O7

The phase diagram of Na2S2O7-K2S2O7 has been measured by thermal analysis [183],

differential thermal analysis [184] and conductivity studies [185]. The enthalpy of mixing

of the Na2S2O7-K2S2O7 liquid phase has been measured at 445°C by drop calorimetry

[185]. The studies show the existence of the intermediate solid phase KNaS2O7 and of

solid solutions in the Na2S2O7-rich and the K2S2O7-rich regions. The liquidus

temperatures reported by Gubareva et al. [184] are significantly lower than those reported

50


by Colombier et al. [183] and Rasmussen et al. [185], whose results are consistent with

each other. In the present work, the most weight has been put on the results of Colombier

et al. [183] and Rasmussen et al. [185].

The Gibbs energy for the formation of the binary quadruplet in the liquid phase

was optimized based on the measured enthalpy of mixing of Rasmussen et al. [185]. The

K2S2O7-rich solid solution has the structure of K2S2O7 (s,β), and no solid solubility of

Na2S2O7 in K2S2O7 (s,α) was assumed. The K2S2O7-rich and Na2S2O7-rich solid solutions

were modeled with two solid sublattices, with Na+ and K+ on the cationic sublattice and

S2O72- on the anionic sublattice.

The two calculated eutectic points of the system are at x(Na2S2O7)=0.40 and

x(Na2S2O7)=0.61 and both at a temperature of 342°C. The calculated phase diagram of

Na2S2O7-K2S2O7 is shown in Figure 3.7.

3.5.2.18 NaCl-KCl

The optimized solution parameters for the binary system NaCl-KCl have been reported

previously [34, 186]. The liquid phase was modeled with the Modified Quasichemical

Model in the Quadruplet Approximation [17], and the solid solution of NaCl-KCl was

modeled with a substitutional model. A single NaCl-KCl solid solution with a cubic

crystal structure is the precipitating phase at the liquidus. The solution parameters of the

solid solution are taken from Sangster and Pelton [34], and the parameters of the liquid

phase are taken from Chartrand and Pelton [186]. The optimized parameters from these

studies were used in the present study and are given in Appendices B and C. The

calculated phase diagram is shown in Figure 3.7.

51


Liquid

(Na,K)2CO3(hexagonal ss)

Na2CO3 - K2CO3

x(Na2CO3)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0650

700

750

800

850

900

950

Liquid

(Na,K)2SO4 (s,hexagonal)

Na2SO4 - K2SO4

x(Na2SO4)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0800

900

1000

1100

Liquid

(Na,K)2S2O7 (ss) + KNaS2O7(s)

(K,Na)2S2O7 (ss)+

(K,Na)2S2O7 (ss)

(Na,K)2S2O7 (ss)

K2S2O7 (s2) + KNaS2O7(s)

KNaS2O7(s)

Na2S2O7 - K2S2O7

x(Na2S2O7)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0250

300

350

400

450

Liquid

(Na,K)Cl(ss)

NaCl-KCl

x(NaCl)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0400

500

600

700

800

900

Figure 3.7. Calculated phase diagrams of Na2CO3-K2CO3, Na2SO4-K2SO4, Na2S2O7-K2S2O7 and NaCl-KCl shown together with experimental data. References to the experimental data of the Na2CO3-K2CO3 system are given in reference [119] (Publication V) and for the Na2SO4-K2SO4 and Na2S2O7-K2S2O7 systems in reference [118] (Publication IV).

3.5.2.19 Ternary systems

Several ternary systems have previously been studied experimentally. The ternary

systems can be divided into common-ion ternary systems and ternary reciprocal systems.

In the common-ion systems either an anion or cation is common for all three end-member

components, while ternary reciprocal systems consist of two cations and two anions,

where the charge balance constrains the mass balance. As only two cations were

considered in the present study, no common-anion ternary systems are considered. The

common-cation ternary systems that have been studied experimentally are NaCl-Na2CO3-

Na2SO4, NaCl-Na2CO3-Na2S, Na2CO3-Na2SO4-Na2S and KCl-K2CO3-K2SO4. All other

52


common-cation ternary systems were considered to have no nonideal ternary interactions,

as no experimental data was found in the literature for these systems. The extrapolation

of the binary interactions in the ternary systems was made using the Kohler

approximation [49] for all systems containing only divalent anions. The Kohler/Toop

approximation [51] was used for the systems containing the monovalent anion Cl- or the

negatively charged vacancy, Va-. The component containing the monovalent anion is

considered to be the asymmetric component if the two other components contain divalent

anions. For ternary systems containing Cl-, Va- and a divalent anion, the component

containing the divalent anion is considered as the asymmetric component.

The ternary reciprocal systems must take into account both first-nearest-neighbor

and second-nearest-neighbor interactions in contrast to common-ion ternary systems,

where only second-nearest-neighbor interactions are taken in to account in the modeling.

The ternary reciprocal systems that have been studied experimentally are Na2SO4-K2SO4-

Na2S2O7-K2S2O7, Na2CO3-K2CO3-Na2SO4-K2SO4, Na2CO3-K2CO3-NaCl-KCl and

Na2SO4-K2SO4-NaCl-KCl. The other ternary reciprocal systems were treated as having

no nonideal reciprocal interactions.

3.5.2.20 Na2CO3-Na2SO4-Na2S

Solidus and liquidus temperatures of the Na2CO3-Na2SO4-Na2S system have been

measured by differential thermal analysis [113]. Andersson [113] reported a minimum

melting temperature of 715±5°C at an approximate composition of x(Na2S)=0.35,

x(Na2CO3)=0.20 and x(Na2SO4)=0.45. The experimental points in the binary Na2S-

Na2SO4 system in the same study show considerable scatter, possibly due to oxidation of

Na2S. The reported melting point of Na2S was about 30°C lower than the melting point

reported in the NIST-JANAF compilations [52]. Andersson [113] reported that the purity

of the Na2S sample was higher than 98.3%. No ternary interaction parameters for the

liquid phase were used due to the considerable experimental scatter in the binary systems

Na2CO3-Na2S and Na2SO4-Na2S, and due to the uncertainties in the determination of the

ternary phase diagram [113].

53


The calculated minimum melting temperature of the Na2CO3-Na2SO4-Na2S

system is 733°C at the composition of x(Na2S)=0.356, x(Na2CO3)=0.308 and

x(Na2SO4)=0.336. The calculated liquidus projection of Na2CO3-Na2SO4-Na2S is shown

in Figure 3.8. Most calculated solidus and liquidus temperatures are within ±20°C of the

measured values, which is a reasonable agreement, given the experimental scatter in the

binary systems Na2CO3-Na2S and Na2SO4-Na2S.

Figure 3.8. Calculated liquidus projection of the Na2CO3-Na2SO4-Na2S system. Isothermal lines are calculated at 50°C intervals. Precipitating solid phases are Na2S (a) and the hexagonal solid solution, Na2(SO4,CO3,S) (b). The dotted line indicates the maximum solubility of the hexagonal solid solution. The minimum melting point is denoted by the symbol .

3.5.2.21 NaCl-Na2CO3-Na2S

The phase diagram of the NaCl-Na2S-Na2CO3 system has been reported by Warnqvist

and Norrström [187] and Shivgulam et al [145]. Magnusson and Warnqvist [146]

reported a ternary eutectic temperature of 590°C. Shivgulam et al [145] reported a

54


eutectic point at x(NaCl)=0.35, x(Na2CO3)=0.62, x(Na2S)=0.03 and a temperature of

598°C. Shivgulam et al [145] also reported the measured liquidus temperatures. Due to

the high uncertainties in the binary NaCl-Na2S system related to the volatilization of

NaCl, the liquidus measurements of Shivgulam et al.[145] must be considered to have a

high uncertainty, especially at high concentrations of Na2S. No additional ternary

parameters were optimized due to the uncertainties in the binary systems containing

Na2S. The calculated ternary eutectic point is at x(NaCl)=0.48, x(Na2CO3)=0.35,

x(Na2S)=0.17 and a temperature of 603°C.

3.5.2.22 NaCl-Na2CO3-Na2SO4

Bergman and Sementsova [100] measured the liquidus temperature for several sections in

the NaCl-Na2CO3-Na2SO4 system using visual-polythermal methods. Based on the

measured liquidus temperatures they estimated the minimum melting point of the system

to be at the composition of x(NaCl)=0.519, x(Na2CO3)=0.241, x(Na2SO4)=0.241 and at a

temperature of 612°C. The solidus temperatures were measured for several compositions

in this study using simultaneous DTA and TGA [147]. Several cycles were made between

temperatures close to the liquidus and solidus in order to homogenize the solid solutions

in the samples. The heating and cooling rates were 20°C/min, with some runs also

conducted with 10°C/min.

The solidus and liquidus temperatures in the system are reproduced by the

thermodynamic model satisfactorily without the use of a ternary interaction parameter.

The extrapolation of the binary interaction parameters was made using an asymmetric

Kohler/Toop model [188], where NaCl is the asymmetric component. The calculated

minimum melting point is at x(NaCl)=0.511, x(Na2CO3)=0.266, x(Na2SO4)=0.224 and a

temperature of 612°C.

Isoplethal sections in the system are shown in Figure 3.9 together with

experimental points from Bergman and Sementsova [100] and from this study, and the

calculated ternary phase diagram is shown in Figure 3.10.

55


NaCl(s) + Na2(SO4,CO3)(hexa ss)

Liquid

Liquid + Na2(SO4,CO3)(hexa ss)

x(Na2CO3)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0500

550

600

650

700

750

800

850

900

Liquid

NaCl(s)+Na2(SO4,CO3)(hexa ss)

Liquid+Na2(SO4,CO3)(hexa ss)

x(Na2SO4)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0550

600

650

700

750

800

850

900

Fig 3.9a. Fig 3.9b

Liquid

NaCl(s)+Na2(SO4,CO3)(hexa ss)

x(NaCl)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0550

600

650

700

750

800

850

900

Fig 3.9c

Figure 3.9. Calculated isoplethal sections in the NaCl-Na2CO3-Na2SO4 section. a) Na2CO3-(0.67 Na2SO4+0.33 NaCl) b) Na2SO4-(0.6 Na2CO3+0.4 NaCl) c) NaCl-(0.5 Na2SO4+0.5 Na2CO3). Experimental points are from Bergman and Sementsova [100](filled circles) and from this study (Publication VI)(Crosses: thermal peaks; filled diamonds: thermal onset).

56


0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.10.20.30.40.50.60.70.80.9

0.10.2

0.30.4

0.50.6

0.70.8

0.9

Na2CO3 Na2SO4mole fraction

NaCl

750

700

650

612

700

800

a

b

Figure 3.10. Calculated liquidus projection of the NaCl-Na2CO3-Na2SO4 system. Isothermal lines are calculated at 50°C intervals. Precipitating solid phases are NaCl (a) and the hexagonal solid solution, Na2(SO4,CO3) (b). The minimum melting point is denoted by the symbol .

3.5.2.23 KCl-K2SO4-K2CO3

Bergman and Sementsova [100] measured the liquidus temperature for several sections in

the KCl-K2CO3-K2SO4 system using visual-polythermal methods. Based on the measured

liquidus temperatures they estimated the minimum melting point of the system to be at

the composition of x(KCl)=0.630, x(K2CO3)=0.312, x(K2SO4)=0.058 and at a

temperature of 622°C. The solidus temperatures were measured for several compositions

in this study [147] using simultaneous DTA and TGA. Several cycles were made between

temperatures close to the liquidus and solidus in order to homogenize the solid solutions

in the samples. The heating and cooling rates were 20°C/min, with some runs also

conducted with 5°C/min.

57


The solidus and liquidus temperatures in the system were not reproduced

satisfactorily with only binary interaction parameters. Therefore, a ternary parameter was

included to give a better prediction of the phase relations. The ternary parameter gives the

effect of one component on the interaction parameter for the binary system containing the

two other components. The common-cation ternary parameter is given in Appendix C.

The extrapolation of the binary interaction parameters was made using an

asymmetric Kohler/Toop model [188], where KCl is the asymmetric component. The

calculated minimum melting point is at x(KCl)=0.626, x(K2CO3)=0.316, x(K2SO4)=0.058

and a temperature of 628°C.

The calculated ternary phase diagram is shown in Figure 3.11, and isoplethal

sections in the system are shown in Figure 3.12 together with experimental points from

Bergman and Sementsova [100] and from this study.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.10.20.30.40.50.60.70.80.9

0.10.2

0.30.4

0.50.6

0.70.8

0.9

K2CO3 K2SO4mole fraction

KCl

900

1000

800

700

700

628

a

b

Figure 3.11. Calculated liquidus projection of the KCl-K2CO3-K2SO4 system. Isothermal lines are calculated at 50°C intervals. Precipitating solid phases are KCl (a) and the hexagonal solid solution, K2(SO4,CO3) (b). The minimum melting point is denoted by the symbol .

58


KCl(s)+K2(SO4,CO3)(ortho ss)

KCl(s)+K2(CO3,SO4)(hexa ss)

Liquid

Liquid+K2(CO3,SO4)(hexa ss)

x(K2SO4)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0500

600

700

800

900

1000

1100

KCl(s)+K2(CO3,SO4)(hexa ss)

Liquid

x(KCl)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0600

700

800

900

Fig. 3.12a Fig 3.12b

Liquid

KCl(s)+K2(SO4,CO3)(hexa ss)

K2(SO4,CO3)(ortho ss)

KCl(s)+

x(A)

T / (

°C)

0.0 0.2 0.4 0.6 0.8 1.0600

620

640

660

680

700

720

Fig 3.12c

Figure 3.12. Calculated isoplethal sections in the KCl-K2CO3-K2SO4 section. a) K2SO4-(0.14 K2CO3+0.86 KCl) b) KCl-(0.7 K2CO3+0.3 K2CO3) c) A-B section: A=(0.29 K2SO4+0.71 KCl), B=(0.43 K2CO3+0.57 KCl). Experimental points are from Bergman and Sementsova [100](filled circles) and from this study (Publication VI)(Crosses: thermal peaks; filled diamonds: thermal onset).

3.5.2.24 Na2SO4-K2SO4-Na2S2O7-K2S2O7

The phase equilibrium in the Na2SO4-K2SO4-Na2S2O7-K2S2O7 system has been studied

with visual-polythermal methods [120] and by thermogravimetry [121]. In these

experiments the liquid phase consists of Na+, K+, SO42- and S2O7

2-, and is therefore a

reciprocal phase. The condensed phases are in equilibrium with the gas phase, which

59


consists of SO2, SO3 and O2. Flood and Førland [121] showed that at specific

temperatures and partial pressures of SO3, liquid Na2SO4-Na2S2O7 will be more sulfate-

rich than liquid K2SO4-K2S2O7. Accordingly, liquid Na2S2O7 will decompose at lower

temperatures than K2S2O7. Flood and Førland also showed that in a reciprocal

Na+,K+/SO42-,S2O7

2- liquid, the composition will become more sulfate-rich as Na/(Na+K)

increases. The experiments were performed at 662°C with controlled SO3 partial

pressure. Coats et al. [120] used visual methods to study the formation of a liquid phase

for mixtures of Na2SO4 and K2SO4 in contact with a gas containing 200 or 2000 ppm of

SO3. They showed that the condensed phases are fully molten at temperatures of 330-

430°C in 200 ppm SO3 and at 330-500°C in 2000 ppm SO3. At lower temperatures the

solid phases are alkali disulfates (also called pyrosulfate), and at higher temperatures the

liquid will decompose to solid alkali sulfates. The liquid phase is a reciprocal Na+,

K+/SO42-,S2O7

2- liquid that is rich in S2O72-. At temperatures above 800°C, the solid

sulfates will melt and form a liquid that is rich in SO42-.

In the present work, no additional reciprocal parameter for the liquid was

included, meaning that 0724/ =Δ OSSONaKg . The Gibbs energy for the reciprocal quadruplets

is directly calculated from the Gibbs energy of the unary and binary quadruplets. The

phase equilibrium in the multicomponent system is satisfactorily predicted without any

additional parameters. The calculated liquidus projection of the reciprocal Na2SO4-

K2SO4-Na2S2O7-K2S2O7 system is shown in Figure 3.13.

60


0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

K2SO4 Na2SO4

K2S2O7 Na2S2O7

500

KNaS2O7

a

b c

d e f

600

700

800

900

Figure 3.13. Calculated liquidus projection of Na2SO4-Na2S2O7-K2SO4-K2S2O7. Isothermal lines are plotted in 50°C intervals. The precipitating solid phases in the different phase fields are annotated with a-f. a) Hexagonal (Na,K)2SO4, b) Orthorhombic K-rich (K,Na)2SO4, c) Glaserite, d) K-rich (K,Na)2S2O7 e) KNaS2O7 f) Na-rich (Na,K)2S2O7. Formation of the gas phase is suppressed in the calculations.

3.5.2.25 Na2CO3-Na2SO4-K2CO3-K2SO4

The liquidus temperatures in the reciprocal ternary Na2CO3-Na2SO4-K2CO3-K2SO4

system have been measured by visual-polythermal methods [164, 189, 190]. The

hexagonal solid solution is the only solid phase in equilibrium with the liquid phase.

Sementsova et al. [190] suggested that the hexagonal solid solution has a miscibility gap,

which can be seen from the solid-liquid equilibrium close to the minimum melting

61


temperature of the system. Small composition-independent reciprocal parameters were

optimized for both the liquid phase and the hexagonal solid solution. When only one

reciprocal parameter was used, either for the liquid phase or the solid solution, poorer

agreement with the experimental data was obtained.

The calculated minimum melting temperature is 671°C at n(SO42-)/(n(SO4

2-)

+n(CO32-))=0.71 and n(Na+)/(n(Na+)+n(K+))=0.60. The calculated liquidus projection of

the Na2CO3-Na2SO4-K2CO3-K2SO4 system is shown in Figure 3.14.

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

Na2SO4

K2SO4

Na2CO3

K2CO3

671

800

900

700

1000

Figure 3.14. Calculated liquidus projection of Na2CO3-Na2SO4-K2CO3-K2SO4. Isothermal lines are plotted in 50°C intervals. The precipitating solid phase is the hexagonal (Na,K)2(CO3,SO4) solid solution. The symbol denotes the composition of the calculated minimum melting temperature in the system.

62


3.5.2.26 NaCl-Na2SO4-KCl-K2SO4

The phase relations in the ternary reciprocal system has been studied with thermal

analysis [128-130] and visual-polythermal methods [135, 138, 191]. The different studies

give similar results for the liquidus temperature, even though a considerable scatter can

be observed. Jänecke [128] reported the (Na,K)Cl solid solution and the hexagonal

(Na,K)2SO4 solid solution as the precipitating phases at the liquidus. In contrast, Akopov

and Bergman [135] reported a third precipitating phase, and in a later study [138] two

additional precipitating phases close to the minimum melting point of the system. The

three phases have a maximum thermal stability of about 680 to 730°C. Akopov and

Bergman [135, 138] did not identify these precipitating phases, but suggested that they

might be binary alkali sulfate compounds, either solid solutions or stoichiometric phases.

It is not fully clear if the additional phases actually have been identified or if their

existence is assumed based on slope changes in the liquidus line of several sections. The

existence of a reciprocal solid phase has not been shown. The three unidentified

precipitating phases in the studies of Akopov and Bergman [135, 138] are not in

agreement with the phase relations in the Na2SO4-K2SO4 system. The exact nature of

these phases is not clear, and they are not mentioned in the other studies of this system.

The three unspecified phases have not been included in the present optimization of the

reciprocal systems, as there is no basis for evaluating their thermodynamic properties.

A reciprocal parameter for the liquid phase was optimized for this system. The

parameter is given in Appendix C.The calculated minimum melting point in the NaCl-

Na2SO4-KCl-K2SO4 system is at the composition of n(K+)/(n(Na+)+n(K+))=0.384 and

n(SO42-)/(n(SO4

2-)+n(Cl-))=0.389 at a temperature of 517°C. The liquidus projection of

the system is shown in Figure 3.15.

63


0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

Na2SO4 K2SO4

(NaCl)2 (KCl)2700

600

900800

700600

517

a

b

Figure 3.15. Liquidus projection of the (NaCl)2-(KCl)2-Na2SO4-K2SO4 system. Isothermal lines are plotted in 50°C intervals. The precipitating solid phases are the hexagonal (Na,K)2SO4 solid solution (a) and the (Na,K)Cl solid solution (b). The minimum melting point of the system is denoted by the symbol .

3.5.2.27 NaCl-Na2CO3-KCl-K2CO3

The liquidus of the NaCl-Na2CO3-KCl-K2CO3 system has been measured using thermal

analysis [129, 140, 167, 192-194] and visual-polythermal methods [164, 191, 195].

Solidus temperatures have been measured with thermal analysis [194]. The liquidus

temperature on the NaCl-K2CO3 and KCl-Na2CO3 sections shows some variation

between the different studies. Differences of up to 60°C can be observed in the Na2CO3-

rich region of the KCl-Na2CO3 section. Similar variations are also observed in the NaCl-

64


Na2CO3 system, suggesting possible experimental difficulties at Na2CO3-rich

compositions. The liquidus projection shows that the (Na,K)Cl solid solution and the

hexagonal (Na,K)2CO3 solid solutions are the precipitating solid phases.

A small reciprocal parameter for the liquid phase was added, mainly on the basis

of the liquidus temperatures in the diagonal sections. The reciprocal parameter is given in

Appendix C. The calculated minimum melting point in the NaCl-Na2CO3-KCl-K2CO3

system is at the composition of n(K+)/(n(Na+)+n(K+))=0.269 and n(CO32-)/(n(CO3

2-)

+n(Cl-))=0.314 and at a temperature of 565°C. The calculated reciprocal liquidus

projection is shown in Figure 3.16.

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

(KCl)2

K2CO3

(NaCl)2

Na2CO3

800800

700

600

800

565

600

a

b

Figure 3.16. Liquidus projection of the (NaCl)2-(KCl)2-Na2CO3-K2CO3 system. Isothermal lines are plotted in 50°C intervals. The precipitating solid phases are the hexagonal (Na,K)2CO3 solid solution (a) and the (Na,K)Cl solid solution (b). The minimum melting point of the system is denoted by the symbol .

65


3.5.3.28 Multicomponent systems: NaCl-Na2SO4-Na2CO3-KCl-K2SO4-K2CO3

Bergman and Sementsova have measured the liqudus temperature in the multicomponent

reciprocal NaCl-Na2SO4-Na2CO3-KCl-K2SO4-K2CO3 system using visual-polythermal

methods [142, 164, 191]. The precipitating solid phases are the (Na,K)Cl solid solution

and the hexagonal (Na,K)2(SO4,CO3) solid solution. An additional primary precipitating

phase at sulfate-rich compositions was proposed by Bergman and Sementsova [142] and

Sementsova and Bergman [164]. The phase was not identified but assumed to be an

intermediate phase in the Na2SO4-K2SO4 system, either 2Na2SO4⋅K2SO4 or

3Na2SO4⋅K2SO4. A similar phase has been reported by Akopov and Bergman [135, 138]

in the NaCl-Na2SO4-KCl-K2SO4 system. A mineral called hanksite has been identified

with the chemical composition Na22K(CO3)2(SO4)9Cl [196-199]. Ramsdell [199]

concluded that if hanksite is heated it will decompose to a solid solution with a

composition of 9Na2SO4·2Na2CO3 and to KCl before any melting occurs.

Correspondingly, hanksite is not a primary precipitating solid phase from a melt with the

hanksite composition. The lowest liquidus temperature in the reported sections is 512°C

[142]. No solidus temperatures have been reported.

The calculated liquidus temperatures versus experimental liquidus temperatures

from Bergman and Sementsova [142, 164, 191] are shown in Figure 3.17. The

thermodynamic properties of the multicomponents liquid phase calculated by the model

are obtained solely from binary, ternary, and ternary reciprocal parameters. No additional

higher-order parameters are added to the liquid model or the solid solution models. The

calculated liquidus temperatures for the multicomponent systems are predictions based on

optimizations of the binary and ternary subsystems.

The calculated liquidus temperatures are generally in good agreement with the

measured liquidus temperatures. The maximum difference between the calculated and

experimental liquidus temperatures is about 30°C. As no experimental section can be

found in more than one study, it is difficult to estimate the experimental error of the

studies. However, the temperature measurements at the intersection of the NaCl-K2SO4-

K2CO3 and KCl-Na2SO4-Na2CO3 systems show differences of up to 20°C at specific

compositions [191]. As the liquidus temperatures in the NaCl-Na2CO3-KCl-K2CO3 and

66


NaCl-Na2SO4-KCl-K2SO4 systems show experimental variations of 30°C or higher, it

must be considered that the liquidus predictions of the multicomponent sections are well

within the experimental error limits.

The lowest calculated melting point of the NaCl-Na2SO4-Na2CO3-KCl-K2SO4-

K2CO3 system is at a temperature of 501°C and a composition of

n(K+)/(n(K+)+n(Na+))=0.341, n(SO42-)/(n(SO4

2-)+n(CO32-)+n(Cl-))=0.294, and n(CO3

2-)/

(n(SO42-)+n(CO3

2-)+n(Cl-))=0.132. The solid phases in equilibrium with the liquid phase

are the alkali chloride solid solution and the hexagonal alkali sulfate-carbonate solid

solution.

500

600

700

800

900

1000

500 600 700 800 900 1000T (meas.) / °C

T(ca

lc.)

/ °C

Figure 3.17. Calculated liquidus temperatures of the Na+,K+/ Cl-,SO4

2-,CO32- system versus measured liquidus temperatures

from Sementsova and Bergman [164] (circles) and Bergman and Sementsova [191] (squares).

67


3.6 Discussion

An extensive thermodynamic evaluation and optimization of the thermodynamic

properties of the phases in the Na+,K+/CO32-,SO4

2-,S2-,S2O72-,Sx

2-,Cl-,Va- system was

conducted in this study. All possible combinations of binary and higher order systems

were not evaluated due to the lack of experimental data. Systems containing alkali

sulfides or polysulfides often show considerable scatter in the experimental phase

relations due to experimental difficulties. Additionally, considerable uncertainties exist

for the low-temperature phase relations involving complex solid solutions. Large

uncertainties in the experimental data also give similarly large uncertainties in the

thermodynamic descriptions of the phases. However, most experimental measurements of

solid-liquid phase equilibrium can be predicted by the obtained thermodynamic database

within the experimental uncertainties in these studies. Additional well-defined

measurements of thermodynamic properties of the liquid phase and the solid solutions

and of the phase relations of the binary and multicomponent systems could contribute to

the validation of the present database and would also provide input data for further

improvements.

3.7 Conclusions

A critical evaluation of all available thermodynamic and phase diagram data for the Na-

K-S system and for the Na+,K+/CO32-,SO4

2-,Cl-,S2-,S2O72- system was performed. The

thermodynamic properties of the liquid phase were modeled using the Modified

Quasichemical Model in the Quadruplet Approximation. The present database reproduces

the solid-liquid equilibrium of the binary, ternary and quaternary systems to within the

experimental uncertainties. The database of thermodynamic data for all phases can be

used, along with other databases and Gibbs energy minimization software, to calculate

the phase equilibria and all thermodynamic properties of multicomponent alkaline salt

mixtures, which are of great importance for ash-related problems in biomass combustion

and for many chemical processes in black liquor combustion.

68

Chapter 4-Borate autocausticizing

4. Alkali borates in the kraft recovery boiler

In the kraft pulping process, the white liquor is produced by a causticizing process, in

which dissolved smelt (green liquor) reacts with lime to form dissolved NaOH and solid

CaCO3. The aqueous phase is separated from the lime mud and is used as the pulping

agent. The CaCO3 is calcined in a lime kiln to CaO. The main reactions in the

causticizing process are given below:

CaO(s) + H2O(l) ⇌ Ca(OH)2(s) [Eq. 4.1]

Ca(OH)2(s) + Na2CO3(aq) ⇌ 2 NaOH(aq) + CaCO3(s) [Eq. 4.2]

CaCO3(s) ⇌ CaO(s) + CO2(g) [Eq. 4.3]

The main stages of the chemical recovery in the kraft pulping process are shown in the

Figure 4.1.

CaO

Na,S

NaOH(aq) Na2S(aq)

Na2CO3(l) Na2S (l)

CaCO3

Wood

PulpNa,S

Na2CO3(aq) Na2S (aq)

Lime Burning

Burning

Evaporation

Washing

Pulping

Causticizing

Dissolving

Figure 4.1. The chemical recovery cycles in the kraft pulping process, showing the chemicals related to causticizing in different processes in the pulp mill

69


The conventional causticizing process using lime is an integral part of the kraft process.

However, it has drawbacks in terms of economy, energy economy, efficiency, and fuel

consumption. These limitations provided the incentive for development of alternative

causticizing processes. In the 1970’s, much of the work on alternative causticizing

processes was conducted in Finland by Kiiskilä [200-206] and Janson [207-214]. There

was renewed interest at the end of the 1990’s. The main focus has been on reducing the

load on the lime cycle; causticizing in pulping processes with low causticizing demand;

and eliminating the increased causticizing demand in black liquor gasification

technologies.

4.1 Definitions of nonconventional causticizing concepts

The main concept behind the alternative causticizing technologies is to add a compound

to the furnace, where it reacts with molten Na2CO3, releasing CO2. Dissolving the

resulting smelt in water yields white liquor directly. The alternative causticizing concepts

can be divided into two categories based on the water solubility of the reaction product:

autocausticizing, and direct causticizing. In autocausticizing, the pulping chemicals

causticize themselves during combustion of the black liquor, without the need for

addition or removal of causticizing compounds or reaction products [215]. The

autocausticized smelt must be water-soluble, and the decarbonating agent or its

derivatives travel through the entire pulping and recovery cycle, either as active agents in

the pulping process or as inert materia. In direct causticizing, a decarbonating agent is

added to the chemical recovery cycle, and the pulping chemicals are causticized in the

recovery boiler furnace. The decarbonating agent is regenerated when the smelt is

dissolved in a separate process. The decarbonating agent must be insoluble in water, and

it is be separated from the aqueous phase as a solid phase. In direct causticizing, the

decarbonating agents do not travel through the pulping process. The term in situ

causticizing is used as a term to include both autocausticizing and direct causticizing. The

term smelt causticizing is used to describe a process in which the decarbonation reactions

70


take place in the recovery boiler smelt. Strictly speaking, the terms autocausticizing and

direct causticizing are not included in the term smelt causticizing, but many of the in situ

causticizing concepts involve causticizing reactions in the smelt.

4.2 Borate autocausticizing

Jan Janson [207-214] proposed an alternative chemical pulping process in the 1970’s, in

which the pulping chemicals (or portions of them) would also act as decarbonating agents

for the Na2CO3 formed in the recovery boiler during the traditional kraft process. The

addition of lime or other chemicals to the green liquor are not required as, ideally, the

green liquor is identical to the white liquor. Janson carried out an extensive study to find

suitable chemicals that would form sufficiently alkaline solutions for effective pulping,

which would also serve as effective decarbonating agents in the recovery boiler furnace.

The chemicals investigated were B2O3, P2O5, SiO2, and Al2O3, or sodium salts of these

oxides [207, 211]. The principle behind autocausticizing can be illustrated by the general

reactions given below, where X represents an above-mentioned oxide:

Pulping:

NaOH(aq) + Org-H ⇌Org-Na + H2O(l) [Eq. 4.4]

Combustion:

Org-Na →Na2CO3(s,l) [Eq. 4.5]

Decarbonation of smelt:

n X(s,l) + Na2CO3(s,l) ⇌Na2XnO(s,l) + CO2(g) [Eq. 4.6]

Dissolving of smelt/formation of pulping agents:

Na2XnO(s,l) + H2O(l) →2 NaOH(aq) + n X(aq). [Eq. 4.7]

The formation of Na2CO3 during the combustion of black liquor (Eq. 4.5) can also be

inhibited by the presence of the causticizing chemicals, if the organically bound sodium

reacts with the causticizing chemicals instead of forming Na2CO3.

71


Several problematic aspects were encountered with many of the compounds

studied. The compound Na4P2O7, sodium diphosphate, was shown to have good

decarbonating ability, but the dissolved salts were not sufficiently alkaline to be utilized

in the normal kraft process. The compounds Na2Si2O5 and Al2O3 were shown to be

associated with the precipitation of solids from alkaline solutions, which in practice could

cause severe problems with scaling on evaporator surfaces.

According to Janson’s studies [207-214], the most promising compounds for

autocausticizing are sodium borates. The compound NaBO2 was shown to be a suitable

decarbonating compound which also yields pulping liquors of acceptable quality. The

main reactions for the autocausticizing concept proposed by Janson are the following:


2 NaBO2(s,l) + Na2CO3(s,l) ⇌Na4BB2O5(s,l) + CO2(g) [Eq. 4.8]


Na4BB2O5(s,l) + H2O(l) → 2 NaOH(aq) + 2 NaBO2(aq). [Eq. 4.9]

A schematic diagram of the borate autocausticizing applied to the kraft pulping process is

given in Figure 4.2.

Na, S, NaBO2(aq) Na4B2O5(l)

Na2S (l)

Wood

Pulp Na, S, B

NaBO2(aq) NaOH(aq) Na2S (aq)

Burning

Evaporation

Washing

Pulping

Dissolving

Figure 4.2. Full borate autocausticizing applied to the kraft pulping process according to Janson [207-214], showing the borate speciation at different stages

72


Janson studied the use of borates in both kraft pulping and alkali pulping. Janson and

Pekkala [208-210] replaced one mole of NaOH by one mole of Na2HBO3 and found no

significant differences in the degree of delignification of the wood or mechanical

properties of the pulp in alkali cooking, oxygen alkali cooking and bleaching, or kraft

cooking. The term Na2HBO3 is used in a nominal sense, as in reality it was a mixture of

NaOH and NaB(OH)4 (or NaBO2⋅2H2O) with an overall Na/B ratio of 2. The exact

speciation of the borates in a solution with an Na/B ratio of 2 is uncertain due to the

complex aqueous chemistry of borates. The results of Janson and Pekkala [208-210]

suggest that with the use of Na2HBO3 (=NaOH + NaBO2), the borate component has

neither a positive nor a negative effect on the cooking and bleaching.

The borate-containing black liquors had considerably lower heating values on a

dry solids basis compared to the borate-free black liquors due to the higher content of

inorganic salts. The endothermic decarbonation reactions will also reduce the heating

value of the black liquor if the reactions occur. Janson [209] measured the viscosity of

borate-containing and borate-free black liquors from kraft pulping. He found no

difference between the viscosity of borate-containing and borate-free liquors from birch,

but borate-containing black liquors from pine had higher viscosities than borate-free

liquors at fixed dry matter contents.

Janson also studied the autocausticizing reactions of sodium compounds as a

function of temperature and Na/B ratio using various gas compositions (N2 or N2/CO2

mixtures) [211]. Organic compounds were added in some experiments to investigate the

reactions in synthetic black liquor from an alkaline cooking process. The results showed

that decarbonation was more or less complete when Na/B<2. Carbonate was retained in

the reaction products at higher Na/B ratios. The decarbonation reactions were inhibited in

experiments with high CO2 content in the gas phase, which is to be expected based on

equilibrium considerations of the autocausticizing reaction (Eq. 4.8). Experiments with

kraft black liquors and with mixtures of Na2CO3, Na2S, sodium borates, and organic

compounds showed that sulfur has no significant effect on the autocausticizing reactions

[212].

73


A full-scale plant trial of borate autocausticizing was carried out at the Enso

Gutzeit liner board mill in Kotka, Finland from 1981-1982. The results were

inconclusive, and the mill trials were discontinued. Grace [216] suggested that full-scale

implementation of borate autocausticizing is technically difficult. The high amount of

borate in the liquor cycle, low heating values and high viscosity of borate-containing

black liquor, the need for auxiliary fuels, and the cost of make-up chemicals are the most

serious issues limiting the full-scale application of borate autocausticizing.

4.2.1 Partial borate autocausticizing

At the end of the 1990’s, there was a renewed interest in borate autocausticizing. Tran et

al. [217] suggested that partial autocausticizing using borates could be an attractive

alternative for reducing the use of lime in the causticizing cycle. In the partial

autocausticizing concept, less borate is used than in the autocausticizing concept of

Janson, and the Na2CO3 is only partially decomposed in the recovery boiler. The

remaining Na2CO3 is causticized in the conventional manner. This reduces the amount of

borates in the liquor cycle, and lessens the effect of borates on the heating value and

viscosity of the black liquor. Partial autocausticizing is of interest mainly to pulp mills

where causticizing is a limiting factor in pulp production. Nonconventional causticizing

concepts, including partial borate autocausticizing, are of interest to pressurized black

liquor gasification technologies, as more Na2CO3 is formed during black liquor

conversion under pressurized conditions than under atmospheric conditions.

Tran et al. [217] studied the reactions between Na2CO3 and sodium borates with

thermogravimetry at varying Na/B ratios using the borate compounds Na2BB4O7 and

NaBO2. They concluded that the decarbonation of Na2CO3 at 925°C is complete at Na/B

ratios of 2 or lower, in agreement with the studies of Janson. However, Tran et al. [217]

found that decarbonation also takes place at Na/B ratios above 2. They proposed that the

reaction product is Na3BO3, sodium orthoborate, rather than Na4B2B O5, as proposed by

Janson. Tran et al. [217] also found that the reaction products can be recarbonated if the

surrounding gas is changed from N2 to CO2.

74


The main reactions for the partial autocausticizing concept proposed by Tran et al.

[217] are the following:


NaBO2(s,l) + Na2CO3(s,l) ⇌Na3BO3(s,l) + CO2(g) [Eq. 4.10]


Na3BO3(s,l) + H2O(l) → 2 NaOH(aq) + NaBO2(aq). [Eq. 4.11]

The implication is that one mole of boron in the liquor cycle can produce two moles of

NaOH, instead one mole of NaOH as found by Janson. If the causticizing reactions

proceed to completion, the amount of borates in the liquor cycle would be lower to

produce white liquor with a specific alkalinity. However, in subsequent studies by Tran et

al. [218] and Lindberg et al. [219, 220], it was shown that the decarbonation reaction

originally proposed by Tran et al. [217] does not go to completion at Na/B ratios of 3 or

higher. Previous studies, unrelated to the autocausticizing process, support these findings.

At Na/B ratios above 3 the borate composition is a mixture of Na4BB2O5 and Na3BO3. The

experimental results of Tran et al. [217] are probably due to the volatilization of Na2CO3,

which was not fully accounted for. The properties of carbonate-borate melts in borate

autocausticizing will be discussed in more detail in Section 4.4.

Mill trials using partial borate autocausticizing have been carried out in North

America [221, 222] and in Sweden [223], showing that the concept is a viable means for

reducing the lime requirements of pulp mills without substantially affecting mill

operations, pulp properties, or quality. A decrease in the dust load was observed in the

Swedish trials [223], probably due to the decrease in Na volatilization associated with

decomposition of Na2CO3. Fouling patterns of the recovery boilers also changed after the

introduction of borates to the liquor cycle, which was expected from the predictions of

Hupa et al. [224]. These changes could be managed by the boiler operators, and no signs

of increased corrosion were observed.

75


4.3 Objective of the experimental study of borate autocausticizing

The objective of this study of borate autocausticizing was to investigate the

decarbonation reactions of alkali carbonate and alkali borates involved in reactions

occurring in the kraft recovery boiler smelt bed. The emphasis was on the effect of

various chemical components and physical conditions in the kraft recovery boiler. The

effects of temperature, gas composition, boron content, and alkali metal contents were

investigated, along with the reversibility of the autocausticizing reactions. The study was

performed using differential thermal analysis and thermogravimetry.

4.4 Properties of borate compounds and phases involved in borate

autocausticizing

The element boron is a metalloid and exists at low concentrations in the earth’s crust

(about 15 ppm) [225]. In nature boron occurs exclusively in the form of borates or

borosilicates. The most common boron mineral is tourmaline, a highly complex

borosilicate which is used mainly as a gemstone or for piezoelectric purposes. The

mineral borax, Na2BB4O5(OH)4⋅8H2O (=Na2B4B O7⋅10H2O), has been known and used since

ancient times. Also known as tincal, it and the partially dehydrated variant kernite,

Na2BB4O7⋅4H2O, are the most important sources of boron. The term borax is sometimes

used for all compounds with the general formula Na2B4B O7⋅nH2O (n≥0). Today, the main

use of borates is in the manufacture of fiber glass and heat resistant glass. Boron

compounds are also used as bleaching agents (sodium perborate, NaBO3) and reducing

agents in organic synthesis (sodium borohydride, NaBH4).

4.4.1 Borates in the recovery boiler

In the borate autocausticizing concept the borate compounds are expected to be sodium

borates with an Na/B ratio higher than 1. Na2BB4O7⋅5H2O is used as the make-up

chemical, but after exiting the recovery boiler, the sodium borates will be NaBO2,

76


Na4B2B O5 or Na3BO3. Corresponding potassium borates may also form, as potassium is an

important nonprocess element in many pulp mills.

Alkali borates are soluble in water, and outside the recovery boiler, borates exist

mainly in aqueous form in the pulp mill. Ingri [226] reviewed the equilibria between

aqueous borate anions. The behavior of borates in aqueous solutions is highly complex

due to the formation of various polyanions, which contain several boron atoms per anion,

and due to the formation of various hydroxyl-complexes. According to Ingri [226] the

borate exists exclusively as a B(OH)4- ion at pH above 11. As most aqueous solutions in

the kraft pulping process are strongly alkaline, B(OH)4- should be the main borate species

in the aqueous phase in the liquor cycle. The smelt dissolving reactions reported by

Janson and Tran should be slightly modified and rather be written as follows:

Na4BB2O5(s,l) + 5 H2O(l) → 4 Na (aq) + 2 OH (aq) + 2 B(OH)+ -4

-(aq) [Eq. 4.12]

Na3BO3(s,l) + 3 H2O(l) → 3 Na+(aq) + 2 OH-(aq) + B(OH)4-(aq) [Eq. 4.13]

The aqueous chemistry of borates will not be discussed further, as it does not lie within

the scope of this study.

The behavior of borates under anhydrous conditions is also complex, and it is

mainly because borates tend to form polymeric units much as silicates do. A complicating

factor is that borates can have both three- and fourfold coordination in the solid and

liquid state, forming both trigonal [BO3] and tetrahedral [BO4] polymeric borate units. In

contrast, silicates form only tetrahedral units at normal pressure. In borate

autocausticizing, the borate compounds of interest are those with an Na/B ratio of 1 or

greater. According to the phase diagram of Na2O-B2O3 measured by Milman and Bouaziz

[227], the solid sodium borate phases with Na/B equal to or larger than 1 are NaBO2

(=Na2O⋅BB2O3); Na6B4B O9 (=3Na2O⋅2B2O3); Na4BB2O5 (=2Na2O⋅B2B O3); Na10BB4O11

(=5Na2O⋅2B2O3); and Na3BO3 (=3Na2O⋅B2B O3). The authors were unable to identify the

composition of the compounds Na6BB4O9 and Na10B4B O11 with certainty; they may

correspond to the compounds Na5BB3O7 (=5Na2O⋅3B2O3) and Na7B3B O8 (=7Na2O⋅3B2O3).

Only NaBO2, Na4BB2O5, and Na3BO3 were shown to co-exist with a liquid phase.

77


Abdullaev et al. [228, 229] also identified the compound Na5BO4 (=5Na2O⋅B2B O3).

Among the above-mentioned compounds, only NaBO2, Na4BB2O5, and Na3BO3 have been

observed independently by several researchers. The compounds Na6B4B O9, Na10BB4O11, and

Na5BO4 are probably of subordinate importance in borate autocausticizing. Na6B4B O9 and

Na10BB4O11 decompose at subsolidus temperatures and will probably not form at the high

temperatures in the recovery boiler. Na5BO4 would most likely be carbonated and form

Na2CO3 and other sodium borates under recovery boiler conditions. The properties of

solid NaBO2, Na4B2B O5, Na3BO3, and the corresponding potassium borates will be

discussed in Sections 4.4.1.1-4.4.1.3.

4.4.1.1 Alkali orthoborates

Alkali orthoborates are compounds containing the simplest borate unit, the trigonal BO33-

ion. The phases Na3BO3 [227, 230] and KNa2BO3 [231] are known to exist, but no report

of potassium orthoborate, K3BO3, has been found. Na3BO3 melts at 675°C [227], but the

thermal stability of KNa2BO3 is not known. During the synthesis of KNa2BO3 [231], the

maximum temperature was 470°C. Both Na3BO3 and KNa2BO3 are strongly hygroscopic.

The orthoborate ion BO33- is a planar, trigonal unit, which is the building block of the

dimeric diborate and trimeric metaborate ions.

4.4.1.2 Alkali diborates

The existence of sodium diborate, Na4BB2O5 (also called sodium pyroborate), has been

shown [227, 232], but the existence of the corresponding potassium diborate has not been

reported. Sodium diborate has a monoclinic crystal structure [232] and melts at 640°C

[227]. It is also very hygroscopic [232]. The diborate ion B2O54- is a dimer of the trigonal

BO33- ion, in which one oxygen atom bridges the boron atoms.

78


4.4.1.3 Alkali metaborates

Alkali metaborates have the general formula MBO2 (M=alkali metal). Potassium is the

only alkali metal besides sodium that exists in appreciable amounts in the kraft pulping

process. Like several other alkali borates, both NaBO2 and KBO2 are highly hygroscopic

and can form several hydrates. Toledano [233] reported that hydrated potassium borates

are not stable above 400°C. Hydrated sodium borates are not expected to be stable at

temperatures above 400°C. TGA experiments performed in this study confirm that both

NaBO2 and KBO2 are fully dehydrated at 400°C. Both NaBO2 and KBO2 are high-

melting compounds. The NIST-JANAF thermochemical data compilations give the

melting temperature for NaBO2 as 967±2°C and for KBO2 as 947±3°C. No intermediate

stoichiometric Na-K metaborate phase has been reported, but a solid solution of NaBO2

and KBO2 has been reported [234].

The metaborate ion does not exist as BO2- ions in solid phases, but rather as

polymeric ions with the general formula (BO2-)n. The metaborate ion in solid NaBO2 and

KBO2 is actually a ring-shaped B3O63- ion [235-237], where, as in LiBO2, it forms

endless chains of (BO2-)n [237].

4.4.1.4 Molten alkali borates

Studies of the properties of liquid alkali borates have been conducted mainly in the field

of glass science. Borates tend to form polymeric units in the liquid state, which means

that they are glass-forming. In the borate autocausticizing concept, molten borates exist

only in the recovery boiler, and the overall alkali-to-boron ratio in the smelt or the black

liquor will always be higher than 1 in the kraft pulping process. This section discusses the

properties of molten alkali borates with an alkali-to-boron ratio higher than 1 and the

interaction of the borates with other common species in the recovery boiler smelt, mainly

alkali carbonates.

The interaction between alkali borates and alkali carbonates in the liquid phase is

the interaction of greatest interest in the autocausticizing concept. The carbonate ion

79


depolymerizes the polymeric borate ions, forming smaller borate ions with more non-

bridging oxygen atoms and gaseous CO2. The alkali-to-boron ratio will increase for the

resulting sodium borate units, which can be seen in the following general reaction:

NaxBByO1/2x+3/2y(l) + Na2CO3(l)⇌Na2+xByB O1/2x+3/2y+1(l) + CO2(g). [Eq. 4.14]

Kamitsos et al. [238, 239] studied the speciation of borates in sodium borate-carbonate

melts and glasses with Raman and IR spectroscopy. They showed that complex borate

units and the metaborate ion, which is a ring unit with the stoichiometry B3O63-, are

depolymerized to B2O54- and BO3

3- as they react with carbonate. B2O54- will further

depolymerize to BO33- as more carbonate is added and the temperature is raised.

The decarbonation reactions vary with the temperature, the composition of the

surrounding gas atmosphere, and the boron concentration in the smelt [220]. Figure 4.3

shows the borate composition calculated as n(Na3BO3)/(n(Na3BO3)+n(NaBO2)) in

sodium carbonate/borate mixtures at different B/Na-ratios. The experiments were

performed at temperatures between 875°C and 1200°C in air or N2 [211, 217, 220, 240-

242] and in CO2 [220, 243-245]. In air and N2, the borate composition varies from NaBO2

at B/Na=1 to a borate composition close to Na3BO3 as B/Na approaches zero. If the

autocausticizing reaction according to the concept of Tran et al. [217] (Eq. 4.10) goes to

completion, the Na3BO3-composition will be reached when B/Na≤0.333. The theoretical

borate composition if the autocausticizing reaction goes to completion is plotted with

solid lines in Figure 4.3. The results from the experiments in air or N2 show that the

autocausticizing reaction goes to completion when B/Na>0.5, but when B/Na<0.5 the

reaction does not go to completion. In CO2 the borate composition varies between NaBO2

when B/Na=1 and Na4BB2O5 at B/Na≈0, and the autocausticizing reaction is incomplete

when B/Na<1. This shows that the extent of the autocausticizing reaction is largely

dependent on the composition of the gas atmosphere and the concentration of boron in

the carbonate/borate mixture. A low B/Na ratio in the salt mixture and a low partial

pressure of CO2 favor the formation of Na3BO3 over NaBO2 in the melt. Carrière et al.

[242] and Kamitsos et al. [238, 239] showed that higher temperatures lead to more

80


decarbonation and higher concentration of Na3BO3 in sodium carbonate/borate melts.

Tran et al. [217, 218] confirmed these results in later studies.

0

20

40

60

80

100

0.0 0.2 0.4 0.6 0.8 1.0

B/Na

Na 3

BO

3/(N

a 3B

O3+

NaB

O2)

[Mol

-%]

Ref [210]: 875 °CRef [216]: 925 °CRef [218]: 900 °CRef [219]: 950 °CRef [239]: 1000 °CRef [240]: 915-1050 °CRef [241]: 950 °C Na2CO3+NaBO2⇌Na3BO3+CO2

Na3BO3

NaBO2

Na4B2O5

Na2CO3+NaBO2→Na3BO3+CO2

0

20

40

60

80

100

0.0 0.2 0.4 0.6 0.8 1.0

B/Na

Na 3

BO

3/(N

a 3B

O3+

NaB

O2)

[Mol

-%]

Ref [218]: 900 °CRef [219]: 1000 °CRef [242]: 1000 °CRef [243]: 1000 °CRef [244]: 1200 °CNa2CO3+NaBO2⇌Na3BO3+CO2

Na3BO3

NaBO2

Na4B2O5

Na2CO3+NaBO2→Na3BO3+CO2

Figure 4.3a Figure 4.3b

Figure 4.3. The borate composition (Na3BO3/(Na3BO3+NaBO2)) of sodium carbonate-borate melts as a function of the B/Na ratio on a molar basis in N2 and air (a) or in CO2 (b) at temperatures between 875°C and 1200°C from different sources [211, 217, 219, 220, 240-245]. References [219, 220] are Publications I and II from this study. The solid line shows the borate composition if the autocausticizing reaction according to Eq. 4.10 goes to completion. The composition of the stoichiometric borate compounds NaBO2, Na4BB2O5, and Na3BO3 are plotted for comparison. The borate composition is based on chemical analysis or thermogravimetric measurements of the samples.

In a recovery boiler, components such as Cl, K and S play a large role in the behavior of

the smelt. Chlorine and sulfur have been considered to play a minor role in the

autocausticizing of the smelt [217, 218]. Tran et al. [218] did not observe any effect of

NaCl or KCl on the autocausticizing reaction rate, but they observed a lowering of the

initial reaction temperature with the addition of KCl. Flood et al. [243] showed that the

addition of Na2SO4 does not affect the decarbonation reactions in pure sodium systems.

Potassium may play a more significant and direct role in the autocausticizing of the

smelt, where potassium borates may react differently than the sodium borates in the

autocausticizing of the recovery boiler smelt. Flood et al. [243], Shibata et al. [246], Lim

et al. [247], and Karki et al. [248] showed that the decarbonation of alkali carbonates by

the addition of borates is lower for potassium systems than for sodium systems, while

lithium systems show higher decarbonation than either sodium or potassium systems.

81


4.5 Experimental setup

The reactions of alkali carbonate with alkali metaborate were studied using simultaneous

DTA/TGA. Weight changes of the sample and changes in the temperature differences

between the samples and a reference were measured. The weight changes correspond to

the release or uptake of gas components in the samples, and the changes in the

temperature difference are related to endothermic or exothermic reactions in the sample,

such as melting, decomposition, and absorption. The experimental parameters were the

(Na+K)/B ratio, the K/(Na+K) ratio, the heating rate, the maximum temperature, the time

spent at isothermal conditions at maximum temperature, and the CO2/N2 ratio in the gas

phase. The starting material was analytical grade alkali carbonates (Na2CO3 and K2CO3)

and hydrated alkali metaborates. The experiments were performed using the hydrated

alkali metaborates directly (NaBO2⋅2H2O) or using dehydrated alkali metaborates

(NaBO2 and KBO2). Dehydrated NaBO2 and KBO2 were produced by heating

NaBO2⋅4H2O and KBO2⋅2H2O in a furnace to 400°C or 500°C, and keeping the samples

at isothermal conditions for 30 to 60 min. The mass loss corresponded well to the amount

of water in the samples, as reported by the manufacturers. Exposure of the alkali

metaborates to air was minimized due to the hygroscopic nature of alkali borates. The

sample size was between 5 and 20 mg, and the samples were placed in open platinum

cups. The melting temperatures of the pure Na2CO3 and K2CO3 in N2 and CO2, and

dehydrated NaBO2 and KBO2 in N2 were also measured. The melting temperatures

corresponded well to the literature values. The alkali carbonates melted at slightly higher

temperatures in CO2 than in N2. Table 4.1 gives the measured melting temperatures of the

compounds.

Both a Mettler/Toledo and a TA Instruments Q600 simultaneous DTA/TGA were

used in the experiments. The DTA/TGA equipment was calibrated prior to the

experiments by standard methods, using materials provided by the manufacturers. The

experiments were run using various gas mixtures in order to investigate the interaction of

the condensed phases with the gas phase. A gas mixer with electronic flow meters was

82


used to provide the appropriate gas flows and mixtures. The gas flow was between 100

and 200 ml/min.

Table 4.1. Melting temperatures of compounds used in the experiments.

Compound Tmelt, literature / (°C) Tmelt, measured / (°C)

100% N2

Tmelt, measured / (°C)

100% CO2

Na2CO3 858 853 859

K2CO3 901 896 904

NaBO2 967 968 -

KBO2 947 950 -

Experiments with NaBO2⋅2H2O as the borate source were all performed using the

TA Instruments apparatus. In these experiments no potassium compounds were added.

After the samples attained the maximum temperature and were maintained at isothermal

conditions, they were cooled to 200°C and subsequently reheated to the maximum

temperature. The experimental matrix for the experiments with hydrated metaborate is

given in Table 4.2.

Table 4.2. Experimental conditions for experiments using hydrated borates

Na/B Gas mixture Heating rate

Maximum temperature

Time at maximum temperature

mol/mol Vol-% °C/min °C min

3 100% N2 20 950 60

3 15% CO2 + 85% N2 10 1000 30

3 100% CO2 10 1000 30

3.2 15% CO2 + 85% N2 20 950 60

5 15% CO2 + 85% N3 20 950 60

The experiments using dehydrated alkali metaborates as the borate source were all

performed using the Mettler Toledo apparatus. The samples were heated to 900°C, kept

at isothermal conditions for 60 min, cooled down to 500°C, and then reheated to 900°C.

83


The heating and cooling rate was 10°C/min. The compositional matrix for experiments

using dehydrated alkali metaborates is shown in Table 4.3.

Table 4.3. Compositional matrix for the experiments using dehydrated alkali metaborates. The (Na+K)/B and K/(Na+K) ratios are calculated on a molar basis.

(Na+K)/B 3, 5

K/(Na+K) 0, 0.1, 0.2, 0.5, 1 (0.8*)

Vol.-% CO2 in gas 0, 1, 100

*The experiment with K/(Na+K)=0.8 was performed only with (Na+K)/B=3 and 100% CO2.

4.6 Results

The starting temperature for the decarbonation of the salt mixtures varies between 650°C

and 820°C with a minimum at K/(K+Na)=0.5. The initial reaction temperature as a

function of K/(K+Na) is shown in Figure 4.4. It is likely that the sample begins to melt

simultaneously with the start of the decarbonation reaction. Visual observation of the

samples after the experiments suggests that the samples were molten at some stage. No

other thermal events which would indicate a separate melting of the sample were

observed. In the pure sodium mixtures, the initial reaction temperature is strongly

influenced by the composition of the gas atmosphere. In N2, the reaction begins at around

700°C, and in CO2, the reaction begins at around 800°C. With 1% CO2 the reaction starts

at around 740°C. The Na/B ratio does not affect the reaction temperatures. In

experiments with higher fractions of potassium, K/(K+Na), the effect of the gas

composition is similar but less pronounced. In pure potassium systems, the reaction starts

at around 800°C.

84


600

650

700

750

800

850

0 0.2 0.4 0.6 0.8 1n(K)/(n(K)+n(Na))

T [°C

]100 % N2, (Na+K)/B=31 % CO2, (Na+K)/B=3100 % CO2, (Na+K)/B=3100 % N2 (Na+K)/B=51 % CO2, (Na+K)/B=5100 % CO2, (Na+K)/B=5

Figure 4.4. Starting temperature for the autocausticizing reaction of alkali metaborate/carbonate mixtures as a function of n(K)/(n(K)+n(Na)). The experiments were performed in different gas atmospheres, with varying alkali-to-boron ratios.

The sample weight decreases after the initial reaction temperature is attained.

Weight loss in the samples is attributed to the release of CO2 from the carbonate in the

melt. As the maximum temperature of 900°C is reached, the weight loss continues in N2,

but in pure sodium mixtures the weight loss stops at 900°C, when the gases contain 1 %

or 100 % CO2 (Figure 4.5). This suggests that equilibrium is attained when the

temperature had reaches 900°C if the surrounding gas atmosphere containes CO2. In N2,

the decarbonation reaction may continue, but volatilization of sodium or boron

components might also contribute to the weight loss. The pure salts Na2CO3, K2CO3,

NaBO2, and KBO2 all tend to volatilize markedly at temperatures above their melting

points. The carbonates volatilize to a much larger extent in atmospheres of pure N2 than

85


in atmospheres of CO2 [249]. The salt KBO2 starts to volatilize below its melting point

(950°C) at around 900°C, and K2CO3 has been shown to volatilize below its melting

point (901°C) [249]. The reaction mechanisms of the volatilization of the pure salts are

however not fully understood.

65

70

75

80

85

90

95

100

0 20 40 60 80 100 120 140 160 180 200 220Time [min]

Wei

ght-%

0

100

200

300

400

500

600

700

800

900

1000

T [°

C]

100 % N2

100 % CO2

1 % CO2

Na/B=5

Na/B=3

Figure 4.5. Weight curves of samples from TGA experiments with Na2CO3/NaBO2 mixtures (Na/B=3: black; Na/B=5: gray) in different gas atmospheres (100% CO2; 1% CO2/99% N2; 100% CO2) as function of time. The temperature profile (dashed line) of the experiments is plotted relative to the right y-axis.

As the temperature is lowered to 500°C, the weight increases in the experiments

run in CO2, which clearly shows that the salts are recarbonated as temperatures are

lowered. Both in 1% CO2 and in 100% CO2, the recarbonation is close to complete in

sodium systems (97-99% of the original weight), which suggests that only CO2 is

released from the sodium salt mixtures if the surrounding CO2 atmosphere is controlled.

86


The fact that recarbonation is not fully complete is probably due to kinetic or diffusion

related constraints of the recarbonation reaction at the lower temperatures. As almost no

weight loss occurs under the isothermal conditions at 900°C in the experiments with

controlled CO2 atmospheres, the release of gaseous sodium or boron components seems

subordinate to the release of CO2. As the temperature is raised again, decarbonation

recurs at the same temperature as in the first heating. The thermogravimetric curves for

pure sodium systems are shown in Figure 4.5.

In pure potassium mixtures the decarbonation reaction starts at around 800°C

(Figure 4.6). Some weight loss occurs at temperatures below 900°C. Under isothermal

conditions at 900°C, the potassium mixtures decrease considerably in weight. This is

considered to be due mainly to the volatilization of KBO2 and/or K2CO3, based on the

fact that the pure salts already show tendencies to volatilize at 900°C. Flood et al. [243]

showed that the borate composition is close to KBO2 in potassium carbonate borate melts,

independent of the B/K-ratio at B/K<1 at 1000°C in 1 atm CO2. Lim et al. [247]

measured carbonate retention in potassium borate glasses made from K2CO3 and B2O3 at

1000°C. The potassium that is not bound as carbonate at B/K ratios between 0.2 and 1

has a composition that varies between K2BB4O7 and KBO2, which shows that K2CO3 and

KBO2 have not reacted according to Equation 4.15 to any great extent in the experiments

by Flood et al. [243] and Lim et al. [247]. Almost no recarbonation occurs in pure

potassium systems, which indicates that the influence of decarbonation analogous to

Equation 4.15 is subordinate to the volatilization of K2CO3 or KBO2 for the weight loss

at 900°C in potassium systems. The decarbonation reaction of potassium compounds is

expressed as

K2CO3 (s,l) + KBO2 (s,l) ⇌ K3BO3 (s,l) + CO2 (g). [Eq. 4.15]

The thermogravimetric curves for pure potassium systems are shown in Figure 4.6.

87


65

70

75

80

85

90

95

100

0 20 40 60 80 100 120 140 160 180 200 220

Time [min]

Wei

ght-%

0

100

200

300

400

500

600

700

800

900

1000

T [°

C]

100 % N2

100 % CO2

1 % CO2

Figure 4.6. Weight curves of samples from TGA experiments with K2CO3/KBO2 mixtures in different gas atmospheres (100% CO2, 1% CO2/99% N2, 100% CO2) as function of time. The temperature profile (dashed line) of the experiments is plotted relative to the right y-axis.

The extent of decarbonation was calculated based on the mass loss, assuming that it

occurred exclusively in the form of gaseous CO2. To compare the different experiments,

the start of the isothermal conditions at the maximum temperature maximum was chosen

as the time to calculate the extent of the autocausticizing reaction. In the experiments

with pure sodium mixtures and controlled CO2 in the gas phase, the mass loss was

negligible during the isothermal conditions, suggesting that equilibrium had been

attained. This was not the case for the experiments performed in N2 or for systems

containing potassium, probably due to the release of gas components other than CO2.

However, quantification of the release of other gas components was not possible in this

study. The borate composition was calculated as the molar ratio of alkali orthoborate to

88


alkali orthoborate and alkali metaborate. In theory, this ratio can be lower than zero or

higher than 1, but this did not occur in these experiments. This ratio is convenient as it

also directly describes the conversion of the alkali metaborates into orthoborates

according to the autocausticizing reaction given by Equation 4.10.

As K/(K+Na) increases, the extent of the autocausticizing reaction decreases. In

pure potassium systems, autocausticizing is almost nonexistent in 100% CO2. For all

compositions, autocausticizing decreases as the concentration of CO2 in the controlled

gas atmosphere increases.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

n(K)/(n(K)+n(Na))

n(M

3 BO

3 )/(n

(M3 B

O3 )

+n(M

BO2 )

)

100% N2, (Na+K)/B=31% CO2, (Na+K)/B=3100% CO2, (Na+K)/B=3100% N2, (Na+K)/B=51% CO2, (Na+K)/B=5100% CO2, (Na+K)/B=5

Figure 4.7. The extent of borate conversion at 900°C of the autocausticizing reaction according to Eq. 4.10 plotted against the molar potassium-to-alkali ratio at different alkali-to-boron ratios and in different gas atmospheres

89


In samples with (Na+K)/B=5, there is an excess of carbonate based on the

stoichiometry of the autocausticizing reaction (Equation 4.10). The experiments show

trends similar to those for (Na+K)/B=3, but most of the compositions show higher

n(M3BO3)/(n(M3BO3) +n(MBO2)) (M=Na,K) in experiments with (Na+K)/B=5. This can

also be expected based on chemical equilibrium considerations. In pure sodium systems,

the borate composition is 91 mol-% Na3BO3, 9 mol-% NaBO2 in N2 and 84 mol-%

Na3BO3, 16 mol-% NaBO2 in 1% CO2, which shows that it is possible to convert almost

all of the borate to Na3BO3 when Na/B>5 (B/Na<0.2) under conditions similar to those

occurring in the smelt bed of a recovery boiler. The extent of the borate autocausticizing

at 900°C as a function of molar ratio of K/(Na+K) is shown in Figure 4.7.

Under isothermal conditions at 900°C for 60 min, the weight decreases in many

of the experiments. The weight loss per time unit is dependent on the K/(K+Na) ratio;

high potassium ratios correspond to higher weight loss. For pure sodium systems with 1%

or 100% CO2, the weight loss is close to zero at 900°C. In pure potassium systems, the

measured weight loss in some experiments is higher than the theoretically predicted

weight loss under the assumption that CO2 is the only volatilized component.

As the samples are cooled from 900°C to 500°C, recarbonation of the salts can

occur if the experiments are run in 1% or 100% CO2. As the n(K)/(n(Na)+n(K)) is

lowered, recarbonation decreases, and no recarbonation occurs in pure potassium

systems. This also indicates that in potassium-rich systems, a volatilization of alkali or

boron components occurs instead, while in sodium-rich systems, CO2 is released and the

alkali and boron components are less volatile.

4.7 Discussion

The decarbonation of alkali carbonate/borate mixtures is dependent on several chemical

and physical factors. An increase in potassium in the smelt leads to lower conversion, but

it will also lead to lower initial reaction temperatures, which can have positive effects on

borate conversion in the kraft recovery boiler. The molar ratio of potassium-to-alkali in

90


virgin black liquors is generally around 0.05, and slightly higher in black liquors that are

fired. These low potassium contents do not affect borate conversion significantly.

The CO2 in the surrounding gas phase has a significant effect on borate

conversion in the autocausticizing reactions. High CO2 partial pressure inhibits

decarbonation of the alkali carbonates. In the char bed of a kraft recovery boiler, the CO2

partial pressure will be low due to the presence of char carbon. This could enhance the

autocausticizing reactions. Similarly, autocausticizing in burning black liquor droplets

may be enhanced by the presence of char carbon. The recarbonation of sodium-rich salt mixtures shows that recovery boiler smelt

is highly sensitive to temperature and the CO2 partial pressure in the smelt bed and that

autocausticized smelt can be recarbonated in the smelt bed if it is exposed to lower

temperatures and higher CO2 pressures.

The borate-carbonate ratio in the smelt or black liquor affects the conversion of

sodium metaborate into sodium orthoborate. A higher carbonate-to-borate ratio increases

the conversion of borates into orthoborate. Components such as sulfate, sulfide, and

chloride do not affect the autocausticizing reaction to a great extent. In this study it was

shown that borate conversion is high in N2 and in gas containing 1% CO2 when Na/B=5

(85-90% borate conversion). In mill trials using partial borate autocausticizing, the Na/B

ratios have been similar to or higher than those considered in this study. The experiments

show that the expected degree of autocausticizing can be attained under full-scale

conditions. However, the viability of partial autocausticizing at pulp mills is dependent

on both economic and operational factors, which are mill-specific.

Thermodynamic modeling of the autocausticizing reaction and of the melting

properties of borate-containing salt mixtures would yield valuable information about the

chemical processes that can occur in kraft recovery boilers firing boron-containing black

liquors. Unfortunately, there is a lack of published thermodynamic data for the critical

phases, especially Na3BO3 and Na4BB2O5. Additionally, the melting properties of alkali

salt mixtures containing borates have been poorly studied. Hupa et al. [224] made

thermodynamic predictions about the combustion of boron-containing black liquors and

about the behavior of the borate-containing alkali salt mixtures involved in partial borate

autocausticizing. However, a more in-depth evaluation of the thermodynamic properties

91


of the borates is needed for more accurate predictions. The experimental results in this

study can be used as input for a future thermodynamic evaluation of the thermodynamic

properties of solid alkali borates and borate-containing salt melts.

4.8 Conclusions

This study shows that the autocausticizing reaction between Na2CO3 and NaBO2 is a

reversible reaction which can give high borate conversion under conditions found in the

smelt bed in kraft recovery boilers. High concentrations of potassium in the black liquor

or smelt and high CO2 partial pressure in the gas phase have negative effects on the

autocausticizing reactions, decreasing the conversion of the borates into the orthoborate

form. The experimental data obtained in this study can be used to evaluate the

thermodynamic properties of sodium borates involved in the borate autocaustcizing

concept, making possible accurate thermodynamic predictions of autocausticizing.

92

Chapter 5-Conclusions and implications

5. Conclusions and implications

The thermochemistry and melting properties of alkali salt mixtures involved in black

liquor and biomass combustion were studied by evaluating and optimizing the

thermodynamic data for all known phases in the Na+,K+/CO32-,SO4

2-,S2-,S2O72-,Sx

2-,Cl-,

Va- system using experimental data as input. Additional experimental data for melting

temperatures in the ternary NaCl-Na2CO3-Na2SO4 and KCl-K2CO3-K2SO4 systems were

obtained by simultaneous differential thermal analysis and thermogravimetry, and the

results were used as input for the thermodynamic optimization. The thermodynamic

properties of the liquid phase were modeled using the Modified Quasichemical Model in

the Quadruplet Approximation, which is a thermodynamic model developed especially

for molten salts. The resulting thermodynamic database reproduces the solid-liquid

equilibria of the binary, ternary, and quaternary systems to within the experimental

uncertainties. The database of thermodynamic data for all phases can be used, along with

other databases and Gibbs energy minimization software, to calculate the phase equilibria

and all the thermodynamic properties of multicomponent alkaline salt mixtures, which

are of great importance for addressing ash-related problems in biomass and for studying

processes in black liquor combustion. Phenomena such as deposit formation and buildup

on superheater tubes in the recovery boiler are connected to the formation of a liquid

phase in alkali salt particles. Also, different types of corrosion are also related to the

formation of a molten phase. The melting behavior of alkali salts involved in such

processes can be calculated with the obtained thermodynamic database. Predictions of the

melting properties are also useful for shedding light on the behavior of the smelt bed in a

kraft recovery boiler

The behavior of alkali salt mixtures of alkali carbonates and alkali borates was

studied using simultaneous differential thermal analysis and thermogravimetry in order to

identify the effect of chemical and physical variations on the borate autocausticizing

concept. It was shown that the borate autocausticizing reactions are reversible and that

high temperatures and low borate contents enhance the conversion of borates into the

preferred orthoborate form, while high potassium content and high CO2 partial pressures

inhibit the autocausticizing reaction. It was shown that high conversion of the borates can

93

Chapter 5-Conclusions and implications

be attained under conditions prevalent in the char bed of a kraft recovery boiler. The

experimental results can be used as input for future thermodynamic evaluations of borate-

containing alkali salt systems involved in the combustion of boron-containing black

liquors.

94

References

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109

Appendix A

Thermodynamic properties of pure stoichiometric phases used in the present optimization. Thermodynamic data optimized in this work is indicated by *.

T range /K aKH o

15.298Δ b

KS o15.298 pC Reference

(J⋅mol-1) (J⋅mol-1⋅K-1) (J⋅mol-1⋅K-1)

Gas

K(g) 89000 160.3400 [52] 298.15-1900 20.7080+7.6779710⋅10-5(T/K)+5916.18(T/K)-2

1900-4300 -648.4359+0.0377245(T/K)+327221723(T/K)-2-1384080(T/K)-1

+53851.3706(T/K)-0.5

4300-5600 972897.1709-98.2407(T/K)+0.0079252(T/K)2-2.849228⋅10-7(T/K)3

+1202498191(T/K)-1-62555672.4686(T/K)-0.5 5600-6000 285.6755+6646736407(T/K)-2-2551763.5(T/K)-1

K2(g) 123683.0 249.6900 [52]

298.15-1000 212.7096-0.0488067(T/K)-2556985(T/K)-2+64186.8(T/K)-1

-5986.7190(T/K)-0.5

1000-4500 90.4840-0.0024884(T/K)-48024379(T/K)-2+213919.6(T/K)-1

-6883.4754(T/K)-0.5

Na(g) 107300.0 153.6670 [52] 298.15-2000 20.7879 2000-4000 -320.9045+0.0182633(T/K)+174135380(T/K)-2-726550.4(T/K)-1

+27946.6911(T/K)-0.5

4000-6000 580.6437-2393169990(T/K)-2-3929424.2(T/K)-1-87921.1790(T/K)-0.5

Na2(g) 142070.0 230.2430 [52] 298.15-1700 166.8484-0.0264705(T/K)-3021766(T/K)-2+60564.8(T/K)-1

-5016.4727(T/K)-0.5

1

1700-4400 -7383.7074+0.7085598(T/K)+1886772999(T/K)-2-4.13915⋅10-5(T/K)2

-10772099.0(T/K)-1+495482.0638(T/K)-0.5

4400-6000 -637.0898+1296595123(T/K)-2-4248696.2 (T/K)-1

+105287.7900(T/K)-0.5

O2(g) 0 205.147 [52] 298.15-1000 26.9241+0.0169787(T/K)+229 329(T/K)-2-6.7661652×10-6(T/K)2

-79.1617(T/K)-0.5

1000-4000 89.6813-0.0014474(T/K)-18 682 686(T/K)-2+95 804.0(T/K)-1

-4126.5372(T/K)-0.5

4000-6000 249.1731-1 184 978 422(T/K)-2+1674792.0(T/K)-1

-34 935.6696(T/K)-0.5

S(g) 277180.0 167.8270 [54] 298.15-1000 25.7047-0.0075027(T/K)+3.2933⋅10-6(T/K)2-6901(T/K)-2

1000-3400 19.8174+0.0004601(T/K)+7.12⋅10-8(T/K)2+1140873(T/K)-2

3400-10000 24.0593+1.20⋅10-6(T/K)-1.22⋅10-8(T/K)2-18736330(T/K)-2

S2(g) 128600.0 228.1640 [54] 298.15-1000 34.0968+0.0046509(T/K)-1.1129⋅10-6(T/K)2-257187(T/K)-2

1000-3400 34.0474+0.0042300(T/K)-5.500⋅10-7(T/K)2-351436.9(T/K)-2

3400-6000 36.1923+0.0011862(T/K)+4.53⋅10-8(T/K)2+14968210(T/K)-2

S3(g) 144738.0 276.2890 [54] 298.15-1000 52.9456+0.0086770(T/K)-4.0098⋅10-6(T/K)2-553877(T/K)-2

1000-6000 58.1624+1.458⋅10-5(T/K)-1.46⋅10-9(T/K)2-1117610(T/K)-2

S4(g) 135632.0 293.5570 [54] 298.15-900 72.6797+0.0180823(T/K)-8.8289⋅10-6(T/K)2-1010556(T/K)-2

900-6000 83.0503+3.656⋅10-5(T/K)-3.72⋅10-9(T/K)2-2047177(T/K)-2

S5(g) 132993.0 354.0780 [54] 298.15-900 74.9902+0.070672950(T/K)-3.46124⋅10-5(T/K)2-454141(T/K)-2

900-2800 130.5370-0.0157580(T/K)+2.5957⋅10-6(T/K)2-6850514(T/K)-2

2800-6000 103.9801-4.518⋅10-5(T/K)+4.76⋅10-9(T/K)2+15665430(T/K)-2

S6(g) 101315.0 357.8040 [54] 298.15-1600 130.1838+0.0008305(T/K)+2.5628⋅10-6(T/K)2-1558237(T/K)-2

1600-4200 155.3363-0.0040624(T/K)+1.066⋅10-7(T/K)2-29816560(T/K)-2

4200-6000 147.3935-0.0031858(T/K)+2.0077⋅10-7(T/K)2+16093550(T/K)-2

S7(g) 111890.0 404.8460 [54] 298.15-1500 153.2939+0.0062057(T/K)-2.1969⋅10-6(T/K)2-1880136(T/K)-2

1500-6000 157.9591+4.8828⋅10-6(T/K)-4.4⋅10-10(T/K)2-2568259(T/K)-2

2

S8(g) 100215.0c 432.5360 [54] 298.15-800 166.1987+0.0219772(T/K)+8.3325⋅10-6(T/K)2-1507268(T/K)-2

800-1500 181.0091+0.0405053(T/K)-1.82726⋅10-5(T/K)2-9571872(T/K)-2

1500-3900 208.7199-0.0122793(T/K)+1.5479⋅10-6(T/K)2+5886180(T/K)-2

3900-6000 180.3439+0.0005160(T/K)-3.10⋅10-8(T/K)2+43690900(T/K)-2

SO2(g) -296842 .0 248.212 [52] 298.15-1700 53.0280+4.342918×10-5(T/K)+2 282 495(T/K)-2-24 439.3(T/K)-1

+744.8739(T/K)-0.5

1700-6000 76.5423-22 531 507(T/K)-2+56 025.9(T/K)-1-1819.1530(T/K)-0.5

SO3(g) -395765.0 256.769 [52] 298.15-1000 91.2686+0.0071051(T/K)+1 916 937(T/K)-2-5.309082×10-6(T/K)2

-19 025.3(T/K)-1

1700-6000 82.0191-3 955 058(T/K)-2-7669.6(T/K)-1+175.8783(T/K)-0.5

Liquid

K(l) 2320.0 71.5718 [55] 298.15-337 77.0571-0.292422(T/K)-486770(T/K)-2+5.096948⋅10-4(T/K)2

+2.01221⋅10-17(T/K)6

337-2200 39.2886-0.0243348(T/K)-86502(T/K)-2+1.58632⋅10-5 T2

4500-6000 50.3657-252082087(T/K)-2313129.0(T/K)-1-5746.3839(T/K)-0.5

K2CO3(l) -1130390.3 170.6837 [52] 298.15-800 266.1904-4284010(T/K)-2 +2.714155×10-5(T/K)2

-4146.0845 (T/K)-0.5+27059.9(T/K)-1

800-3000 209.2000 KCl(l) -421824.9 86.5225 [53] 298.15-3000 73.5966 K2S(l) -346484.7 141.1725 [52]

298.15-820 66.9194+0.0260108(T/K) 820-3000 100.9600 K2S2(l) -424454.9 175.3419 * 298.15-3000 Cp(K2S(l))+Cp(S(l)) K2S3(l) -460585.0 209.5113 * 298.15-3000 Cp(K2S(l))+ 2⋅Cp(S(l))

3

K2S4(l) -475795.2 243.6807 * 298.15-3000 Cp(K2S(l))+ 3⋅Cp(S(l)) K2S5(l) -480545.4 277.8501 * 298.15-3000 Cp(K2S(l))+ 4⋅Cp(S(l)) K2S6(l) -480065.5 312.0196 * 298.15-3000 Cp(K2S(l))+ 5⋅Cp(S(l)) K2S7(l) -476970.7 346.1890 * 298.15-3000 Cp(K2S(l))+ 6⋅Cp(S(l)) K2S8(l) -472568.4 380.3584 * 298.15-3000 Cp(K2S(l))+ 7⋅Cp(S(l)) K2SO4(l) -1393665.4 211.5102 [52]

298.15-800 -223.9595+0.3505255(T/K)-6 082 803(T/K)-2-7.210252×10-5(T/K)2

+5621.6377(T/K)-0.5

800-3000 201.4600 K2S2O7(l) -1971380.1 285.7865 *

298.15-3000 267.0000 [56] Na(l) 2584.85 58.2644 [55] 298.15-371 51.0394-0.144613(T/K)-264308(T/K)-2+2.618297⋅10-4(T/K)2

+1.1228238⋅10-16(T/K)6

371-2300 38.1199-0.0194917(T/K)-68684(T/K)-2+1.023984⋅10-5 (T/K)2

NaCl(l) -394956.0 76.0761 [54] 298.15-1500 77.7638-0.0075312(T/K) 1500-3000 66.9440

Na2CO3(l) -1356407.9 181.1470 [52] 298.15-723 87.1219+0.0262992(T/K)+110905(T/K)-2+1.666823⋅10-4(T/K)2

723-3000 197.0330 Na2S(l) -328289.3 131.7243 * 298.15-970 77.4634+0.0175631(T/K) +27880(T/K)-2-2.2903⋅10-6(T/K)2 [52]

970-3000 92.0480 Na2S2(l) -374879.5 163.3834 * 298.15-3000 Cp(Na2S(l))+Cp(S(l)) Na2S3(l) -396365.7 195.0424 * 298.15-3000 Cp(Na2S(l))+ 2⋅Cp(S(l)) Na2S4(l) -405299.8 226.7014 * 298.15-3000 Cp(Na2S(l))+ 3⋅Cp(S(l)) Na2S5(l) -407958.0 258.3604 *

4

298.15-3000 Cp(Na2S(l))+ 4⋅Cp(S(l)) Na2S6(l) -407478.1 290.0195 * 298.15-3000 Cp(Na2S(l))+ 5⋅Cp(S(l)) Na2S7(l) -405429.3 321.6785 * 298.15-3000 Cp(Na2S(l))+ 6⋅Cp(S(l)) Na2S8(l) -402596.0 353.3375 * 298.15-3000 Cp(Na2S(l))+ 7⋅Cp(S(l)) Na2SO4(l) -1356407.9 181.1470 [52]

298.15-800 191.8357+0.0598038(T/K)-3 775 793(T/K)-2+52 366.0(T/K)-1

-3163.706(T/K)-0.5

800-3000 197.0330 Na2S2O7(l) -1895345.3 283.6012 *

298.15-3000 244.8000 [57] S(l) 1525.8 35.8430 [55] 298.15-388 15.5040+0.0372580(T/K)+1.4965⋅10-6(T/K)2+227890(T/K)-2

388-428 19762.4000-65.5855000(T/K)+0.0613285000(T/K)2-529347000(T/K)-2

428-432 57607.3000-270.6090000(T/K)+0.3179840000(T/K)2

432-453 1371.8500-5.6900700(T/K)+0.0060828000(T/K)2

453-717 -202.9580+0.5063830(T/K)-3.113001⋅10-4(T/K)2+16404400(T/K)-2

717-1300 32.0000 Solid K(s) 0 64.6800 [55]

298.15-337 77.0571-0.292422(T/K)-486770(T/K)-2+5.096948⋅10-4 (T/K)2

337-2200 39.2886-0.0243348(T/K)-86502(T/K)-2+1.58632⋅10-5 (T/K)2

-5.53176⋅1023(T/K)-10

K2CO3(s, α) -1150182.0 155.5190 [52] 298.15-1178 266.1904-4284010(T/K)-2 +2.714155×10-5(T/K)2

-4146.0845 (T/K)-0.5+27059.9(T/K)-1

1178-3000 209.2000 K2CO3(s, β) -114952.0 155.8499 [52] 298.15-1178 266.1904-4284010(T/K)-2 +2.714155×10-5(T/K)2

-4146.0845 (T/K)-0.5+27059.9(T/K)-1

1178-3000 209.2000

5

KCl(s) -436684.1 82.5503 [53] 298.15-2500 40.0158+0.025468(T/K)+364845(T/K)-2

2500-3000 103.7442 KNa2(s) -1033.2 166.9416 *

2⋅Cp(Na(s))+Cp(K(s)) KNaS2O7(s) -1974414.5 239.1637 *

298.15-692 0.5Cp(Na2S2O7(s)) +0.5Cp(K2S2O7(s, β)) K2S(s) -376560.0 115.0600 [52] 298.15-800 66.9153+0.0260208(T/K) 800-1050 -1781.8925+1.5214365(T/K)+417584199(T/K)-2

1050-1100 -4924.9043+2.8110052(T/K)+2389917691(T/K)-2

1100-1400 142.3400 1400-1401 100.9600 K2S2(s) -447500.0 146.0000 *

298.15-750 79.9981+ 0.1017130(T/K)-6.31658⋅10-5(T/K)2 [58] K2S3(s) -471100.0 192.0000 *

298.15-410 464.2148-1.9882368(T/K) +2.9283816⋅10-3(T/K)2 [58] 410-562 1043.4478-4.4810640(T/K)+0.0056233(T/K)2

K2S4(s) -480200.0 238.0000 * 298.15-432 43.0000+0.2900000(T/K) [58]

K2S5(s) -497900.0 249.0000 * 298.15-480 514.2554-2.4777648(T/K) +0.0044019864(T/K)2 [58]

K2S6(s) -496700.0 286.4000 * 298.15-470 899.9784-3.9555536(T/K) +0.0056421240(T/K)2 [58]

K2SO4(s, α) -1437706.0 175.5440 [52] 298.15-1342 -223.9595+0.3505255(T/K)-6 082 803(T/K)-2-7.210252×10-5(T/K)2

+5621.6377(T/K)-0.5

1342-3000 201.4600 K2SO4(s, β) -1424200.5 192.4077 [52] 298.15-1342 114.3634+0.081251(T/K) 1342-3000 201.46 K2S2O7(s, α) -1997959.4 258.0887 * 298.15-591 134.6525+0.1770000(T/K) [56] K2S2O7(s, β) -1989823.1 261.0446 *

298.15-692 260.0000 [56] Na(s) 0 51.3000 [55]

6

298.15-371 51.0394-0.1446133(T/K)-264308(T/K)-2+2.618297⋅10-4 (T/K)2

371-2300 38.1199-0.0194917(T/K)-68684(T/K)-2+1.023984⋅10-5 (T/K)2

-1.446417⋅1025(T/K)-10

Na2CO3(s, α) -1130768.0 138.7970 [52] 298.15-758 87.1219+0.0262992(T/K)+110905(T/K)-2+1.666823⋅10-4(T/K)2

758-1131 117.3602+0.10574432(T/K)+20126029(T/K)-2-64039.3(T/K)-1

1131-3000 189.5350 Na2CO3(s, β) -1130400.0 139.3793 [52]

298.15-758 87.1219+0.0262992(T/K)+110905(T/K)-2+1.666823⋅10-4(T/K)2

758-1131 117.3602+0.10574432(T/K)+20126029(T/K)-2-64039.3(T/K)-1

1131-3000 189.5350 Na2CO3(s, γ) -1127864.0 142.7249 [52]

298.15-758 87.1219+0.0262992(T/K)+110905(T/K)-2+1.666823⋅10-4(T/K)2

758-1131 117.3602+0.10574432(T/K)+20126029(T/K)-2-64039.3(T/K)-1

1131-3000 189.5350 NaCl(s) -411119.8 72.1322 [53]

298.15-2000 45.9403+0.016318(T/K) 2000-3000 78.5755 Na2S(s) -370284.0 100.4160 *

298.15-1000 78.9784+0.0138953(T/K) -29076(T/K)-2 [52] 1000-1276 -2151.5344+1.4883211(T/K)+417584199(T/K)-2

1276-1445 -5403.9151+2.5759776(T/K)+3791261493(T/K)-2

1445-1700 133.8880 1700-1701 92.0480

Na2S2(s,β) -403421.7 131.7960 * 298.15-1000 82.0080+0.0557288(T/K) [52] Na2S4(s) -425094.4 202.9240 * 298.15-1000 149.7872 [59] Na2S5(s) -424257.6 241.4168 * 298.15-515 179.0752 [60] Na2SO4(s, I) -1380899.0 160.1320 [52] 298.15-1157 191.8357+0.0598038(T/K)-3 775 793(T/K)-2+52 366.0(T/K)-1

-3163.7059(T/K)-0.5

1157-3000 197.0330 Na2SO4(s, IV) -1387559.0 150.1570 [52] 298.15-1157 127.6519+0.0961269(T/K)+3401(T/K)-2-8409.9(T/K)-1

1157-3000 197.0330

7

Na2SO4(s, V) -1387816.0 149.5950 [52] 298.15-1157 127.6519+0.0961269(T/K)+3401(T/K)-2-8409.9(T/K)-1

1157-3000 197.0330 Na2S2O7(s) -1949561.3 217.2828 *

298.15-590 110.2000+0.1870000(T/K) [57] 590-633 -1547.9000+2.9911000(T/K) * 633-673 485 376.0-1524.6(T/K)+1.1982(T/K)2 * 673-675 110.2000+0.1870000(T/K) S(s, α,ortho) 0 32.0700 [55] 298.15-368 11.0070+0.0530580(T/K)-4.65260⋅10-5(T/K)2

368-1300 17.9418+0.0217903(T/K)-8.4153⋅10-6(T/K)2-79820(T/K)-2

S(s, β,mono) 361.6 33.0397 [55] 298.15-388 17.3180+0.0202430(T/K) 388-1300 21.1094+0.0172083(T/K)-6.7084⋅10-6(T/K)2-241480(T/K)-2

a Enthalpy relative to the enthalpy of the elements in their stable standard states at 298.15 K. b Absolute (third law) entropy. c of So

KH 15.298Δ 8(g) is changed from the SGTE-value [54] of 101277 J/mol to 100215 J/mol to get better agreement with the boiling temperature of sulfur (Peter Waldner, private communication 2004).

8

Appendix B Thermodynamic functions for the solid solutions. G° for the stoichiometric compounds is derived from appendix A. Na-K alloy solid solution, BCC structure: One sublattice, one site: K, Na

)/(184.447.706

24.8305

))(()/(

)/()lnln()/()/()/(

1,

0,

1,

0,

1

11)(

1)(

1

KTL

L

yyLLyymolJG

molJGyyyyRTmolJGymolJGymolJG

KNa

KNa

KNaKNaKNaKNaem

emKKNaNasKKsNaNam

+=

=

−+=⋅

⋅+++⋅+⋅=⋅−

−−−− oo

Alkali chloride solid solution, NaCl-KCl: Two sublattices: Cationic sublattice, C, one site: K+, Na+

Anionic sublattice, A, one site: Cl-

1639

)/ln()/(593.5)/(796.3215972

))(()/(

)/()/(

)/()/(

)/()lnln()/()/()/(

1:,

0:,

1:,

0:,

1

1)(

1:

1)(

1:

11:

1:

1

2

2

=

−+=

−+=⋅

⋅=⋅

⋅=⋅

⋅+++⋅+⋅=⋅

−++

−++

++−++−++−++

−+

−+

++++−+−+−+−+

−

−−

−−

−−−−

ClKNa

ClKNa

CK

CNaClKNaClKNa

ACl

CK

CNa

em

sKClSK

sNaClSNa

em

CK

CK

CNa

CNaClK

ACl

CKClNa

ACl

CNam

L

KTKTKTL

yyLLyyymolJG

molJGmolJG

molJGmolJG

molJGyyyyRTmolJGyymolJGyymolJG

oo

oo

oo

1

Alkali sulfide solid solution, Na2S-K2S: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice,A, one site: S2-

6.26777

)/(

)/()/(

)/()/(

)/()lnln(2)/()/()/(

0:,

0:,

1

1)(

1:

1)(

1:

11:

1:

1

2

22

22

22

2222

=

=⋅

⋅=⋅

⋅=⋅

⋅+++⋅+⋅=⋅

−++

−++−++

−+

−+

++++−+−+−+−+

−

−−

−−

−−−−

SKNa

SKNaAS

CK

CNa

em

sSKSK

sSNaSNa

em

CK

CK

CNa

CNaSK

AS

CKSNa

AS

CNam

L

LyyymolJG

molJGmolJG

molJGmolJG


oo

oo

oo

Alkali disulfide solid solution, Na2S2-K2S2: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice,A, one site: S22-

6.26777

)/(

)/()/(

)/()/(

)/()lnln(2)/()/()/(

0:,

0:,

1

1)(

1:

1)(

1:

11:

1:

1

22

22

22

2222

2222

22

22

22

22

=

=⋅

⋅=⋅

⋅=⋅

⋅+++⋅+⋅=⋅

−++

−++−++

−+

−+

++++−+−+−+−+

−

−−

−−

−−−−

SKNa

SKNaAS

CK

CNa

em

sSKSK

sSNaSNa

em

CK

CK

CNa

CNaSK

AS

CKSNa

AS

CNam

L

LyyymolJG

molJGmolJG

molJGmolJG


oo

oo

oo

2

Hexagonal solid solution, Na2CO3-Na2SO4-Na2S-K2CO3-K2SO4-K2S: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice, A, one site: CO32-

, SO42-, S2-

1590

4910

))((

))(())/()(

())/()(()/(

)/(2146.2315.32925)/()/(

)/(8033.20.16736)/()/(

)/()/(

)/()/(

)/()/(

)/()/(

)/()/())lnlnln(

)lnln(2()/()/()/(

)/()/()/()/(

1,:

0,:

0,:,

1:,

0:,

1:,

0:,

0,:

1,:

0,:

1,:

0,:

1

1)(

1:

1)(

1:

1),(

1:

1),(

1:

1),(

1:

1),(

1:

11

1:

1:

1:

1:

1:

1:

1

24

23

24

23

24

23

24

23

23

24

24

23

23

23

24

2224

24

23

24

23

24

23

24

23

24

23

24

23

24

23

24

23

24

23

24

23

22

22

4224

4224

3223

3223

2224

24

23

23

222224

24

24

24

23

23

23

23

=

=

+−++

−++++−+

++−+=⋅

−+⋅=⋅

−+⋅=⋅

⋅=⋅

⋅=⋅

⋅=⋅

⋅=⋅

⋅+⋅+++

++⋅+⋅+⋅+

⋅+⋅+⋅=⋅

−−+

−−+

−−++−−++++−++−++−++

++−++−++−++−−+−−+−−−−−−+

−−+−−+−−−−−−+−−+−−+

−+

−+

−+

−+

−+

−+

−−−−−−

++++−+−+−+−+−+−+

−+−+−+−+−+−+

−

−−

−−

−−

−−

−−

−−

−−

−−−

−−−−

SOCONa

SOCONa

SOCOKNaASO

ACO

CK

CNa

CNa

CKCOKNaSOKNa

ASO

CK

CNa

CNa

CKCOKNaCOKNa

ACO

CK

CNaSOSK

AS

ASO

CK

ASO

ACO

ASO

ACOSOCOK

SOCOKASO

ACO

CK

ASO

ACO

ASO

ACOSOCONaSOCONa

ASO

ACO

CNa

em

sSKSK

sSNaSNa

sSOKSOK

IsSONaSONa

sCOKCOK

sCONaCONa

em

AS

AS

ASO

ASO

ACO

ACO

CK

CK

CNa

CNaSK

AS

CKSNa

AS

CNaSOK

ASO

CK

SONaASO

CNaCOK

ACO

CKCONa

ACO

CNam

L

L

LyyyyyyLLyyy

yyLLyyyLyyyyyyyL

LyyyyyyyLLyyymolJG

KTmolJGmolJG

KTmolJGmolJG

molJGmolJG

molJGmolJG

molJGmolJG

molJGmolJG

molJGmolJyyyyyy

yyyyRTmolJGyymolJGyymolJGyy

molJGyymolJGyymolJGyymolJG

oo

oo

oo

oo

oo

oo

ooo

ooo

β

β

γ

3

272.1401

)/(686.44.3556

)/(686.45.12577

36.4392

52.10417

21.9444

5.157

5.4872

0,:,

1:,

0:,

1:,

0:,

0,:

1,:

0,:

24

23

24

24

23

23

224

24

23

24

23

=

−=

−=

−=

=

−=

=

=

−−++

−++

−++

−++

−++

−−+

−−+

−−+

SOCOKNa

SOKNa

SOKNa

COKNa

COKNa

SSOK

SOCOK

SOCOK

L

KTL

KTL

L

L

L

L

L

Na2SO4-rich low-temperature solid solution, Na2CO3-Na2SO4-K2CO3-K2SO4: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice, A, one site: CO32-

, SO42-

4184)/()/(

8.7112)/()/(

)/()/())lnln()lnln(2(

)/()/()/()/()/(

1),(

1:

1),(

1:

11

1:

1:

1:

1:

1

3223

3223

24

24

23

23

24

24

24

24

23

23

23

23

+⋅=⋅

+⋅=⋅

⋅+⋅++++

⋅+⋅+⋅+⋅=⋅

−−

−−

−−

−−−−−

−+

−+

−−−−++++

−+−+−+−+−+−+−+−+

molJGmolJG

molJGmolJG

molJGmolJyyyyyyyyRT

molJGyymolJGyymolJGyymolJGyymolJG

sCOKCOK

sCONaCONa

em

ASO

ASO

ACO

ACO

CK

CK

CNa

CNa

SOKASO

CKSONa

ASO

CNaCOK

ACO

CKCONa

ACO

CNam

oo

oo

oooo

α

β

4

2.3347

)/(

33472)/()/(

)/()/(

0,:

0,:

1

1),(

1:

1),(

1:

24

23

24

23

24

23

4224

4224

=

=⋅

+⋅=⋅

⋅=⋅

−−+

−−+−−+

−+

−+

−

−−

−−

SOCONa

SOCONaASO

ACO

CNa

em

sSOKSOK

IVsSONaSONa

L

LyyymolJG

molJGmolJG

molJGmolJGoo

oo

α

K2SO4-rich, low-temperature orthorhombic solid solution, Na2CO3-Na2SO4-K2CO3-K2SO4: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice, A, one site: CO32-, SO4

2-

32.2008

6.3765

))(()/(

)/()/(

)/(92.2029288)/()/(

2.209)/()/(

20920)/()/(

)/()/())lnln()lnln(2(

)/()/()/()/()/(

1,:

0,:

1,:

0,:

1

1),(

1:

1),(

1:

1),(

1:

1),(

1:

11

1:

1:

1:

1:

1

24

23

24

23

24

23

24

23

24

23

24

23

4224

4224

3223

3223

24

24

23

23

24

24

24

24

23

23

23

23

=

=

−+=⋅

⋅=⋅

−+⋅=⋅

+⋅=⋅

+⋅=⋅

⋅+⋅++++

⋅+⋅+⋅+⋅=⋅

−−+

−−+

−−−−+−−+−−+

−+

−+

−+

−+

−−−−++++

−+−+−+−+−+−+−+−+

−

−−

−−

−−

−−

−−

−−−−−

SOCOK

SOCOK

ASO

ACOSOCOKSOCOK

ASO

ACO

CK

em

sSOKSOK

IVsSONaSONa

sCOKCOK

sCONaCONa

em

ASO

ASO

ACO

ACO

CK

CK

CNa

CNa

SOKASO

CKSONa

ASO

CNaCOK

ACO

CKCONa

ACO

CNam

L

L

yyLLyyymolJG

molJGmolJG

KTmolJGmolJG

molJGmolJG

molJGmolJG

molJGmolJyyyyyyyyRT


oo

oo

oo

oo

oooo

α

α

β

5

Na2CO3-rich, low temperature solid solution, Na2CO3-Na2SO4-K2CO3-K2SO4: Two sublattices: Cationic sublattice, C, two sites: K+, Na+


2-

4184

10460

))(()/(

4184)/()/(

88.5522)/()/(

2.1255)/()/(

)/()/(

)/()/())lnln()lnln(2(

)/()/()/()/()/(

1:,

0:,

1:,

0:,

1

1),(

1:

1),(

1:

1),(

1:

1),(

1:

11

1:

1:

1:

1:

1

23

23

23

23

23

4224

4224

3223

3223

24

24

23

23

24

24

24

24

23

23

23

23

−=

=

−+=⋅

+⋅=⋅

+⋅=⋅

+⋅=⋅

⋅=⋅

⋅+⋅++++

⋅+⋅+⋅+⋅=⋅

−++

−++

++−++−++−++

−+

−+

−+

−+

−−−−++++

−+−+−+−+−+−+−+−+

−

−−

−−

−−

−−

−−

−−−−−

COKNa

COKNa

CNa

CKCOKNaCOKNa

ACO

CK

CNa

em

sSOKSOK

IVsSONaSONa

sCOKCOK

sCONaCONa

em

ASO

ASO

ACO

ACO

CK

CK

CNa

CNa

SOKASO

CKSONa

ASO

CNaCOK

ACO

CKCONa

ACO

CNam

L

L

yyLLyyymolJG

molJGmolJG

molJGmolJG

molJGmolJG

molJGmolJG

molJGmolJyyyyyyyyRT


oo

oo

oo

oo

oooo

α

α

β

Na2CO3-rich, very-low temperature solid solution, Na2CO3-Na2SO4-K2CO3-K2SO4: Two sublattices: Cationic sublattice, C, two sites: K+, Na+


2-

)/()/())lnln()lnln(2(

)/()/()/()/()/(11

1:

1:

1:

1:

1

24

24

23

23

24

24

24

24

23

23

23

23

−−

−−−−−

⋅+⋅++++

⋅+⋅+⋅+⋅=⋅

−−−−++++

−+−+−+−+−+−+−+−+

molJGmolJyyyyyyyyRT

molJGyymolJGyymolJGyymolJGyymolJGem

ASO

ASO

ACO

ACO

CK

CK

CNa

CNa

SOKASO

CKSONa

ASO

CNaCOK

ACO

CKCONa

ACO

CNam

oooo

6

4184

10460

))(()/(

4184)/()/(

4.5690)/()/(

8.1882)/()/(

)/()/(

1:,

0:,

1:,

0:,

1

1),(

1:

1),(

1:

1),(

1:

1),(

1:

23

23

23

23

23

4224

4224

3223

3223

−=

=

−+=⋅

+⋅=⋅

+⋅=⋅

+⋅=⋅

⋅=⋅

−++

−++

++−++−++−++

−+

−+

−+

−+

−

−−

−−

−−

−−

COKNa

COKNa

CK

CNaCOKNaCOKNa

ACO

CK

CNa

em

sSOKSOK

IVsSONaSONa

sCOKCOK

sCONaCONa

L

L

yyLLyyymolJG

molJGmolJG

molJGmolJG

molJGmolJG

molJGmolJG

oo

oo

oo

oo

α

α

α

K2CO3-rich, low-temperature solid solution, Na2CO3-Na2SO4-K2CO3-K2SO4: Two sublattices: Cationic sublattice, C, two sites: K+, Na+


2-

32.7238)/()/(

04.11757)/()/(

)/()/(

)/(3472.32.9100)/()/(

)/())lnln()lnln(2(

)/()/()/()/()/(

1),(

1:

1),(

1:

1),(

1:

1),(

1:

1

1:

1:

1:

1:

1

4224

4224

3223

3223

24

24

23

23

24

24

24

24

23

23

23

23

+⋅=⋅

+⋅=⋅

⋅=⋅

−+⋅=⋅

⋅++++

⋅+⋅+⋅+⋅=⋅

−−

−−

−−

−−

−

−−−−−

−+

−+

−+

−+

−−−−++++

−+−+−+−+−+−+−+−+

molJGmolJG

molJGmolJG

molJGmolJG

KTmolJGmolJG

molJyyyyyyyyRT


sSOKSOK

IVsSONaSONa

sCOKCOK

sCONaCONa

ASO

ASO

ACO

ACO

CK

CK

CNa

CNa

SOKASO

CKSONa

ASO

CNaCOK

ACO

CKCONa

ACO

CNam

oo

oo

oo

oo

oooo

α

α

β

7

Glaserite, K3Na(SO4)2-Na3(Na)(SO4)2: Three sublattices: Cationic sublattice 1, C1, three sites: K+, Na+ Cationic sublattice 2, C2, one site: Na+

Anionic sublattice, A, two sites: SO42-

)/(711.1016736)/(2)/(

)/(7906.94.10878)/(5.0)/(5.1)/(

)/()lnln(3)/()/()/(

1),(

1::

1),(

1),(

1::

111111::

211::

211

4224

424224

24

24

24

24

KTmolJGmolJG

KTmolJGmolJGmolJG

molJyyyyRTmolJGyyymolJGyyymolJG

IsSONaSONaNa

IsSONasSOKSONaK

CK

CK

CNa

CNaSONaNa

ASO

CNa

CNaSONaK

ASO

CNa

CKm

−+⋅=⋅

+−⋅+⋅=⋅

⋅++⋅+⋅=⋅

−−

−−−

−−−−

−++

−++

++++−++−++−++−++

oo

ooo

oo

α

Na-rich alkali disulfate Na2S2O7-K2S2O7: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice, A, one site: S2O72-

29288)/()/(

)/()/(

)/()lnln(2)/()/()/(

1),(

1:

1)(

1:

11:

1:

1

722272

722272

272

272

272

272

+⋅=⋅

⋅=⋅

⋅++⋅+⋅=⋅

−−

−−

−−−−

−+

−+

++++−+−+−+−+

molJGmolJG

molJGmolJG

molJyyyyRTmolJGyymolJGyymolJG

sOSKOSK

sOSNaOSNa

CK

CK

CNa

CNaOSK

AOS

CKOSNa

AOS

CNam

oo

oo

oo

β

8

K-rich alkali disulfate Na2S2O7-K2S2O7: Two sublattices: Cationic sublattice, C, two sites: K+, Na+

Anionic sublattice, A, one site: S2O72-

)/()/(

)/(8193.326.26777)/()/(

)/()lnln(2)/()/()/(

1),(

1:

1)(

1:

11:

1:

1

722272

722272

272

272

272

272

−−

−−

−−−−

⋅=⋅

−+⋅=⋅

⋅++⋅+⋅=⋅

−+

−+

++++−+−+−+−+

molJGmolJG

KTmolJGmolJG

molJyyyyRTmolJGyymolJGyymolJG

sOSKOSK

sOSNaOSNa

CK

CK

CNa

CNaOSK

AOS

CKOSNa

AOS

CNam

oo

oo

oo

β

9

Appendix C. Interaction parameters for the liquid phase in binary, ternary common-ion and ternary reciprocal systems. Binary systems Na-S

22 /1

/ 4.2510)/( SSNaNaSSNaNa molJg χ=⋅Δ −

)/(6944.68.19664)/( 1/ KTmolJg SVaNaNa −=⋅Δ −

K-S 2

//

1/

)(6.6276.627

)/(837.08996)/(

SVaKKSVaKK

SVaKK KTmolJg

χχ ++

−=⋅Δ −

Na-K* ( )32

1/

)/(9508.1)/(6986.1

)/(4335.061.468)/(2103.037.750)/(

NaNa

Na

VaVaNaK

YKTYKT

YKTKTmolJg

+−

−++=⋅Δ −

Na2CO3-Na2SO4 2.385)/( 1/ 432

=⋅Δ −molJg SOCONa

Na2CO3-Na2S SCONa

SCONaSCONa molJg

32

3232

/

/1

/

0.2092

5.22170.2092)/(

χ

χ

−

+−=⋅Δ −

Na2SO4-Na2S 75.1790)/( 1/ 42

−=⋅Δ −molJg SSONa

Na2SO4-Na2S2O7 0.1223)/( 1/ 7242

=⋅Δ −molJg OSSONa

NaCl-Na2SO4 1.276)/( 1/ 42

=⋅Δ −molJg ClSONa

NaCl-Na2CO3 3232 /1

/ 9.1861.276)/( ClCONaClCONa molJg χ−=⋅Δ −

K2CO3-K2SO4 0.251)/( 1/ 432

=⋅Δ −molJg SOCOK

K2CO3-K2S 7.2011)/( 1/ 32

−=⋅Δ −molJg SCOK

K2SO4-K2S 4.6258)/( 1/ 42

−=⋅Δ −molJg SSOK

K2SO4-K2S2O7 )/(042.74.6376)/( 1/ 7242

KTmolJg OSSOK +−=⋅Δ −

KCl-K2SO4 4242 /1

/ 1.5711.412)/( ClSOKClSOK molJg χ+=⋅Δ −

KCl-K2CO3 ClCOKClCOK molJg3232 /

1/ 2.16659.496)/( χ+=⋅Δ −

Na2CO3-K2CO3 2323 )/(1

)/( 1.3549.1714)/( CONaKCONaK molJg χ−−=⋅Δ −

Na2SO4-K2SO4 6.1419)/( 1)/( 24

−=⋅Δ −molJg SONaK

Na2S2O7-K2S2O7 4.1623)/( 1)/( 272

−=⋅Δ −molJg OSNaK

NaCl-KCl 22 /

1/ 0.675.695)/( ClNaKClNaK molJg χ−−=⋅Δ −

Ternary common-ion systems KCl-K2CO3-K2SO4 8.1882)/( 1001

)(/ 342−=⋅ −molJg COClSOK

1

Ternary reciprocal systems Na2CO3-Na2SO4-K2CO3-K2SO4 15.640)/( 1

/ 34−=⋅Δ −molJg COSONaK

NaCl-Na2SO4-KCl-K2SO4 2424 )/(1

/ 0.58662.619)/( SONaClSONaK xmolJg −−=⋅Δ −

NaCl-Na2CO3-KCl-K2CO3 8.1882)/( 1/ 3

−=⋅Δ −molJg ClCONaK

*YNa =xNaNa/VaVa+1/2 xNaK/VaVa

2

RECENT REPORTS FROM THE COMBUSTION AND MATERIALS CHEMISTRY

GROUP OF THE ABO AKADEMI PROCESS CHEMISTRY CENTRE: 02-1 E. Coda Zabetta, P. Kilpinen,

H. Pokela CFD Testing of an Improved Model for Simulating NOx in Internal Combustion Engines

02-2 Ulla Koponen Surface Electrochemistry of Ru- and Os- Modified Pt Electrodes 02-3 Mikael Bergelin The Impinging-Jet Flow-Cell as Measurement Tool in Interfacial

Electrochemistry 02-4 J. Konttinen, S. Kallio,

P. Kilpinen Oxidation of a Single Char Particle - Extension of the Model and Re-Estimation of Kinetic Rate Constants

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02-7 Kristoffer Sandelin Chemical Equilibrium Studies on Trace Elements and on Two Process Problems in Solid Fuel Combustion

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RECENT REPORTS FROM THE COMBUSTION AND MATERIALS CHEMISTRY

GROUP OF THE ABO AKADEMI PROCESS CHEMISTRY CENTRE: 05-01 Edgardo Coda Zabetta, Mikko

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05-02 J. Konttinen, R. Backman, M. Hupa, A. Moilanen, E. Kurkela

Trace element behaviour in the fluidized bed gasification of solid recovered fuels -A thermodynamic study

05-03 Edgardo Coda Zabetta, Clifford Ekholm, Mikko Hupa, Tommi Paanu, Mika Laurén, Seppo Niemi

TEKES FINE-BioPM “Dieselmoottorin nanohiukkaspäästöt biopohjaisia öljyjä poltettaessa” (Nanoparticles from diesel engines operated with bio-derived oils)-Project report

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06-01 Edgardo Coda Zabetta

Gas-phase detailed chemistry kinetic mechanism “ÅA” a mechanism, for simulating biomass conversion including methanoland nitrogen pollutants-validation, verification and parametric tests

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07-02 Andrius Gudzinskas, Johan Lindholm and Patrik Yrjas

Sulphation of solid KCl

ISSN 1459-8205 ISBN 978-952-12-1886-6

Åbo Akademis tryckeri Åbo, Finland, 2007

thermochemistry of salts 0703

Documents

modeling work

experimental work

professor chartrand

borate autocausticizing

professor patrice chartrand

professor rainer backman

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preface publications