Physicochemical calculations on metallurgical processes

№259 

МИНИСТЕРСТВО ОБЩЕГО И ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ 
РОССИЙСКОЙ ФЕДЕРАЦИИ 

МОСКОВСКИЙ ГОСУДАРСТВЕННЫЙ 

ИНСТИТУТ СТАЛИ и СПЛАВОВ 

Технологический университет 

МИСиС 

Physicochemical calculations 
on metallurgical processes 

Москва 2000 

№ 259 

МИНИСТЕРСТВО ОБПдаГО И ПРОФЕСИОНАЛЬНОГО ОБРАЗОВАНИЯ 
РОССИЙСКОЙ ФЕДЕРАЦИИ 

московский ГОСУДАРСТВЕННЫЙ ИНСШТУТ СТАЛИ И СПЛАВОВ 

(технологический университет) 

Одобрено методическны 
советом института 

Physicochemical calculations 
on metallurgical processes 

Москва 2000 

Distrlbixtion: 
Helsinki University of Technology 
Laboratory of Metallurgy 
P. 0. Box 6200 
FIN-02015HUT 
Finland 
Tel. +358-9-4512756 
Fax +358-9-4512798 
E-mail: Marja-Litsa.Kivikangas®hutfi 

О Heikki Jatkanen 

ISBN 951-22-4790-9 
ISSM 1455-2329 

PICA-SET OY 
£spool999 

ПРЕДИСЛОВИЕ 
к московскому изданию книги 

Учебное пособие "Физико-химические расчеты металлургических процессов" является 
результатом совместной работы русских и финских ученых и объединяет опыт 
теоретической подготовки инженеров-металлургов и инженеров-исследователей 
металлургических процессов в Московском Государственном Институте Стали и Сплавов 
(технологическом универсигеге) и в Технологическом Университете г, Хельсинки. 
Учебное пособие отражает огромный прогресс в металлургии за последние два десятилетия. 

1 ермодинамика, термохимия и кинетика высокотемпературных процессов составляют 
теоретическую основу процессов получения и рафинирования металлов. На этой основе 
книга позволяет освоить проведение теоретического анализа сложных металлургических 
систем и процессов и их моделирование, формулировать и решать задачи, имеющие 
практическое значение. В книгу включены теория, модели и расчеты металлургических 
систем и процессов. 

В главе "Термохимия" приведены методы расчета энергетических равновесий при 
высоких температурах. В главе "Химическая термодинамика пиромегаллургических систем и 
процессов" изложены основные теоретичесгие положения равновесий химических реакций в 
металлургических системах, включающих металлическую, шлаковую и газовую фазы, и 
решения практических задач. Термодинамика металлических растворов и взаимодействие в 
системе металл-газ даны на примерах систем медь-сера и медь-сера-кислрод, вакуумного 
рафинирования меди и обезуглероживания хромсодержащего расплава на основе железа. На 
основе традиционных и новейших термодинамических моделей оксвдных расплавов 
применительно к металлургическим шлакам {ионные и полимерные ионные модели 
силикатньрс растворов) приведены расчеты активности компонентов основных и кислых 
шлаков. Представлены методика и результаты элек1рохимических измерений в оксидных 
расплавах и шлаках, расчеты активности оксида железа и парциальных мольных величин 
компонента по результатам электрохимических измерений. Рассмотрены примеры расчетов 
реакций между металлом и шлаком: раскисление, десульфурация и дефосфорация стали, а 
также распределение элементов между медью и шлаком, медным штейном и шлаком. 
В главе "Кинетика гетерогенных металлургических процессоов» показано использование 
теоретических представлений о скоростях сложных процессов взаимодействия в сисгемах 
металл-шлак-газ, теории и критериев подобия для оценки коэффициентов массопереноса. 
Рассмотрены кинетические модели процессов обезуглероживания и окислительного 
рафинирования стали и задачи с использованием модельных уравнений. Изложена 
кинетическая модель абсорбции азота расплавами на основе железа из низкотемпературной 
плазмы и выполнены расчеты по уравнениям модели. 

Книга издана на английском языке, что делает ее полезной и доступной для 
использования студентами не только России и стран СНГ, но и Финляндии и других стран. 
Для русских студентов дополнительно к изучению теории и овладению методами физикохимических расчетов книга позволит освоить физико-химическую и металлургическую 
терминологию на английском языке, на котором издается большая чаеть периодической 
литературы, журналов и книг по металлургии и материаловедению. 

• 3 
CONTENTS 

PREFACE 
....5 

INTRODUCTION:...; 
6 

1. THERMOCHEMISTRY 
7 

1.1 SHORT BASIS OF CALCULATION OF ENERGY BAlJANCES 
- 
7 

L2 CALCULATION OF ADIABATIC REACITON TEMPERATURES 
„ 
10 

1.3 ENERGY BALANCES OF INDUSTRIAL PROCESSES 
- 
16 

2.CEEMICAL THERMODYNAMICS OF 
PYROMETALLURGICAL SYSTEMS AND PROCESSES .. 28 

2.1 ON THE DRIVING FORCE AND EQUILIBRIUM CONDITIONS FOR CHEMICAL 
REACTIONS AND SYSTEMS 
28 

2.1.1 Gtbbs energy change in an isothermal chemical reaction 
28 

2.L2 Refractory'St eel interaction as an example for chemical system undergoing chemical 
reaction 
,.,32 

2.L3 Manual calculation of (complex) reaction equilibria in a gaseous mixture. 
35 

2.1.4 Substitutional and competing chemical reactions 
39 

2.2 GAS AND SIMPLE GAS-SOLID SYSTEMS 
„45 

2.2.1 Composition and properties of gas systems most common in metallurgical processes 
45 

23 METALLIC SOLUTIONS. 
.'. 
.^48 

2.3. ] Standard states and composition co-ordinates for mixtures and solution phases 
48 

2.4 INTERACTIONS IN META1.-GAS -SYSTEMS... 
52 

2.4.1 Copper-sulphur and copper-sulphur-oxygen systems.. 
52 

2.4.2 Vacuum refining of blister copper 
55 

2.4.3 Decarburisation of chromium hot metal 
* 
58 

2.5 OXIDE SOLUTIONS AND METALLURGICAL SLAGS 
63 

2.5.1 Model of perfect ionic solution (Temkin's model) 
63 

2.5.2 Usi^g the model of a perfect ionic solution in calculation of metallurgical slag component 
activities 
70 

2.5.3 Polymeric models of silica melts (Masson's model) 
76 

2.5.4 The model of regular ionic solution (Kozheurov's model) 
89 

2.5.5 Thermodynamic nwdel of slag as a phase, which has a shared electron system 
(Ponomarenko's model) 
114 

2.5.6 Optical basicity 
118 

2.5 J Electrochemical measurements and calculations in oxide solutions 
122 

2.6 EXAMPLES OF REACTIONS BETWEEN METAL AND SLAG 
« 
134 

2.6.1 Deoxidation of steel 
„ 
134 

2.6.2 DesulphuHsation 
136 

2.6.3 Dephosphorisation of steel 
141 

2.7 DISTRIBUTION OF ELEMENTS BETWEEN MOLTEN COPPER OR COPPER MATTE 
AND SLAG 
, 
145 

2.7.1 Copper-slag distribution 
145 

2.7.2 Distribution of elements between copper matte and slag 
148 

3. KINETICS OF HETEROGENEOUS METALLURGICAL 
PROCESSES 
155 

3.1 KINETIC EQUATIONS. 
„ 
155 

3,IJ Temperature dependence of the rate constant. 
»..* 
155 

$J.2 Kinetic equtuions for multistage reactions. 
157 

3JJ Conditions of the steady state. The limiting stage, 
162 

3 J,4 Mass transfer and chemical reaction 
163 

3,L5 Similarity criteria and calculations of the mass transfer coefficients 
165 

3.2 KINETICS OFFEO REDUCTION FROM SLAG MELT BY SOLID CARBON 
273 

13 KINETIC REGULARITIES OF ALLOYED STEEL DECARBURISATION 
177 

3.3.1 Kinetic models of steel decarburisation process and steel oxidising refining process 
173 

3.4 KINETICS OF NITROGEN ABSORPTION BY MELTS FROM LOW TEMPERATURE 
PLASMA.. 
„ 
188 

4. NOMENCLATURE 
195 

PREFACE 

Great advances have taken place in metallurgical processes during the past two 
decades. Modem, energy saving blast furnace technology or emerging direct reduction 
technologies for iron production, as well as the breaJcthrough of flash and in-bath 
smelting processes in copper, lead or other non-ferrous metals production are some 
examples of the recent progress. 

Energy and environmental issues have been generally considered as the main driving 
forces for this development. It is. however, clear that the key factor for the progress 
has been better knowledge of the basic phenomena in the processes. This means both 
thermodynamic basis of the phases present and the reactions as well as chemical 
kinetics and transport phenomena in the reaction system, i, e. transport of heat, mass 
and momentum. All these are needed to create a representative model or a scries of 
submodels to describe and to simulate the process. 

This book is mostly directed to thermochemical and thermodynamic properties of 
phases and reactions. However, in some parts also structure of phases, e. g. of slags, is 
discussed along with kinetic and mass transport phenomena. 

This book was written as a joint project by the Laboratory of Metallurgy at Helsinki 
University of Technology (HUT) and the Chair of Theory of Metallurgical Processes 
at Moscow Steel and Alloys Institute (MlSiS) during the 90*s. Its purpose is to be a 
general textbook for undergraduate or graduate students who have metallurgy or 
materials science as their main subject. It is also suitable for self-studies as it has, in 
each chapter, first a fairly thorough theoretical description of the problem, followed by 
calculation examples and plenty of working examples and control questions. 

Autumn 1999 

The authors 

-6
INTRODUCTIQN 

The most important applications of thermochemistry and thermodynamics in 
metallurgy are determination of energy balances and equilibrium properties of 
whole reaction systems or their crucial parts in order to derive energy and material 
requirements and optimal thermomechanicai and chemical conditions for 
processes. 

Real metallurgical (chemical) processes are quite rarely isothermic, i.e. take 
place at constant temperature. The most conunon and convenient simplification for 
thermochemical processes is, however, an isothermal one. Another useful and 
conunon approach is isobaric as most metallurgical processes take place at constant 
pressure, which often is atmospheric. The overwhelmingly most common 
thermodynamic abstraction for metallurgical processes is to treat them as a single 
isobaric-isothermic process or as a set of isobaric-isothermic processes. In some cases 
isochoric i.e. constant volume approach is the most proper one as for processes taking 
place in closed pressurised chambers (autoclaves) or extremely rapid, explosionlike 
reactions. 

Industry processes are cither 1) continuous, steady-state processes which means 
that physicochemical and thermodynamic properties of the reaction system will vary 
along the length of a reactor but not with time. 2) non-steady state, batch processes in 
which the charge is treated in one stage and its composition and temperature are 
continuously changing. 

The final properties of the reaction system are often decisive and it is often 
enough to carry out the thermochemical and thermodynamic analyses only for the final 
(and initial if necessary) state of the process. All isobaric or isochoric continuous or 
batch processes can also be presented as a series of separate nonisothermal 
thermomechanic and isothermal chemical changes. So, isothermal thermodynamic 
analysis can be employed almost without restriction to the nonisothermic 
metallurgical processes. 

There are available several computer programs for computing thermomechanicai 
effects and equilibrium compositions of high temperature reaction systems. However, 
as the main task of this book is to help students to understand and apply physical 
chemistry as a tool for solving problems in metallurgy and material technology the 
exercises in this book are aimed mainly for manual computing. 

Theoretical analyses of many metallurgical processes include thermodynamic 
calculations of interactions in slag-metal liquid systems. Activities of slag components 
should be calculated previously. 

Liquid slag is considered as an ionic solution. By comparing it with real liquid 
slags one can find out the reasons for deviations and create more complex models: 
polymeric models of silica melts, models of regular ionic solutions for basic and acid 
slags. These models are discussed below. There are some complicated models of 
subregular oxide solutions (Lumsden and Shiro-Baaya models), which are not given 
in this book. The study of thermodynamic models allows us to approach critically one 
or another model for calculation of the component activities of a slag, to determine 
and to specify model parameters on the base of phase diagrams and electrochemical 
measurements in slags. 

. 7 
Kinetic calculations of metallurgical processes help to reveal mechanisms and 
duration of real processes. It is of great importance to choose correct kinetic equations. 
Ь some complicated cases it is convenient to use the criteria of similarity for 
calculations of mass transfer coefficients. Therc are examples of kinetic calculations: 
fem)us oxide reduction from ^lag melts by solid carbon» kinetic models of steel 
decarburisation process and steel oxidising refining process and nitrogen absorpti№ 
by melts from low temperature plasma. 

1, THERMOCHEMISTRY 

1.1 SHORT BASIS OF CALCULATION OF ENERGY BALANCES 

Thermochemical analysis and calculations are employed for determining energy 
balances of processes as whole or of their particular parts or zones in order to derive 
energy consumption or heat evolution and exchange with the environment (energy 
loss), etc. Energy balances give basis also for computation of reaction temperatures 
and temperature distribution in reaction environments. 

A material system can exchange energy with its environment in the form of heat 
or work. Energy exchange takes place with the expense of kinetic energy of atoms, 
molecules or lattice, phase transformations (solid state phase transition, melting, 
evaporation) and chemical reactions (including dissolution, solution formation and 
chemisoфtion). Energy balances are computed either for isobaric as usual or isochoric 
conditions. 

The thermodynamic function employed in thermochemical analysis of chemical 
reaction systems undergoing isobaric changes is enthalpy, H. For an isochoric process 
energy exchange equals to the changes in internal energy, U (or E). 

In Fig. 1ЛЛ the principles of an isobaric energy (heat) balance are presented 
schematically. The basic principle for an energy balance is: energy and matter 
transferred into the system equals to the sum of the energy and matter 
transferred from the system in different forms and accumulated inside the 
system. 

There arc different ways to establish an energy or heat balance even when the 
basis for all them is basically the same. The method presented here is based on the 
computation of enthalpy of input and output substances and phases relative to pure 
elements at some reference temperature for which frequently room temperature is 
chosen. Another method is to compute the physical heat contents of input and output 
matter, and the extents of expected chemicd reactions and the heat liberated/absorbed 
in them. Other methods are between these two extremes. As enthalpy and internal 
energy are state properties there are no other restrictions for construction the hett 
balance but the same reference is employed for both input and output matter. 

The enthalpy of a phase relative to pure elements at the reference tenфeratUIe 
can be divided in two categories. The isobaric chemical heat content consists of heats 
of formation of all individual compounds present in the '^hase as well as heat of 
formation of solution (heat of mixing). The isobaric physical heat content consists of 
all heat absorbed in heating up the individual substances to the temperature, concerMd 
including heats absorbed in phase transformations (solid-solid transfoimationt melting 
and evaporation). 

REACTOR OR REACTION ZONE 
UNDER CONStDERATION 

Hph 
Hch 

Q . 
HEAT BALANCE FOR AN ISOBARIC PROCESS: 

Hph + H5, + Qp- (H.CC + H;S + H ^ + Qi) = 0 

fum of "physicar heat» or heat content» of Input (") or output f"^ subslancee or phase»; 
•um of corresponding *сНвт1саГ heats or energies i.e. heats of formatton of compounds 
or phases; 
'pure' energy transferred Into the reactor or reaction zone through heat conduction or by 
trenaformtng electric energy Into hest; 
heat accumulated In the system during heat baiance peHod by Increasing of heat cont&nt 
(temperature) of substances or with eccomulation of substances inside the mador or 
reaction 2one considered; 
: heat loss from the reactor or reaction zone by conduction or radiation during the bafance 

period. 

Reference state for computing enthaipy of charge and products consists of pure elements 
under atmospheric pressure at a given reference Lemperature T (usually room temperature 
298K). 

Fig. 1.1.1. Principles of energy (heat) balances. 

The quantities readily available for the most common substances are isobaric 
heat capacities, 
Cp(T), standard 
enthalpies 
of 
phase 
transformations 
and formation of chemical compounds. The corresponding isochoric quantities the 
isochoric heat capacity function, 
Су(Т) and the corresponding 
internal 
energy changes (AU or ДЕ) can be readily computed from the isobaric ones. Several 
data compilations and computer databases give directly the "absolute enthalpies" of 
elements and compounds ix. the sum of physical and chemical heat contents which 
are tabulated relative to elements at room temperature. Data for thermal effects 
involved in solution formation is very limited except for dilute molten or solid alloys 
of some common metals. 

For an isobaric process, in which the heats absorbed or evolved equal to the 
enthalpy changes we have, accordingly 

I 
П 

AHph = XCHT - HT.)i = InJCpidT + Zn-A^H^ 
(1ЛЛ) 

in which (Hj -H-pX, Cp^ and AjjHj are the molar heat content, heat capacity and heat 
of phase transformation of an element, compound or solution, present in the input or 
output. 

Accordingly, the first term (I) is the sum of heats absorbed by homogeneous 
phases in heating, the second term (П) is the sum of isothermal heats absorbed in 

-9 

phase transformations which take place in substances between the reference 
temperature and the input or output temperatures. 

Chemical heat is the sum of heats of formation of compounds and solutions they 
form. 

I 
П 

AHch = ^Щ' AfH^ + XH""^ 
(1 Л.2) 

The first term on the right side of equation is the sum of heats of formation of all 
compounds from elements and the second term is the sum of heats of mixing 
(formation of solution from its components) of all solution phases. 

Pure energy (Qp) can be transferred into the reactor or reaction zone by 
conduction and radiation of heat or by direct transformation of other forms of energy 
into heat inside the reactor - e.g. resistive, inductive, arc, plasma, electron beam 
heating and other methods to transform electric energy into heat. The accumulation of 
heat in non-steady state processes may take place by direct increase of heat content of 
substances or with the expense of accumulation of substance in the reactor or reaction 
zone. 

The most serious problem in calculation of energy balances for high temperature 
processes is often the lack of thermochemical data for solutions, heat capacities, heats 
of mixing, solidification, devitrification etc. Accurate values for heats of mixing for 
metallurgical solutions are not commonly available. In some cases they are given 
within the total heat content of the given molten phase measured relative to room 
temperature or some other reference temperature. As heats of mixing are small 
relative to heats of reactions they can often be neglected without causing any serious 
error in heat balance. 

The procedure presented in the following examples for computing energy 
balances of isobaric processes is valid for isochoric ones when enthalpy (H) and 
isobaric heat capacity (Cp) functions are substituted by internal energy (U or E) and 
isochoric heat capacity (Cv) functions. Relations between the isobaric and isochoric 
thermochemical functions are as follows: 

For chemical reactions 

AjU\ ^ \Wj 
- Ang • RT 
(1.1.3) 

For heat capacities of condensed substances 

CvCr)-Cp(T) 
(1.1.4) 

and of perfect (ideal) gases 

Cv(D = Cp(T). R 
(1.1.5) 

Attg is the change in number of moles of gaseous reaction components in reaction and 
R is the common gas constant = 8.314 Jmol'^K'^ (1.987 cal-mol'^-K"^) 

The first step in construction of energy balance of a chemical process is to 
establish a stoichiometric material balance, which gives the amounts, stoichiometric 
forms of substances and phases in the feed and product of process concerned. There 

are several ways to construct and compute an energy balance the main differences 
depending on the choice of reference state for substances and on the forms of 
available enthalpy data. It is not always reasonable to choose room temperature for the 
reference temperature and pure elements for the standard state of substances. If the 
material system includes exceptionally stable compounds, which do not undergo any 
chemical chaa^^s in processes concerned there is no need ttf compute the standard 
heats of fonnation at room temperature as they are equal on input and output side of 
the energy balance and cancel, accordingly, each other. 

Methods to establish energy balances for high temperature processes are better 
visualised in the following examples. 

1.2 Calculation of adiabatic reaction tennperatures 

H.U 

In an adiabatic process there is no 
heat exchange between the system and 
its environment. Heat evolved in an 
adiabatic isochoric process is fully 
consumed in heating up the products of 
the reaction(s) and phase transition 
processes 
(phase 
transformation, 
melting, evaporation etc.) in an isobaric 
process also to mechanical (pneumatic) 
work against an external pressure. In an 
isochoric adiabatic process the thermal 
balance equals to the sum the internal 
energy changes, in an isobaric process 
to the sum of enthalpy changes in the 
system. Adiabatic reaction temperature 
is good approximation for true temperature when the reaction rate is very high relative 
to the rate of heat transfer from the reaction zone to the environment. The principle of 
calculation of adiabatic reaction (flame) temperatures is presented in Fig. 1.2.1. 

298K 

Fig.1.2.1 
Principle of 
temperatures. 

T^ 

caicuiatton of adiabatic reaction 

Worked example 1. Adiabatic flame temperature of coal dust combustion and explosion 
temperature 

A. Isobaric combustion 

The adiabatic flame temperature of coal dust burning in air is computed assuming the heat evolved 
at room being absorbed by the reaction products. Nitrogen should be included in the reaction products. 
Coal is assumed to bum at atmospheric pressure fully to carbon dioxide and nitrogen (plus noble gases) 
in air amounts to 79/21 mole per one п:ю1е oxygen. The adiabatic combustion reaction is, accordingly 

C(gr) + 02(g) + 79/21N2(g) = C02(g) + 79/21N2(g) 

The corresponding adiabatic thermal balance equation is 

AHR(298) + J CpoojdT + 79/21 J CpjodT = 0 

298 
298 

(1.2.1)