Investigation of Electric Arc Furnace Chemical Reactions ...580469/FULLTEXT01.pdf · From “Perry’s Chemical Engineers’ Handbook” and “NIST-JANAF Thermochemical Tables”,

1

Investigation of Electric Arc Furnace Chemical Reactions and stirring effect

Lei Deng

Supervisor：Dr. Xiaojing Zhang (ABB)

Niloofar Arzpeyma (KTH)

Master Degree Thesis

School of Industrial Engineering and Management

Department of Materials Science and Engineering

Royal Institute of Technology

SE-100 44 Stockholm

Sweden

2

Abstract

Chemical energy plays a big role in the process of modern Electric Arc Furnace (EAF). The

objective of this study is to compare the results of chemical reaction enthalpies calculated by four

different methods.

In general, the “PERRY-NIST-JANAF method” is used to calculate the chemical energies.

However, this method heavily depend on heat capacities of the substances which have to be

deduced from “Perry’s Chemical Engineers’ Handbook” and “NIST-JANAF Thermochemical

Tables”, even the calculation process is complicated. Then, some other methods are introduced:

Total enthalpy method, HT (High Temperature) enthalpy method and Atomic energy method.

In this thesis, the above four methods have been used to calculate the enthalpies of chemical

reactions in EAF process. Both of “Total enthalpy method” and “HT enthalpy method” are not

complicated, but some basic data are not available. The calculation for chemical reaction

enthalpies cannot be completely made by these two methods. “Atomic energy method” is more

complicated than “Total enthalpy method” and “HT enthalpy method”, even almost all data are

available, but some results of these methods are far from those of the other three methods’.

The results show that values of enthalpies obtained by “PERRY-NIST-JANAF method” are more

reasonable, though the calculation process is more complicated. In this study, it is also discussed

two influencing factors on EAF process: electric power and electromagnetic stirring (EMS).

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Contents 1. Introduction ............................................................................................................................................... 4

2. Literature Review ...................................................................................................................................... 5

2.1 Enthalpy of a Reaction ........................................................................................................................ 5

2.2 Hess’s law............................................................................................................................................ 6

2.3 Kirchhoff’s law .................................................................................................................................... 6

2.4 Total enthalpy method ......................................................................................................................... 7

2.4.1 Total enthalpy ............................................................................................................................... 7

2.4.2 Calculation of the thermal effects ................................................................................................. 8

2.5 Electromagnetic Stirring in Electric Arc Furnace (EAF – EMS) ........................................................ 9

3. Calculation of chemical reaction energy in EAF..................................................................................... 10

Reaction 1: ......................................................................................................... 12

Reaction 2: ................................................................................................... 14

Reaction 3: ........................................................................................ 17

Reaction 4: .............................................................................................................. 20

Reaction 5: ........................................................................................................... 22

Reaction 6: ............................................................................................................. 24

Reaction 7: ................................................................................................................. 26

Reaction 8: ..................................................................................... 29

Reaction 9: ( .................................................................................................. 31

Reaction 10: ........................................................................................... 33

Reaction 11: ............................................................................ 36

Reaction 12: ............................................................................................. 38

Reaction 13: ................................................................................ 41

Reaction 14: ................................................................................................ 43

Comparison of enthalpies calculated by four methods ............................................................................ 46

4. Influencing Factors on EAF process ....................................................................................................... 52

4.1 Power on EAF process ...................................................................................................................... 52

4.2 Effects of EMS .................................................................................................................................. 57

5. Summary ................................................................................................................................................. 62

6. Future works ............................................................................................................................................ 63

7. References ............................................................................................................................................... 64

Appendix 1 – Abbreviation Index ............................................................................................................... 65

Appendix 2 – Symbol List ........................................................................................................................... 65

Appendix 3 – Heat capacities of the substances .......................................................................................... 65

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1. Introduction

EAF process is an essential part of steelmaking. Melting is the main task of EAF process, and it

is accomplished by energy supply which includes both electric power and chemical energy. The

electric power is supplied by the graphite electrodes and is the main energy supplier. Chemical

energy is supplied via several sources which mainly include oxy-fuel burners and oxygen

injection.

Fig. 1 Schematic diagram of Electric Arc Furnace (EAF)

In electric arc furnace, some oxidation and reduction reactions happen subsequently [1]

:

𝐶 𝐹𝑒𝑂 𝐹𝑒 𝐶𝑂 2 𝑀𝑛𝑂 𝑆𝑖 2 𝑀𝑛 𝑆𝑖𝑂2

𝐹𝑒 0 5𝑂2 𝐹𝑒𝑂 (𝑀𝑛𝑂 𝐶 𝑀𝑛 𝐶𝑂

𝑆𝑖 2 𝐹𝑒𝑂 2 𝐹𝑒 𝑆𝑖𝑂2 𝑀𝑛 𝐹𝑒𝑂 𝐹𝑒 𝑀𝑛𝑂

𝑆𝑖 𝑂2 𝑆𝑖𝑂2 3 𝐹𝑒𝑂 2 𝐶𝑟 3 𝐹𝑒 𝐶𝑟2𝑂3

𝐶𝑂 0 5𝑂2 𝐶𝑂2 2 𝐶𝑟 1 5𝑂2 𝐶𝑟2𝑂3

𝐶 0 5𝑂2 𝐶𝑂 5 𝐹𝑒𝑂 2 𝑃 5 𝐹𝑒 𝑃2𝑂5

𝐶 𝑂2 𝐶𝑂2 𝐶 𝐹𝑒𝑂 𝐹𝑒 𝐶𝑂

These chemical reactions generate a lot of chemical energy which can also improve the efficiency

and reduce the time of EAF process. In EAFs, chemical reactions can affect the temperature of

steel which is one of the most important factors for steelmaking. However, there are several ways

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to calculate the EAF chemical reaction energy. In this study, four methods are applied to

calculate EAF chemical energy as follows:

1) PERRY-NIST-JANAF method

2) Total enthalpy method

3) HT (High-Temperature) enthalpy method

4) Atomic energy method

In this study, the enthalpies of chemical reactions are calculated by these four methods. Besides,

the effects of two factors on EAF process are also studied through simulation:

1) Electric power

2) Electromagnetic stirring

The results showed that the changing of these factors influence EAF process.

2. Literature Review

2.1 Enthalpy of a Reaction

“Enthalpy of a Reaction” is defined as the amount of heat absorbed or evolved in the

transformation of the reactants at a given temperature and pressure into the products at the same

temperature and pressure [2]

. It depends on the conditions under which the reaction is carried out.

When a chemical reaction happens at constant pressure, the thermal change will not only involve

the change of internal energy of the system but also the work performed either in expansion or

contraction of the system. According to the “First law of thermodynamics” [3]

, it can be obtained

that the heat of reaction is equal to the enthalpy of reaction at constant pressure as follows:

Based on “First law of thermodynamics”: Qp Δ E W, (1)

Where Qp is heat, W is work and E is internal energy.

When the pressure p is constant, it can be expressed as: Qp Δ E PΔV (2)

Heat of the reaction is the internal energy difference between products and reactants:

Qp Σ Ep – Σ Er P Vp – Vr Σ Ep PVp – Σ Er PVr (3)

Enthalpy can be defined by the equation: H E PV (4)

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Therefore Qp Σ Hp – Σ Hr so: Qp Δ H (6)

2.2 Hess’s law

Experiments show that thermal effects of a chemical reaction are not influenced by number of

reaction steps. In other words, the thermal effect of a chemical reaction is only related to the

initial and final state, which is stated as “Hess’s law” [4]

. Hess’s law can be used only when

pressure or volume is constant. Based on the definition, Hess’s law can be expressed as the

following equation:

(7)

Bekker [5]

calculated the chemical reaction power using the enthalpy of formation of substances

which are assumed at high temperature. The law of his method also lies in “Hess’s law”.

2.3 Kirchhoff’s law

When a chemical reaction is carried out in two different temperatures T1 and T2 at constant

pressure, the thermal effects normally will not be the same.

The enthalpy of the reaction at T1, (T1), can be related to that at T2, (T2), by using

the following procedure:

T1: eE → f

H H

T2: eE → f

(1) An increase/decrease of the temperature of the reactants ( eE，……) from T1 to T2, gives

the enthalpy .

(2) At T2, the chemical reaction occurs , which gives the enthalpy T2

(3) An decrease/increase of the temperature of the products (f ，……) from T2 to T1, gives

the enthalpy as .

As enthalpy is a state function, the sum of the enthalpies of the three reactions is equal to the

enthalpy of the reaction at the temperature of T1. Therefore:

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T1 T2 (8)

Or

T2 T1 (9)

Also, the following formulas are given:

∫ 𝐶 T ∫ 𝑒𝐶 T

… (10)

∫ 𝐶 T ∫ 𝐶 T

… (11)

Then, we can have: T2 T1 ∫ 𝐶 T

(12)

The above equation is named “Kirchhoff’s law”. For a chemical reaction, if the values of

T1 and all 𝐶 are given, then T2 can be calculated based on Kirchhoff’s law.

The values of 𝐶 can be found from “Perry’s Chemical Engineers’ Handbook” [6]

and “NIST-

JANAF Thermochemical Tables” [7]

. Vito [1]

obtained the enthalpies of EAF chemical reactions

by the difference between enthalpies of products and those of reactants as well as by the

temperature integral of the difference between the heat capacities of the products and reactants.

The method totally lies in “Kirchhoff’s law”.

2.4 Total enthalpy method

2.4.1 Total enthalpy

The total enthalpy of the chemical compound is the enthalpy of its formation at the

temperature T from the elements in their standard state at the temperature T0 [8]

.

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Table 1.Total enthalpies of some chemical compounds

Table 2.Total enthalpies of some individual elements

Tables 1 and 2 [8]

show the values of the total enthalpies of some chemical compounds and

individual elements.

2.4.2 Calculation of the thermal effects

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In traditional method, it is necessary to know the value of heat capacities when calculating the

enthalpy of a chemical reaction. However, the data of heat capacities which are temperature

dependent are not always available, especially for high temperature steelmaking processes.

In total enthalpy method, the quantity of heat released is also named the resultant thermal effects,

and designated as 𝑅𝐸𝑆 [8]

. As enthalpies of reactions depend significantly on temperature

conditions, so 𝑅𝐸𝑆 depends on temperatures of original substances and those of final

products. Using total enthalpy method to calculate the resultant thermal effect, 𝑅𝐸𝑆 can be

determined as the difference between the absolute values of total enthalpies of products of the

reaction and total enthalpies of original substances.

Compared to the traditional method to calculate the enthalpies, total enthalpy method is more

convenient and now is used in different fields of technology, but not widespread in steelmaking

field, perhaps because metallurgists are more familiar with the traditional method [8]

.

2.5 Electromagnetic Stirring in Electric Arc Furnace (EAF – EMS)

Since 1947, ABB has supplied various electromagnetic stirring (EMS) systems for steel

industries. In the early days, EMS system was used for secondary refining for EAF process.

Because of the strong electromagnetic force in the melt, stirring intensity can be enhanced which

will reduce the melting time. See figures [9]

below.

Fig. 2 Electromagnetic Stirring (EMS) in EAF

Nowadays, EAF-EMS is still used for making high alloyed tool steel where some alloys with

high melting points are added. For example, Uddeholm, which works on processing tool steel,

10

still takes advantage of EAF-EMS for steelmaking processes.

EAF-EMS has several benefits for steelmaking, such as reducing the electric energy consumption

and decreasing disturbances, both of which improve the productivity. In fact, EAF-EMS can

stabilize the EAF process.

3. Calculation of chemical reaction energy in EAF

In EAFs, chemical reactions can affect the temperature of steel which is one of the most

important factors for steelmaking. However, there are several ways to calculate the chemical

reaction energy in EAFs. In this study, four methods are applied to calculate EAF chemical

energy as follows:

1) PERRY-NIST-JANAF method:

Based on the formula below [10]

, we can calculate the enthalpies of chemical reactions one by one.

dTtsreacproductstsreacproducts

T

PpT CCHHH 298

0

298

0

298

0)tan()()tan()(

(13)

Before calculation, it is necessary to find the values of standard enthalpies of products and

reactants as well as the expressions of heat capacities of the substances. From “Perry’s Chemical

Engineers’ Handbook” and “NIST-JANAF Thermochemical Tables”, heat capacities and standard

enthalpies of substances can be found, so the method is named “PERRY-NIST-JANAF method”.

This principle of this method lies in “Kirchhoff’s law”, which calculate the chemical reaction

energies by the difference between enthalpies of products and those of reactants as well as by the

temperature integral of the difference between the heat capacities of the products and reactants.

The curves of heat capacities of the substances are shown in Appendix 3.

2) Total enthalpy method:

The value of the total enthalpy of a chemical compound at a certain temperature, I0, is used to

estimate the resultant thermal effect of the reaction, ΔHRES.

3600*)tan()(00

tsreacT

productsT IIH

RPRES

Compared with “PERRY-NIST-JANAF method”, it is not necessary to conclude the expressions

of heat capacities for “Total enthalpy method”. To calculate the chemical reaction enthalpies, it is

important to clear the temperatures of original substances and those of final products as ΔHRES

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depends on temperature conditions. The resultant thermal effect of the reaction, ΔHRES can be

obtained by the difference between the absolute values of total enthalpies of products and total

enthalpies of original substances.

3) HT (High-Temperature) enthalpy method:

The calculation of this method is totally conducted by the enthalpies at high temperature. The

calculation formula [5]

as following shows:

)tan()(000

tsreacproducts HHH TTT (14)

Similar to “Total enthalpy method”, this method is also not related to heat capacities of the

substances. In order to conduct the calculation, it is necessary to find the values of enthalpies of

reactants and products at temperature T. Then, the chemical reaction enthalpies can be

determined by the difference between the values of enthalpies of products at T and enthalpies of

reactants at T. This method is treated as the simplified method of “PERRY-NIST-JANAF

method”.

4) Atomic energy method [11, 12]

:

This calculation formula is consisted by standard enthalpies of formation and enthalpies at

temperature T. Similar to “PERRY-NIST-JANAF method”, the chemical reaction enthalpies can

be determined by the difference between standard enthalpies of products and those of reactants as

well as the enthalpy change by increasing temperature. However, the way to calculate is different

from “PERRY-NIST-JANAF method”. “Atomic energy method” is no related to heat capacities,

but to calculate the enthalpy changes of increasing temperature by using the formulas of all

substances which are functions of final temperatures of the reactions. The calculation formula can

be concluded as following:

)tan()()tan()(000

25

0

25

0tsreacproductstsreacproducts HHHHH TTT (15)

Based on the above methods, chemical energies of listed reactions (1 -14) can be obtained. To be

mentioned, since the basic data of some substances are not sufficient, some methods in several

reactions cannot be conducted. However, for most reactions, chemical reaction energies can be

calculated by these four methods. Abbreviations used in this thesis can be found in Appendix 1

and symbol list can be found in Appendix 2.

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Reaction 1:

Method 1: PERRY-NIST-JANAF method

Heat capacities of substances ( )

𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝐶𝑂 0 0 00120 2 3 2500

𝐶 𝐶 𝑟 𝑛 {2 3 0 002 1

11 00

2 3 11 3

0 000 31 11 3 1 00

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50 1 3 1 50 1 00

Enthalpies of formation used in the model. ( )

5.110)(,27,5.249)(0

298

0

298

COFeO HHH SC

)()(

0

298

0

2981FeOCO HHHH SC

∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

+∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶

𝐶 𝐹𝑒𝑂 ) +∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

+∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂

𝐶 𝐶 𝐶 𝐹𝑒𝑂 ) +∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

∫ (𝐶 𝐹𝑒

𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

110 5 2 2 5 ∫ ( 13 0 00 3 0 0 00120 2 3

0 002 1

12 2 0 001 2

) +∫ ( 12 0 0033

0 0 00120 2 3 0 002 1

12 2 0 001 2

) ∫ 12 0 0033 0 0 00120 0 000 31

12 50 0 001 3 ∫ 0 0 00120 0 000 31

13

12 50 0 001 3 ∫ 0 0 00120 0 000 31

1 3 ∫ 10 0 0 0 00120 0 000 31 1 3

1 1000

1 ∫ ( 5 3 0 003 1

)

∫ ( 2 5 3 0 000 51

) ∫ 2 0 0020 1

∫ 1 0 00131 1

∫ 5 0 000 1 ∫ 1 0 000 1 1 1000

1 5 3 0 003 1 0 5

2 5 3 0 000 51

0 5

2 0 0020 1 0 5

1 0 00131 1

0 5 5 0 000 1 0 5

1 0 000 1 0 5

1 1000

1 1201 21 252 11 2 3 1 20 35 122 331 3

1 1000

150 1

Method 2: Total enthalpy method

When the chemical reaction happens at 1800K, 1mole iron oxide reacts with 1 mole carbon to

form 1 mole iron and 1 mole carbon monoxide. All the reactants and products are at 1800K, so

the chemical reaction energy can be calculated as the following formula:

3600*)0

)1800(

0

)1800(

0

)1800(

0

)1800(RES (H IIII CFeOCOFe

0 01 21 0 01 0 0 02 0 00 53 3 00

5 2

Method 3: HT enthalpy method

To use HT enthalpy method, the formula can be made when the chemical reaction happens at

1800K. In addition, the energy of carbon dissolved should also be taken into account in this

chemical reaction.

)()(0

1800

0

1800

'

1FeOCO HHH SC

11 2 2 3

14

153

Method 4: Atomic energy method

E press o for e h p of p re s s es Ws

1000/3600*)03,5*196,0()( TFeH (25-1527℃)

28

4.22*3600*0117,0

10000

*4

100000000

*3)(

2

TCOH T (25-1527℃)

1000/3600*)174*572,0()( TCH (1400-1724℃)

1000/3600*08,6*226,0)( TFeOH (25-1527℃)

He of for o Ws :

0)(,3600*057,1)(,3600*055,1)(,0)( fCHfFeOHfCOHfFeH

)()()()()()()()(1 CHFeOHCOHFeHfCHfFeOHfCOHfFeHH

)072*3600*057,128*3600*055,10( 0 1 152 5 03

5

(

0 011 ) 3 00 22 0 22 152 0

2

0 5 2 152 1

12]

1 2 15

Reaction 2:



𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝑂2 2 0 00025 1 00

300 5000

15

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50 1 3 1 50 1 00


0,5.249)(0

298 HH SFe

FeO

HHH SFeFeO

)(0

2982+

∫ (𝐶 𝐹𝑒𝑂 𝐶 𝐹𝑒 0 5 𝐶 𝑂2 )

∫ (𝐶 𝐹𝑒𝑂 𝐶 𝐹𝑒 0 5

𝐶 𝑂2 ) ∫ (𝐶 𝐹𝑒𝑂 𝐶 𝐹𝑒 0 5 𝐶 𝑂2 )

∫ (𝐶 𝐹𝑒𝑂 𝐶 𝐹𝑒

0 5 𝐶 𝑂2 ) + ∫ (𝐶 𝐹𝑒𝑂 𝐶 𝐹𝑒 0 5 𝐶 𝑂2 )

∫ (𝐶 𝐹𝑒𝑂

𝐶 𝐹𝑒 0 5 𝐶 𝑂2 )

2 5 0 ∫ ( 12 2 0 001 2

13 0 00 3 0 5

2 0 00025

) +∫ ( 12 2 0 001 2

12

0 0033 0 5 2 0 00025

) +∫ ( 12 50 0 001 3

12 0 0033 0 5 2 0 00025

) +∫ ( 12 50

0 001 3 0 5 2 0 00025

) +∫ (1 3 0 5

2 0 00025

) +∫ (1 3 10 0 0 5 2 0 00025

) ]*4.184/1000

2 5 ∫ ( 355 0 00501

)

∫ (2 3 5 0 001

) +∫ (2 25 0 001 53

)

+∫ ( 0 02 0 001 0

) ∫ (3 5 0 00012

)

∫ (2 1 5 0 00012

) 1 1000℃

2 5 355 0 00501 0 5

2 3 5 0 001

0 5

2 25 0 001 53 0 5

0 02 0 001 0

0 5

3 5 0 00012 0 5

2 1 5 0 00012

0 5

1 1000

16

2 5 2 3 22 2 1 5 2 10 1 11 03 2

2 0 2


When the chemical reaction happens at 1800 K, 1 mole iron reacts with 0.5 mole oxygen to form

1 mole iron oxide. The temperature of oxygen is 298 K since it is from the ambient medium, but

iron and iron oxide are at 1800 K. The chemical reaction energy can be calculated as the

following formula

3600*)*5.00

)298(2

0

)1800(

0

)1800(RES (H III OFeFeO

0 0 02 0 01 21 0 5 0 3 00

1


To use HT enthalpy method, the formula is calculated for the chemical reaction at 1800 K. In

addition, the enthalpy of dissolved iron should also be taken into account in this chemical

reaction.

HHH SFeFeO

)(0

18002

2 3 0

2 3



1000/3600*08,6*226,0)( TFeOH (25-1527℃)

1000/3600*)03,5*196,0()( TFeH (25-1527℃)

32

4,22*3600*0142,0

10000

*4

100000000

*3)2(

2

TOH T (25-2000℃)

He of for o Ws :

17

0)2(,0)(,3600*057,1)( fOHfFeHfFeOH

)2(*5,0)()()2(*5.0)()(2 OHFeHFeOHfOHfFeHfFeOHH

1 05 3 00 2 0 0 0 22 152 0

2

0 1 152 5 03

5 0 5 (

0 01 2) 3 00 22

2 2 2

Reaction 3:



𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝑆𝑖𝑂2 12 0 0 00 302000

2 3 1 3

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50

1 3 1 50 1 00

𝐶 𝑆𝑖 {5 0 000 1

101000

2 3 11

5 3 0 001 11 1 5

5 1 5 1 00


45,132,9.910)2(,5.249)(2

0

298

0

298 HHHH SSiOSSi

SiOFeO

HHHHH SSiSSiOFeOSiO

)()2( *20

298

0

29823+

∫ (2𝐶 𝐹𝑒 𝐶 𝑆𝑖𝑂2 𝐶 𝑖 2𝐶 𝐹𝑒𝑂 )

+∫ (2𝐶 𝐹𝑒 𝐶 𝑆𝑖𝑂2

𝐶 𝑖 2𝐶 𝐹𝑒𝑂 ) +∫ (2𝐶 𝐹𝑒 𝐶 𝑆𝑖𝑂2 𝐶 𝑖

2𝐶 𝐹𝑒𝑂 ) +∫ (2𝐶 𝐹𝑒 𝐶 𝑆𝑖𝑂2 𝐶 𝑖 2𝐶 𝐹𝑒𝑂 )

+∫ (2𝐶 𝐹𝑒

18

𝐶 𝑆𝑖𝑂2 𝐶 𝑖 2𝐶 𝐹𝑒𝑂 ) +∫ (2𝐶 𝐹𝑒 𝐶 𝑆𝑖𝑂2 𝐶 𝑖

2𝐶 𝐹𝑒𝑂 ) +∫ (2𝐶 𝐹𝑒 𝐶 𝑆𝑖𝑂2 𝐶 𝑖 2𝐶 𝐹𝑒𝑂 )

10 5 2 2 5 132 + ∫ (2 13 0 00 3 12 0 0 00

5 0 000 1

2 12 2 0 001 2

) +∫ (2

12 0 0033 12 0 0 00

5 0 000 1

2

12 2 0 001 2

) +∫ (2 12 0 0033 12 0 0 00

5 3 0 001 2 12 50 0 001 3 ) +∫ (2 12 0

0 00

5 3 0 001 2 12 50 0 001 3 ) +∫ (2

12 0 0 00

5 3 0 001 2 1 3) ∫ (2 10 0 12 0

0 00

5 3 0 001 2 1 3) ∫ (2 10 0 12 0

0 00

5 2 1 3) *4.184/1000

32 ∫ ( 2 0 013 3

)

∫ ( 5 0 00 5

) ∫ ( 5 2 0 00 1

)

∫ ( 0 1 0 000002

) ∫ ( 30 0 003

)

∫ ( 5 10 0 003

) ∫ ( 30 0 00

)

]*4.184/1000

32 {[ 2 0 013 3 0 5

]

[ 5 0 00 5

0 5

]

[ 5 2 0 00 1 0 5

]

[ 0 1 0 000002

0 5

]

[ 30 0 003 0 5

]

[ 5 10 0 003

0 5

]

[ 30 0 00 0 5

]

}

32 0 31 1 2 12 3 3 13 2 15

32 5 53

330 3


19

When the chemical reaction happens at 1800K, 2mole iron oxide reacts with 1 mole silicon to

form 2 mole iron and 1 mole silicon oxide. All the reactants and products are at 1800K, so the

chemical reaction energy can be calculated as the following formula:

3600*)*2(0

)1800(

0

)1800(

0

)1800(2

0

)1800(RES *2H IIII SiFeOSiOFe

2 0 01 21 0 22 32 2 0 0 02 0 02 3 00

5 3 2


According to the HT enthalpy method, the formula is written for the chemical reaction at 1800 K.

In addition, the enthalpy of the dissolved carbon should also be taken into account in this

chemical reaction.

HHHHH SSiSSiOFeOSiO

)()2( *20

18002

0

1800

'

3

0 5 2 2 3 132

3



1000/3600*)03,5*196,0()( TFeH (25-1527℃)

1000/3600*09,8*316,0)2( TSiOH (25-2000℃)

1000/3600*30,7*272,0)( TSiH (25-1527℃)

1000/3600*08,6*226,0)( TFeOH (25-1527℃)

He of for o Ws :

3600*071,4)2(,3600*057,1)(,0)(,0)( fSiOHfFeOHfSiHfFeH

)()(2)2()(2)()(2)2()(22 SiHFeOHSiOHFeHfSiHfFeOHfSiOHfFeHH

0 0 1 3 00 0 2 1 05 3 00 2 0 2 0 1 152 5 03

20

5 0 31 152 0

0 2 0 22 152 0

2

0 2 2 152 30

2

331 3 2

32 1 1

Reaction 4:



𝐶 𝑆𝑖𝑂2 12 0 0 00 302000

2 3 1 3

𝐶 𝑆𝑖 {5 0 000 1

101000

2 3 11

5 3 0 001 11 1 5

5 1 5 1 00

𝐶 𝑂2 2 0 00025 1 00

300 5000


45,132,9.910)2(2

0

298 HHH SSiOSSi

SiO

HHHH SSiSSiOSiO )2(

0

29824

∫ (𝐶 𝑆𝑖𝑂2 𝐶 𝑖 𝐶 𝑂2 )

+∫ (𝐶 𝑆𝑖𝑂2

𝐶 𝑖 𝐶 𝑂2 ) +∫ (𝐶 𝑆𝑖𝑂2 𝐶 𝑖 𝐶 𝑂2 )

10 5 132 [∫ ((12 0 0 00

) (5

0 000 1

) ( 2 0 00025

)) ∫ ((12 0 0 00

) 5 3 0 001 ( 2 0 00025

)) ∫ ((12 0 0 00

) 5 ( 2 0 00025

)) ]

21

23 ∫ ( 1 21 0 0035 5

)

∫ ( 0 0 003212

) ∫ ( 1 0 00 212

) 1 1000

23 {[ 1 21 0 0035 5 0 5

]

[ 0 0 003212

0 5

]

[ 1 0 00 212 0 5

]

}

23 122 5 1 23 2 13 15

0 1


When the chemical reaction happens at 1800K, 1 mole silicon reacts with 0.5 mole oxygen to

form 1 mole silicon oxide. Because oxygen is injected from normal environment, so the

temperature of oxygen is 298K, but silicon and silicon oxide are at 1800K. The chemical reaction

energy can be calculated as the following formula:

3600*)0

)298(2

0

)1800(

0

)1800(2RES (H III OSiSiO

0 223 2 0 02 0 3 00

1 2



1800K. In addition, the energy of silicon dissolved and silicon oxide dissolved should also be

taken into account in this chemical reaction.

HHHH SSiSSiOSiO

2

0

1800

'

4)2(

0 5 132

53



22

1000/3600*09,8*316,0)2( TSiOH (25-2000℃)

1000/3600*30,7*272,0)( TSiH (25-1527℃)

32

4,22*3600*0142,0

10000

*4

100000000

*3)2(

2

TOH T (25-2000℃)

He of for o Ws :

3600*071,4)2(,0)2(,0)( fSiOHfOHfSiH

)2()()2()2()()2(4 OHSiHSiOHfOHfSiHfSiOHH

0 1 3 00 0 0 0 0 31 152 0

0 0 2 2

152 30

2 (

3 152 2

100000000

152

10000 0 01 2) 3 00 22

1 3

Reaction 5:



𝐶 𝐶𝑂2 {10 3 0 002

1 5500

2 3 1200

11 0 0 00133 1200 1 00

𝐶 𝐶𝑂 0 0 00120 2 3 2500

𝐶 𝑂2 2 0 00025 1 00

300 5000


5.393)2(,5.110)(0

298

0

298 COCO HH

)()2(0

298

0

2985COCO HHH

∫ (𝐶 𝐶𝑂2 𝐶 𝐶𝑂 0 5 𝐶 𝑂2 )

+∫ (𝐶 𝐶𝑂2 𝐶 𝐶𝑂 0 5

𝐶 𝑂2 )

23

3 3 5 110 5 ∫ ( 10 3 0 002

0 0 00120

0 5 2 0 00025

) ∫ ( 11 0 0 00133 0

0 00120 0 5 ( 2 0 00025

)) 1 1000

2 3 ∫ ( 0 3 5 0 001 11

)

∫ (1 125 0 00000

) 1 1000

2 3 {[ 0 3 5 0 001 11 0 5

]

[1 125 0 00000

0 5

]

}

2 3 3 0 5 0 1

2 0


When the chemical reaction happens at 1800K, 1 mole carbon monoxide reacts with 0.5 mole

oxygen to form 1 mole carbon dioxide. Because oxygen is injected from normal environment, so

the temperature of oxygen is 298K, but carbon monoxide and carbon dioxide are at 1800K. The


3600*)*5.00

)298(2

0

)1800(

0

)1800(2RES (H III OCOCO

0 0 31 0 01 0 5 0 3 00

253 2



1800K:

)()2(0

1800

0

1800

'

5COCO HHH

3 11

2

24


E press o for e h p of p re s s es Ws :

44

4,22*3600*0308,0

10000

*6

100000000

*6)2(

2

TCOH T (25-2000℃)

28

4,22*3600*0117,0

10000

*4

100000000

*3)(

2

TCOH T (25-2000℃)

32

4,22*3600*0142,0

10000

*4

100000000

*3)2(

2

TOH T (25-2000℃)

He of for o Ws :

3600*476,2)2(,0)2(,3600*055,1)( fCOHfOHfCOH

)2(*5,0)()2()2(*5,0)()2(5 OHCOHCOHfOHfCOHfCOHH

2 3 00 1 055 3 00 2 (

0 030 )

3 00 22 (

0 011 ) 3 00 22 0 5 (

0 01 2) 3 00 22

2 5 5 1 53

2 0

Reaction 6:



𝐶 𝐶𝑂 0 0 00120 2 3 2500

𝐶 𝐶 𝑟 𝑛 {2 3 0 002 1

11 00

2 3 11 3

0 000 31 11 3 1 00

𝐶 𝑂2 2 0 00025 1 00

300 5000

25


27,5.110)(0

298 HH SC

CO

HHH SC)298(

0

2986

∫ (𝐶 𝐶𝑂 𝐶 𝐶 0 5 𝐶 𝑂2 )

+∫ (𝐶 𝐶𝑂 𝐶 𝐶 0 5 𝐶 𝑂2 )

110 5 2 [∫ ( 0 0 00120 2 3 0 002 1

0 5 2 0 00025

) ∫ ( 0 0 00120

0 000 31 0 5 2 0 00025

) ]*4.184/1000

3 5 ∫ 0 20 0 0015

∫ 2 025 0 0002

]*4.184/1000

3 5 {[ 0 20 0 0015 0 5

]

[ 2 025 0 0002

0 5

]

}

3 5 3

10 2


When the chemical reaction happens at 1800K, 1 mole carbon reacts with 0.5 mole oxygen to

form 1 mole carbon monoxide. Because oxygen is injected from normal environment, so the

temperature of oxygen is 298K, but carbon and carbon monoxide are at 1800K. The chemical

reaction energy can be calculated as the following formula:

3600*)*5.00

)298(2

0

)1800(

0

)1800(RES (H III OCCO

0 01 0 00 53 0 5 0 3 00

30 3


26


1800K. In addition, the energy of carbon dissolved should also be taken into account in this

chemical reaction.

HHH SCCO

)(0

18006

11 2

0



28

4,22*3600*0117,0

10000

*4

100000000

*3)(

2

TCOH T (25-2000℃)

32

4,22*3600*0142,0

10000

*4

100000000

*3)2(

2

TOH T (25-2000℃)

1000/3600*)174*572,0()( TCH (1400-1724℃)

He of for o Ws :

0)(,0)2(,3600*055,1)( fCHfOHfCOH

)2(*5,0)()()2(*5,0)()(6 OHCHCOHfOHfCHfCOHH

1 055 3 00 2 0 0 (

0 011 ) 3 00 22

0 5 2 152 1

12 0 5 (

0 01 2) 3 00 22

10 3

Reaction 7:



27

𝐶 𝐶𝑂2 {10 3 0 002

1 5500

2 3 1200

11 0 0 00133 1200 1 00

𝐶 𝐶 𝑟 𝑛 {2 3 0 002 1

11 00

2 3 11 3

0 000 31 11 3 1 00

𝐶 𝑂2 2 0 00025 1 00

300 5000


27,5.393)2(0

298 HH SC

CO

HHH SCCO

)2(0

2987+

∫ (𝐶 𝐶𝑂2 𝐶 𝐶 𝐶 𝑂2 )

+∫ (𝐶 𝐶𝑂2 𝐶 𝐶

𝐶 𝑂2 ) +∫ (𝐶 𝐶𝑂2 𝐶 𝐶 𝐶 𝑂2 )

3 3 5 2 ∫ ((10 3 0 002

) (2 3 0 002 1

) ( 2 0 00025

)) ∫ ( 10 3 0 002

0 000 31 2 0 00025

)

∫ ( 11 0 0 00133 0 000 31 ( 2 0 00025

)) 1 1000

3 5 ∫ ( 0 03 0 000135

)

∫ ( 2 2

0 001

) ∫ ( 0 0 0002

) 1 1000

3 5 {[ 0 03 0 000135 0 5

]

[ 2 2 0 001

0 5

]

[ 0 0 0002 0 5

]

}

3 5 3 1 0 11 0 5 220 51

3


28

When the chemical reaction happens at 1800K, 1 mole carbon reacts with 1 mole oxygen to form

1 mole carbon dioxide. Because oxygen is injected from normal environment, so the temperature

of oxygen is 298 K, but carbon and carbon dioxide are at 1800 K. The chemical reaction energy

can be calculated as the following formula:

3600*)0

)298(2

0

)1800(

0

)1800(2RES (H III OCCO

0 0 31 0 00 53 0 3 00

2 3



1800 K. In addition, the energy of carbon dissolved should also be taken into account in this

chemical reaction.

HHH SCCO

)2(0

1800

'

7

3 2

3



44

4,22*3600*0308,0

10000

*6

100000000

*6)2(

2

TCOH T (25-2000℃)

32

4,22*3600*0142,0

10000

*4

100000000

*3)2(

2

TOH T (25-2000℃)

1000/3600*)174*572,0()( TCH (1400-1724℃)

He of for o Ws :

0)(,0)2(,3600*476,2)2( fCHfOHfCOH

)2()()2()2()()2(6 OHCHCOHfOHfCHfCOHH

29

2 3 00 0 0 (

0 030 ) 3 00 22

0 5 2 152 1

12 (

0 01 2) 3 00 22

3 2 2 1 2

3 3

Reaction 8:



𝐶 𝑀𝑛

{

3 0 00 2 3 110

5 0 0 003 5 110 131

0 0 00 22 131 1 3

11 0 1 3 1 00

𝐶 𝑆𝑖𝑂2 12 0 0 00

(273-1973K)

𝐶 𝑀𝑛𝑂 3 0 0103 0 000003 2 2 3 1 23

𝐶 𝑆𝑖 {5 0 000 1

101000

2 3 11

5 3 0 001 11 1 5

5 1 5 1 00


45,132,9.910)2(,385)(2

0

298

0

298 HHHH SSiOSSi

SiOMnO

HHHHH SSiSSiOMnOSiO )()2( 2

0

298

0

29828

∫ (2𝐶 𝑀𝑛 𝐶 𝑆𝑖𝑂2 2𝐶 𝑀𝑛𝑂 𝐶 𝑆𝑖 )

+∫ (2𝐶 𝑀𝑛 𝐶 𝑆𝑖𝑂2

2𝐶 𝑀𝑛𝑂 𝐶 𝑆𝑖 ) +∫ (2𝐶 𝑀𝑛 𝐶 𝑆𝑖𝑂2 2𝐶 𝑀𝑛𝑂

𝐶 𝑆𝑖 ) +∫ (2𝐶 𝑀𝑛 𝐶 𝑆𝑖𝑂2 2𝐶 𝑀𝑛𝑂 𝐶 𝑆𝑖 )

∫ (2𝐶 𝑀𝑛

𝐶 𝑆𝑖𝑂2 2𝐶 𝑀𝑛𝑂 𝐶 𝑆𝑖 ) ∫ (2𝐶 𝑀𝑛 𝐶 𝑆𝑖𝑂2 2𝐶 𝑀𝑛𝑂

𝐶 𝑆𝑖 )

30

10 5 2 3 5 132 ∫ (2 3 0 00 (12 0

0 00

) 2 3 0 0103 0 000003 2 5 0 000 1

) ∫ (2 5 0 0 003 5 (12 0 0 00

) 2 3

0 0103 0 000003 2 5 0 000 1

) ∫ (2 5 0

0 003 5 (12 0 0 00

) 2 3 0 0103 0 000003 2

5 3 0 001 ) ∫ (2 0 0 00 22 (12 0 0 00

) 2

3 0 0103 0 000003 2 5 3 0 001 ) ∫ (2 11 0

(12 0 0 00

) 2 3 0 0103 0 000003 2 5 3

0 001 ) ∫ (2 11 0 (12 0 0 00

) 2 3 0 0103

0 000003 2 5) 1 1000

53 ∫ ( 0 2 0 001 0 00000 2

)

∫ (2 32

0 00 00 0 00000 2

) ∫ (2 0 00 3 0 00000 2

) ∫ (2 2 0 00 5 0 00000 2

)

∫ (1

0 01 2 0 00000 2

) ∫ (13 0 01 2 0 00000 2

) 1 1000

53 {[ 0 2 0 001 0 5 0 00000 2

]

[2 32 0 00 00 0 5 0 00000 2

]

[2 0 00 3

0 5 0 00000 2

]

[2 2 0 00 5 0 5 0 00000 2

]

[1 0 01 2 0 5 0 00000 2

]

[13 0 01 2 0 5 0 00000 2

]

}

53 13 2 05 302 15 51 102 2 3

35


31


1000/3600*)71,5*213,0()( TMnH (25-1527℃)

1000/3600*09,8*316,0)2( TSiOH (25-2000℃)

1000/3600*30,7*272,0)( TSiH (25-1527℃)

1000/3600*31,5*226,0)( TMnOH (25-1527℃)

He of for o Ws :

3600*071,4)2(,3600*517,1)(,0)(,0)( fSiOHfMnOHfSiHfMnH

)()(2)2()(2)()(2)2()(28 SiHMnOHSiOHMnHfSiHfMnOHfSiOHfMnHH

0 0 1 3 00 0 2 1 51 3 00 1 0 2 0 213 152 5 1

55 0 31 152 0

0 2 0 22 152 5 31

1

0 2 2 152 30

2

1

Reaction 9: (



𝐶 𝑀𝑛

{

3 0 00 2 3 110

5 0 0 003 5 110 131

0 0 00 22 131 1 3

11 0 1 3 1 00

𝐶 𝐶𝑂 0 0 00120 2 3 2500

𝐶 𝑀𝑛𝑂 3 0 0103 0 000003 2 2 3 1 23

𝐶 𝐶 𝑟 𝑛 {2 3 0 002 1

11 00

2 3 11 3

0 000 31 11 3 1 00


32

27,20,9.110)(,385)(0

298

0

298 HHHH SCSMn

COMnO

HHHHH SCSMnMnOCO )()(

0

298

0

2989

∫ (𝐶 𝑀𝑛 𝐶 𝐶𝑂 𝐶 𝑀𝑛𝑂 𝐶 𝐶 )

+∫ (𝐶 𝑀𝑛 𝐶 𝐶𝑂 𝐶 𝑀𝑛𝑂

𝐶 𝐶 ) +∫ (𝐶 𝑀𝑛 𝐶 𝐶𝑂 𝐶 𝑀𝑛𝑂 𝐶 𝐶 )

+∫ (𝐶 𝑀𝑛 𝐶 𝐶𝑂

𝐶 𝑀𝑛𝑂 𝐶 𝐶 ) ∫ (𝐶 𝑀𝑛 𝐶 𝐶𝑂 𝐶 𝑀𝑛𝑂 𝐶 𝐶 )

110 20 3 5 2 ∫ ( 3 0 00 0 0 00120

3 0 0103 0 000003 2 2 3 0 002 1

) ∫ ( 5 0

0 003 5 0 0 00120 3 0 0103 0 000003 2 2 3

0 002 1

) ∫ 5 0 0 003 5 0 0 00120 3

0 0103 0 000003 2 0 000 31 ∫ ( 0 0 00 22

0 0 00120 3 0 0103 0 000003 2 0 000 31 )

∫ (11 0 0 0 00120 3 0 0103 0 000003 2

0 000 31 ) 1 1000

2 1 1 ∫ (0 25 0 00 32 0 000003 2

)

∫ (1 55

0 00 0 000003 2

) ∫ 0 2 0 00 0131

0 000003 2 ∫ 0 52 0 005 31 0 000003 2

∫ 5

0 00 31 0 000003 2 1 1000

2 1 1 {[0 25 0 00 32 0 5 0 000003 2

]

[1 55 0 00 0 5 0 000003 2

]

[0 2 0 00 0131

0 5 0 000003 2

]

[0 52 0 005 31 0 5 0 000003 2

]

[5 0 00 31 0 5 0 000003 2

]

}

2 1 1 2 5 3 11 25 13 105 2 2 0 1

2 35


33


1000/3600*)71,5*213,0()( TMnH (25-1527℃)

28

4,22*3600*0117,0

10000

*4

100000000

*3)(

2

TCOH T (25-2000℃)

1000/3600*31,5*226,0)( TMnOH (25-1527℃)

1000/3600*)174*572,0()( TCH (1400-1724℃)

He of for o Ws :

3600*055,1)(,3600*517,1)(,0)(,0)( fCOHfMnOHfCHfMnH

)()()()()()()()(9 CHMnOHCOHMnHfCHfMnOHfCOHfMnHH

0 1 055 3 00 2 1 51 3 00 1 0 0 213 152 5 1

55 (

0 011 ) 3 00 22 0 22 152 5 31

1

0 5 2 152 1

12

2 1 55

Reaction 10:



𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝑀𝑛𝑂 3 0 0103 0 000003 2 2 3 1 23

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50

1 3 1 50 1 00

34

𝐶 𝑀𝑛

{

3 0 00 2 3 110

5 0 0 003 5 110 131

0 0 00 22 131 1 3

11 0 1 3 1 00


20,5.249)(,385)(0

298

0

298 HHH SMn

FeOMnO

HHHH SMnFeOMnO )()(

0

298

0

29810

∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 )

+∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂

𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 ) +∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂

𝐶 𝑀𝑛 ) +∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 )

+∫ (𝐶 𝐹𝑒

𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 ) ∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂

𝐶 𝑀𝑛 ) ∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 )

+∫ (𝐶 𝐹𝑒

𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 ) ∫ (𝐶 𝐹𝑒 𝐶 𝑀𝑛𝑂 𝐶 𝐹𝑒𝑂 𝐶 𝑀𝑛 )

3 5 2 5 20 ∫ ( 13 0 00 3 3 0 0103

0 000003 2 (12 2 0 001 2

) 3 0 00 )

∫ ( 12 0 0033 3 0 0103 0 000003 2 (12 2 0 001 2

) 3 0 00 ) ∫ ( 12 0 0033 3 0 0103

0 000003 2 12 2 0 001 2

5 0 0 003 5 ) ∫ 12

0 0033 3 0 0103 0 000003 2 12 50 0 001 3 5 0

0 003 5 ∫ 3 0 0103 0 000003 2 12 50

0 001 3 5 0 0 003 5 ∫ 3 0 0103 0 000003 2

12 50 0 001 3 0 0 00 22 ∫ 3 0 0103

0 000003 2 12 50 0 001 3 11 0 ∫ 3 0 0103

0 000003 2 1 3 11 0 ∫ 10 0 3 0 0103 0 000003 2

1 3 11 0 1 1000

115 5 ∫ ( 2 0 00 T 0 000003 2T

) T

∫ ( 2 3

0 00 0 000003 2

) ∫ ( 13 0 00 2 0 000003 2

35

) ∫ ( 01 0 00 05 0 000003 2

)

∫ 1 3

0 00 0 000003 2 ∫ 1 0 00 2 0 000003 2

∫ 0 00 0 000003 2 ∫ 11 0 0103

0 000003 2 ∫ 0 0103 0 000003 2 1 1000

115 5 {[ 2 0 00 0 5 0 000003 2

]

[ 2 3 0 00 0 5 0 000003 2

]

[ 13 0 00 2

0 5 0 000003 2

]

[ 01 0 00 05 0 5 0 000003 2

]

[ 1 3 0 00 0 5 0 000003 2

]

[ 1 0 00 2 0 5 0 000003 2

]

[ 0 00

0 5 0 000003 2

]

[ 11 0 0103 0 5 0 000003 2

]

[ 0 0103 0 5 0 000003 2

]

}

115 5 051 121 32 3 3 00 210 22 25 3 3 355

101 23 3 2 1 1000

125



1000/3600*)03,5*196,0()( TFeH (25-1527℃)

1000/3600*31,5*226,0)( TMnOH (25-1527℃)

1000/3600*08,6*226,0)( TFeOH (25-1527℃)

1000/3600*)71,5*213,0()( TMnH (25-1527℃)

He of for o Ws :

3600*507,1)(,3600*517,1)(,0)(,0)( fFeOHfMnOHfFeHfMnH

)()()()()()()()(10 FeOHMnHMnOHFeHfFeOHfMnHfMnOHfFeHH

36

1 51 3 00 1 1 50 3 00 2 0 1 152 5 03

5

0 22 152 5 31

1 0 213 152 5 1

55 0 22 152

0

2

2 1

Reaction 11:

(Only when the steel contains chromium, this chemical reaction will be taken into account.)



𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝐶𝑟2𝑂3 2 0 0 00 00 2 3 22 3

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50 1 3 1 50 1 00

𝐶 𝐶𝑟 0 002 5 2 3 1 23


42,5.249)(,4.1018)32(0

298

0

298 HHH SCr

FeOOCr

HHHH SCrFeOOCr )(3)32(

0

298

0

29811

∫ (3𝐶 𝐹𝑒 𝐶 𝐶𝑟2𝑂3 3𝐶 𝐹𝑒𝑂 2𝐶 𝐶𝑟 )

+∫ (3 p e p r2 3

3 p e 2 p r ) T +∫ (3 p e p r2 3 3 p e

2 p r ) T +∫ (3𝐶 𝐹𝑒 𝐶 𝐶𝑟2𝑂3 3𝐶 𝐹𝑒𝑂 2𝐶 𝐶𝑟 )

+∫ (3𝐶 𝐹𝑒

𝐶 𝐶𝑟2𝑂3 3𝐶 𝐹𝑒𝑂 2𝐶 𝐶𝑟 ) ∫ (3𝐶 𝐹𝑒 𝐶 𝐶𝑟2𝑂3 3𝐶 𝐹𝑒𝑂

2𝐶 𝐶𝑟 )

37

101 3 2 5 2 [∫ (3 13 0 00 3 2 0 0 00 00 3

(12 2 0 001 2

) 2 0 002 5 ) ∫ (3 12

0 0033 2 0 0 00 00 3 (12 2 0 001 2

) 2

0 002 5 ) T ∫ (3 12 0 0033 2 0 0 00 00 3 12 50

0 001 3 2 0 002 5 ) T ∫ (3 2 0 0 00 00 3

12 50 0 001 3 2 0 002 5 ) ∫ (3 2 0 0 00 00

3 1 3 2 0 002 5 ) ∫ (3 10 0 2 0 0 00 00 3 1 3

2 0 002 5 ) ]

22 ∫ ( 15 0 012

)

∫ ( 3 1 0 003 0

) T ∫ ( 2 0 002 2

) T

∫ 3 3 0 00 10

∫ 3 0 001

∫ 2 5 0 001 1 1000

22 {[ 15 0 012 0 5

]

[ 3 1 0 003 0 0 5

]

[ 2 0 002 2 0 5

]

3 3 0 00 10

0 5 3 0 001 0 5

2 5 0 001 0 5 }

1 1000

22 3 3 1 1 5 2 5 5 252 0 0 1 1

1000

2 2 5


When the chemical reaction happens at 1800K, 3 mole iron oxides react with 2 mole chromium

to form 3 mole iron and 1 mole chromium oxide. All the reactants and products are at 1800K.

The chemical reaction energy can be calculated as the following formula:

3600*)*3( *2*3H0

)1800(

0

)1800(

0

)1800(32

0

)1800(RES IIII CrFeOOCrFe

3 0 01 21 0 2 0 3 0 0 02 2 0 01 25 3 00

5 1

38



1800K. In addition, the energy of chromium dissolved should also be taken into account in this

chemical reaction.

HHHH SCrFeOOCr

)()32( *30

1800

0

1800

'

11

1125 3 2 3 2

35



1000/3600*)03,5*196,0()( TFeH (25-1527℃)

1000/3600*84,5*231,0)32( TOCrH (25-1527℃)

1000/3600*08,6*226,0)( TFeOH (25-1527℃)

1000/3600*)43,4*173,0()( TCrH (25-1527℃)

He of for o Ws :

3600*101,2)32(,3600*507,1)(,0)(,0)( fOCrHfFeOHfFeHfCrH

)(2)(3)(3)32()()(3)(3)32(11 CrHFeOHFeHOCrHfCrHfFeOHfFeHfOCrHH

2 101 3 00 152 3 1 05 3 00 2 0 231 152 5

152 3 0 1 152 5 03

5 3 0 22 152 0

2 2

0 1 3 152 3

52

22 1 2

2 0

Reaction 12:

(Only when the steel contains chromium, this chemical reaction will be taken into account.)

39


Heat capacity of substances ( )

𝐶 𝐶𝑟2𝑂3 2 0 0 00 00 2 3 22 3

𝐶 𝐶𝑟 0 002 5 2 3 1 23

𝐶 𝑂2 2 0 00025 1 00

300 5000


42,4.1018)32(0

298 HH SCr

OCr

HHH SCrOCr

*2)32(0

29812+∫ (𝐶 𝐶𝑟2𝑂3 2𝐶 𝐶𝑟 1 5𝐶 𝑂2 )

101 2 2 ∫ ( 2 0 0 00 00 2 0 002 5 1 5

( 2 0 00025

)) 1 1000

3 ∫ (3 15 0 0022

) 1 1000

3 [3 15 0 0022 0 5

]

1 1000

21 5 5


When the chemical reaction happens at 1800K, 2 mole iron reacts with 1.5 mole oxygen to form

1 mole chromium oxide. Because oxygen is from normal environment, so the temperature of

oxygen is 298K, but chromium and chromium oxide are at 1800K. The chemical reaction energy

can be calculated as the following formula:

3600*)*5.10

)298(2

0

)1800(

0

)1800(32RES *2(H III OCrOCr

0 2 0 0 01 25 0 3 00

31

40



1800K. In addition, the energy of chromium dissolved should also be taken into account in this

chemical reaction.

HHH SCrOCr

*2)32(0

1800

'

12

1125 2 2

10 1



1000/3600*84,5*231,0)32( TOCrH (25-1527℃)

1000/3600*)43,4*173,0()( TCrH (25-1527℃)

32

4,22*3600*0142,0

10000

*4

100000000

*3)2(

2

TOH T (25-2000℃)

He of for o Ws :

3600*101,2)32(,0)2(,0)( fOCrHfOHfCrH

)2(*5,1)(2)32()2(*5,1)(2)32(12 OHCrHOCrHOHfCrHfOCrHH

2 101 3 00 152 0 231 152 5

152 2 0 1 3 152

3

52 1 5 (

3 152 2

100000000

152

10000 0 01 2) 3 00 22

113 1

41

Reaction 13:



𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝑃 𝑂10 {15 2 0 10 2 2 3 31

3 31 1 00

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50 1 3 1 50 1 00

𝐶 𝑃 {

5 5 2 3 31

30 31 11 0

11 0 1 00


29,5.249)(,9.3009)52(0

298

0

298 HHH SCr

FeOOP

HHHH SPFeOOP *2)(*5)52(

0

298

0

29813

∫ (5𝐶 𝐹𝑒 𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂 2𝐶 𝑃 )

+∫ (5𝐶 𝐹𝑒 𝐶 𝑃2𝑂5

5𝐶 𝐹𝑒𝑂 2𝐶 𝑃 ) +∫ (5𝐶 𝐹𝑒 𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂

2𝐶 𝑃 ) +∫ (5𝐶 𝐹𝑒 𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂 2𝐶 𝑃 )

+∫ (5𝐶 𝐹𝑒

𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂 2𝐶 𝑃 ) ∫ (5𝐶 𝐹𝑒 𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂

2𝐶 𝑃 ) ∫ (5𝐶 𝐹𝑒 𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂 2𝐶 𝑃 )

∫ (5𝐶 𝐹𝑒

𝐶 𝑃2𝑂5 5𝐶 𝐹𝑒𝑂 2𝐶 𝑃 )

300 5 2 5 2 2 [∫ (5 13 0 00 3 15 2 0 10 2

5 (12 2 0 001 2

) 2 5 5) ∫ (5 13 0 00 3

42

15 2 0 10 2 5 (12 2 0 001 2

) 2 30 ) ∫ (5

13 0 00 3 3 5 (12 2 0 001 2

) 2 30 )

∫ (5 12 0 0033 3 5 (12 2 0 001 2

) 2 30 )

∫ 5 12 0 0033 3 5 12 50 0 001 3 2

30 ∫ 5 3 5 12 50 0 001 3 2 ∫ 5

3 5 1 3 2 ∫ 5 10 0 3 5 1 3 2

1 1000

1 0 ∫ ( 3 23 0 133

)

∫ ( 3 33 0 133

) ∫ (1 55 0 02

)

∫ (2 5 0 0 3

) ∫ 2 055 0 00 12

∫ 135

0 00 ∫ 25 1

∫ 33 1 1 1000

1 0 {[ 3 23 0 133 0 5

]

[ 3 33 0 133 0 5

]

[1 55 0 02 0 5

]

[2 5 0 0 3 0 5

]

2 055 0 00 12 0 5 135 0 00 0 5

25 1 33 1

}

1 0 131 052 13 12 1 220 3 1 51 1 2 0 25 1 0 1

0 32 1 0 1 1000

1 0 25 2 2

1 5 12



1800K. In addition, the energy of phosphorus dissolved should also be taken into account in this

chemical reaction.

HHHH SPFeOOP

*2)(*5)52(0

1800

0

1800

'

13

3115 5 2 3 2 2

43

1 2

Reaction 14:



𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

𝐶 𝐶𝑂 0 0 00120 2 3 2500

𝐶 𝐶 𝑟 𝑛 {2 3 0 002 1

11 00

2 3 11 3

0 000 31 11 3 1 00

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50 1 3 1 50 1 00


5.110)(,5.249)(0

298

0

298 COFeO HH

)()(0

298

0

29814FeOCO HHH

∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

+∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶

𝐶 𝐹𝑒𝑂 ) +∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

+∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂

𝐶 𝐶 𝐶 𝐹𝑒𝑂 ) +∫ (𝐶 𝐹𝑒 𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

∫ (𝐶 𝐹𝑒

𝐶 𝐶𝑂 𝐶 𝐶 𝐶 𝐹𝑒𝑂 )

110 5 2 5 ∫ ( 13 0 00 3 0 0 00120 2 3

0 002 1

12 2 0 001 2

) +∫ ( 12 0 0033

0 0 00120 2 3 0 002 1

12 2 0 001 2

) ∫ 12 0 0033 0 0 00120 0 000 31

12 50 0 001 3 ∫ 0 0 00120 0 000 31

44

12 50 0 001 3 ∫ 0 0 00120 0 000 31

1 3 ∫ 10 0 0 0 00120 0 000 31 1 3

1 1000

13 ∫ ( 5 3 0 003 1

)

∫ ( 2 5 3 0 000 51

) ∫ 2 0 0020 1

∫ 1 0 00131 1

∫ 5 0 000 1 ∫ 1 0 000 1 1 1000

13 5 3 0 003 1 0 5

2 5 3 0 000 51

0 5

2 0 0020 1 0 5

1 0 00131 1

0 5 5 0 000 1 0 5

1 0 000 1 0 5

1 1000

13 1201 21 252 11 2 3 1 20 35 122 331 3

1 1000

122 1


When the chemical reaction happens at 1800K, 1mole iron oxide reacts with 1 mole carbon to

form 1 mole iron and 1 mole carbon monoxide. Because carbon is injected from normal

environment, so the temperature of carbon is 298K, but other substances are at 1800K. The


3600*)0

)298(

0

)1800(

0

)1800(

0

)1800(RES (H IIII CFeOCOFe

0 01 21 0 01 0 0 02 3 00

25 5



1800:

)()(0

1800

0

1800

'

14FeOCO HHH

45

110 2 3

133



1000/3600*)03,5*196,0()( TFeH (25-1527℃)

28

4,22*3600*0117,0

10000

*4

100000000

*3)(

2

TCOH T (25-2000℃)

12*860

3600*1972

273

100000*1,2

1000*2

*02,1273*1,4)(

2732

TTCH

T (25-2727℃)

1000/3600*08,6*226,0)( TFeOH (25-1527℃)

He of for o Ws :

0)(,3600*057,1)(,3600*055,1)(,0)( fCHfFeOHfCOHfFeH

)()()()()()()()(14 CHFeOHCOHFeHfCHfFeOHfCOHfFeHH

)072*3600*057,128*3600*055,10( { 0 1 152 5 03

5

(

0 011 ) 3 00 22 0 22 152 0

2

[ 1 152 2 3

1 2]

12}

1 3 2

1 2

46

Table 3.Comparison of enthalpies calculated by four methods (KJ/mole)

PERRY-NIST-JANAF Total

enthalpy

method

HT

Enthalpy

method

Atomic energy method

Heat of

formation

Increasing

temperature Total

Heat of

formation

Increasing

temperature Total

167 -16,086 150,914 56,268 153

167.63

-4.815 162.815

-249,5 9,3 -240,2 86.616 -243 -273.974 1.676 -272.298

-324.9 -5,53 -330.43 543,24 -367 -324.81 -2,331 -327.141

[

-823,9 15,736 -808,164 716,472 -853 -831.399 -40,339 -871.738

-283 4,392 -278,608 253,26 -279 -239.338 -48,369 -287.707

-83,5 -20,79 -104,29 30,348 -90 -92.311 -17,172 -109.483

-366,5 -2,398 -368,898 283,6 -369 -319.29 -74,196 -393.486

-53.9 17,954 -35.946 -95.255 5,594 -89.661

(

281,1 16,835 297,935 289.26 -7,704 281.556

[

-115,,5 -10,47 -125,97 2.753 -4,853 -2.1

)

-227,9 -15,059 -242,959 588,168 -354 86.541 -57,445 29.096

)

-934,4

12,825

-921,575 899,316 -1041 1301.043 -163,325 -1137.718

]

)

-1704,4

259,272

-

1445,128

-1842

139

-16,086

122,914

25 5

133

215.496

-52,508

162.988

47

Through the above table, it’s obvious that the calculation results of these four methods show

some difference for all the reactions. Besides, because some basic data are not available, so the

corresponding final results cannot be obtained.

In EAF process, carbon plays a major role in the process of EAF and contributes lots of chemical

energy in reactions:

𝐶 𝐹𝑒𝑂 𝐹𝑒 𝐶𝑂 ( 𝐶 𝑀𝑛 𝐶𝑂

𝐶 0 5𝑂2 𝐶𝑂 𝐶 𝐹𝑒𝑂 𝐹𝑒 𝐶𝑂

𝐶 𝑂2 𝐶𝑂2

Obviously, dissolved carbon participates in most of the chemical reactions, but the injected

carbon only take part in the reaction which happens with iron oxide.

In general, 𝐶 𝐹𝑒𝑂 𝐹𝑒 𝐶𝑂 is the main reaction in EAF process and contributes to

most of the chemical energy. The Comparison of the results of four methods on this reaction

shows that the values calculated from all methods, except the “Total enthalpy method”, are very

close. This also happens on the other three reactions ( 𝐶 0 5𝑂2 𝐶𝑂, 𝐶 𝑂2 𝐶𝑂, 𝐶

𝐹𝑒𝑂 𝐹𝑒 𝐶𝑂 ) which also shows the results of “Total enthalpy method” is a bit far from

the calculation results of the other three methods.

For the reaction, manganese oxide reacts with carbon, since some basic data are not available for

“Total enthalpy method” and “HT enthalpy method”, only the results of the other two methods

can be obtained which are quite close.

Besides carbon, oxygen injected during EAF process also contributes a lot to chemical energy. In

the process, oxygen mainly reacts with iron, but also reacts with some other elements in the metal

through the following reactions:

𝐹𝑒 0 5𝑂2 𝐹𝑒𝑂 𝐶 0 5𝑂2 𝐶𝑂

[𝑆𝑖 𝑂2 𝑆𝑖𝑂2 𝐶 𝑂2 𝐶𝑂2

𝐶𝑂 0 5𝑂2 𝐶𝑂2 2 𝐶𝑟 1 5𝑂2 𝐶𝑟2𝑂3

For the main reaction, oxygen reacts with iron oxide, it can be found that the result of chemical

energy calculated by “Total enthalpy method” is different from the values of the other three

48

methods. However, for the other five reactions, the values of chemical energies calculated by four

methods are quite close. To be mentioned, the oxidation reaction of chromium is very important

for stainless steel making process.

During EAF process, although carbon plays a major role in reducing iron oxide, some other

alloying elements can also reduce iron oxides through the following reactions:

(1) 2 e 2 e 2 (2) 3 e 2 r 3 e r2 3)

(3) [ e e (4) 5 e 2 P] 5 e P2 5)

Investigating on the values of chemical energies of these four reactions, it was found that the data

regarding on the calculation are not sufficient. For the reaction which happens between iron oxide

and manganese, the basic data of “Total enthalpy method” and “HT enthalpy method” are not

available. Besides, for iron oxide reaction with phosphorous, the data of “Total enthalpy method”

and “Atomic energy method” are not available. Besides the insufficient data, for reaction (3), it is

obvious that the results of the other two methods have a big difference. For reaction (4), the

results of the other two methods are relatively similar.

For the reaction which happens between silicon and iron oxide, the results calculated by four

methods are close, except for the result of “Total enthalpy method” which shows a bit difference.

For reaction (2), the four results are different, especially for the one obtained by “Atomic energy

method” which is far from the other three.

Manganese oxide, generated due to oxidation of dissolved Mn in steel, can react with carbon and

silicon:

(5) (𝑀𝑛𝑂 𝐶 𝑀𝑛 𝐶𝑂 (6) 2 𝑀𝑛𝑂 𝑆𝑖 2 𝑀𝑛 𝑆𝑖𝑂2

In table 3, it can be seen that basic data of both of “Total enthalpy method” and “HT enthalpy

method” are not available. The Comparison of the results of the other two methods shows that for

reaction (5), the results are very close; but for reaction (6), the results are different.

Considering the background of metallurgy, some chemical reactions listed might contribute little

to chemical energy. For example, the reaction between iron oxide and phosphorous:5 𝐹𝑒𝑂

49

2 𝑃 5 𝐹𝑒 𝑃2𝑂5 , since the content of 𝑃 is very low in steel, the chemical reaction

energy is quite limited.

Compare “PERRY-NIST-JANAF method” and “Atomic energy method”, it is found that the

values of the chemical reaction enthalpies are composed by two parts: heat of formation and

enthalpy change by increasing temperature. In order to distinguish the two methods, Enthalpy

change by increasing temperature/ Heat of formation (EC/HF) is used to study:

Table 4.Comparison between “PERRY-NIST-JANAF method” and “Atomic energy method”

PERRY-NIST-JANAF Atomic energy method

Heat of

formation

Increasing

temperature EC/HF

Heat of

formation

Increasing

temperature EC/HF

167 -16,086 -0.096

167.63

-4.815 -0.0287

-249,5 9,3 -0.037 -273.974 1.676 -0.00612

-324.9 -5,53 -0.017 -324.81 -2,331 0.00712

[

-823,9 15,736 -0.019 -831.399 -40,339 0.0485

-283 4,392 -0.0053 -239.338 -48,369 0.202

-83,5 -20,79 0.248 -92.311 -17,172 0.186

-366,5 -2,398 0.0065 -319.29 -74,196 0.232

-53.9 17,954 -0.333 -95.255 5,594 -0.0587

(

281,1 16,835 0.06 289.26 -7,704 -0.266

[

-115,,5 -10,47 0.091 2.753 -4,853 -1.763

)

-227,9 -15,059 0.066 86.541 -57,445 -0.664

50

)

-934,4

12,825

-0.0137 1301.043 -163,325 -0.126

]

)

-1704,4

259,272

-0.152

139

-16,086

-0.116

215.496

-52,508

-0.244

Investigating on the values of “EC/HF” of the two methods, it finds that values of “EC/HF” in

“PERRY-NIST-JANAF method” are in a stable range (0.005 - 0.35), but those in “Atomic energy

method” show some special values:

For the reaction [ e e , the “EC/HF” value in “Atomic energy method”

is -1.763, which means enthalpy change by increasing temperature is almost twice of the heat of

formation. Considering the “EC/HF” values of other chemical reactions, this value seems not

reasonable. In addition, another “EC/HF” value of in “Atomic energy method” is -0.664, which

also seems out of reasonable range.

Through the comparison, it is clear that the results of “PERRY-NIST-JANAF method” are more

reasonable than those of “Atomic energy method”.

Above all, although the calculation process is more complicated to that of other methods, it is still

recommended to use “PERRY-NIST-JANAF method” to obtain the values of chemical reaction

energies in order to reach more reasonable final results.

From the Table.3 and Table.4, the comparison of the four methods can be made as above.

Moreover, the comparison can also be made through the principles of each method:

In general, the chemical reaction enthalpies are obtained by “PERRY-NIST-JANAF method”, we

have to search the basic data to conclude the expressions of heat capacities before conducting the

calculation. Investigated on the calculation process of these four methods, it finds that “PERRY-

NIST-JANAF method” is a kind of calculation which totally based on the thermodynamics of the

EAF chemical reactions. Therefore, the calculation results of the reactions should be the most

accurate.

51

To make a simplification, “HT enthalpy method” and “Total enthalpy method” are generated:

“HT enthalpy method” which does not concern the heat capacities is an approximate method of

“PERRY-NIST-JANAF method”. This method simply treats the enthalpy change by increasing

temperature is equal to the changes of enthalpies formation from standard state to the temperature

T. Therefore, the final calculation results are different from the results of “PERRY-NIST-JANAF

method”.

In engineering field, it is possible to conduct the work if the approximate values of chemical

enthalpies can be obtained. Besides “HT enthalpy method”, “Total enthalpy method” is another

way to get the approximate results of chemical enthalpies. The method concludes the total

enthalpy values of the substances which show in Table.1 and Table.2, then conduct the

calculation based on the total enthalpy values of the reactants and products at their temperatures

when the reactions happen. Similar to “HT enthalpy method”, “Total enthalpy method” also

makes some changes for simplification: first, the enthalpies of formation are changed to the form

of total enthalpies; second, thermal effects of dissolution of the substances are ignored; third,

thermal effects of evolution of the substances are also ignored [8]

. In fact, the calculation of this

method is totally based on the states of the reactants and products. That’s why the calculation

results show some differences from the results of the other methods.

“Atomic energy method” is a kind of calculation which is usually used in nuclear power field. It

simplifies the changes of enthalpies of increasing temperature by using some particular formulas.

However, from the point of view of thermodynamics, the enthalpy change by increasing

temperature should be calculated by using the heat capacities of the substances. In addition, as

this method is usually used in nuclear power field, the values of standard enthalpies of formation

are also different from those of “PERRY-NIST-JANAF method”. Therefore, the final calculation

results show the difference.

Through the investigation of the principles of the four methods, the same conclusion can also be

made: “PERRY-NIST-JANAF method” can obtain more reasonable calculation results, but other

methods can also be used in suitable situations if it is necessary to simplify the calculation

process.

52

4. Influencing Factors on EAF process

In EAFs, besides chemical energy, there are some other factors can affect the process of EAF. In

this chapter, two influencing factors are discussed: electric power and electromagnetic stirring

(EMS). Given the initial conditions and operating actions, it is possible to simulate the process of

EAF. If change one variable, but keep other conditions same as before, then the effects of the

changed variable can be shown.

In order to study the two factors, some related items are used to show the effects on EAF process:

(1) Change of scrap mass

(2) Change of liquid metal mass

(3) Change of solid slag mass

(4) Change of liquid slag mass

(5) Change of FeO mass

(6) Change of liquid metal temperature

(7) Change of solid group temperature

Based on Bekker’s EAF dynamic model [5]

, it is possible to simulate the above research items in

some particular condition. Varying the value of investigated factor, then the original curves might

be changed. In order to discuss the effects of electric power and electromagnetic stirring (EMS),

three values of the power and three different heat transfer coefficients will be given for making

comparison.

4.1 Power on EAF process

In EAFs, the electric power melts the scrap into liquid steel during the EAF process. If we vary

the level of power and assume the other conditions are fixed, then it is possible to find the effects

of electric power on EAF process.

In order to make the EAF process more efficient, it is necessary to investigate the effects of EAF

power. Through the simulation, the effects of EAF power (50 MW, 70 MW and 90 MW) on

scrap melting are shown by the following figures:

53

Fig.3 Comparison of the changes of solid scrap mass at different power

Fig.4 Comparison of the changes of liquid metal mass at different power

54

Fig.5 Comparison of the changes of solid slag mass at different power

Fig.6 Comparison of the changes of liquid slag mass at different power

55

Fig.7 Comparison of the changes of FeO mass at different power

Fig.8 Comparison of the changes of liquid metal temperature at different power

56

Fig.9 Comparison of the changes of solid group temperature at different power

In Fig.3, the amount of solid scrap mass decreases with time at three investigated powers. At t =

30 min (1800 s), at power of 90 MW, solid scrap mass almost reach zero which means the scrap

totally melt into liquid metal. At t = 50 min (3000 s), for the power of 70 MW, scrap mass totally

melt into liquid metal. However, for the power of 50 MW, scrap mass cannot be totally melted

even in one hour.

In Fig.4, Fig.6 and Fig.7, it can be seen that liquid metal mass, liquid slag mass and FeO mass

show the same tendency. In general, the amount of these three substances increase as time goes

by. Investigating on each of them, it is found that the amount of each substance can reach higher

point in one hour at higher power which means that the melting process goes faster at higher

power.

In Fig.5, the result of solid slag mass is similar to that of solid scrap mass: at the power of 90

MW. The equilibrium is reached faster than that at the power of 70 MW, but the equilibrium

cannot be reached even after one hour at 50 MW.

Fig.8 and Fig.9 show the effects of three powers on the temperature of liquid group and solid

group: compared to the power of 70 MW, solid group melt and the temperature of liquid group

57

increases faster at 90 MW, but the solid group cannot even reach its melting temperature (1800 K)

at 50 MW even in one hour.

Above all, EAF process goes faster at higher electric power.

4.2 Effects of EMS

Since 1947, ABB has supplied various electromagnetic stirring (EMS) systems for steel industries

[9]. Until now, EMS is still applied to improve the efficiency of steelmaking process.

When changing the electric current, the stirring intensity can be changed and the heat transfer

coefficient can also be changed indirectly. If using kther as the original heat transfer coefficient

(without EMS), and kther-ems as the heat transfer coefficient with EMS. Taking kther, kther-ems

(2*kther, 4*kther) into account, the results can be obtained through simulation:

Fig.10 Comparison of the changes of solid scrap mass at different heat transfer coefficient

58

Fig.11 Comparison of the changes of liquid metal mass at different heat transfer coefficient

Fig.12 Comparison of the changes of solid slag mass at different heat transfer coefficient

59

Fig.13 Comparison of the changes of liquid slag mass at different heat transfer coefficient

Fig.14 Comparison of the changes of FeO mass at different heat transfer coefficient

60

Fig.15 Comparison of the changes of liquid metal temperature at different heat transfer coefficient

Fig.16 Comparison of the changes of solid group temperature at different heat transfer coefficient

61

In Fig.10, the amount of solid scrap mass decreases with time at three investigated heat transfer

coefficients. In the beginning, the decreasing rates of three curves can be roughly measured:

Scrap mass: for kther-ems = 4*kther, Vd (1) = 200kg/s; for kther-ems = 2*kther, Vd (2) = 100kg/s;

for kther, Vd (3) = 40kg/s.

Then, it is obvious that the scrap mass decreases faster with higher heat transfer coefficient when

other conditions are equal. Due to higher decreasing rate, it is also found scrap is totally melt

earliest when kther-ems = 4*kther.

In Fig.11, Fig.13 and Fig.14, it can be seen that the amount of liquid metal mass, liquid slag mass

and FeO mass increase as time increases. For the increasing rates of these three substances in the

beginning, the rates of liquid metal and liquid slag can be measured, but the differences of FeO at

three heat transfer coefficients are not obvious.

Liquid metal: for kther-ems = 4*kther, Vi (1) = 140kg/s; for kther-ems = 2*kther, Vi (2) = 70kg/s;

for kther, Vi (3) = 35kg/s.

Liquid slag: for kther-ems = 4*kther, Vi (1’) = 180kg/s; for kther-ems = 2*kther, Vi (2’) = 90kg/s;

for kther, Vi (3’) = 45kg/s.

It can be seen that the amount of liquid metal and liquid slag increase faster at higher heat

transfer coefficient in the beginning. For FeO, although the increasing rates of three curves

cannot be distinguished, it still can also be found that FeO mass is a bit more at higher heat

transfer coefficient in the beginning which also means the increasing rate of FeO mass is a bit

faster at higher heat transfer coefficient.

In Fig.12, the final result of solid slag mass is similar to that of solid scrap mass. For the

decreasing rates of solid slag in the beginning:

Solid slag: for kther-ems = 4*kther, Vd (1’) = 120kg/s; kther-ems = 2*kther, Vd (2’) = 60kg/s; for

kther, Vd (3’) = 30kg/s.

From the rates of solid slag at three heat transfer coefficients, it is also found that solid slag mass

decreases faster at higher heat transfer coefficient. Due to higher decreasing rate, solid slag mass

reach equilibrium earliest when kther-ems = 4*kther.

62

Fig.15 and Fig.16 show the effects of three heat transfer coefficients on the temperature of liquid

group and solid group:

In Fig.15, It shows higher heat transfer coefficient, representative of higher force convection in

the melt due to EMS, leads to a lower melt temperature. This is due to the higher heat loss to the

solid scrap when the heat transfer coefficient is higher. It means, at higher heat transfer

coefficient, the effect on transferring heat from liquid metal to solid group is better than that at

lower heat transfer coefficient. Fig.16 shows that the temperature of solid group reach the

melting point faster at higher heat transfer coefficient which means that the melting rate of solid

group is faster at higher heat transfer coefficient.

To quantify the changing rates of liquid metal temperature and solid group temperature, the rates

in the beginning can also be measured to compare:

Liquid metal temperature: for kther-ems = 4*kther, Vd (1’’) = 10K/s; kther-ems = 2*kther, Vd (2’’) =

5K/s; for kther, Vd (3’’) = 2K/s.

Solid group temperature: for kther-ems = 4*kther, Vi (1’’) = 8K/s; for kther-ems = 2*kther, Vi (2’’) =

4K/s; for kther, Vi (3’’) = 2K/s.

The data of changing rates also show that temperature of solid group and liquid metal change

faster at higher heat transfer coefficient.

Above all, EAF process goes faster at higher heat transfer coefficient.

5. Summary

In this study, the calculation of EAF chemical reaction energies is studied and four methods are

applied to compare: Through the comparison, it is obvious that the calculation process of

“PERRY-NIST-JANAF method” is the most complicated, because it is necessary to conclude the

expressions of related heat capacities before calculation. However, this method is also the only

one which can obtain all the values of EAF chemical reaction energies. Moreover, as this method

is conducted totally based on the thermodynamics of chemical reactions in EAF, the calculation

results should be accurate. Investigating on the values of “EC/HF”, it is also shown that the range

63

of “EC/HF” resulted by “PERRY-NIST-JANAF method” is more reasonable compared to that

obtained by “Atomic energy method”.

Except the “PERRY-NIST-JANAF method”, other three methods are able to conduct the

calculation even without the expressions of heat capacities of the substances. As some basic data

are not available for “Total enthalpy method” and “HT enthalpy method”, some final results of

EAF chemical energies cannot be obtained, but it is also possible to make a rough estimation of

EAF chemical energies. In engineering field, these two methods can also be applied to conduct

the calculation if the accuracy of the results is not necessary. “Atomic energy method” is a

method used in nuclear power field, and is not suitable to be used for the calculation of EAF

chemical reaction energies. Even investigating on the values of “EC/HF”, it is found that the

range of “EC/HF” of this method is not reasonable.

Besides the calculation of EAF chemical energies, the effects of electric power and EMS on EAF

process are also studied through simulation based on Bekker’s EAF dynamic model:

Using “50MW”, “70MW” and “90MW” as EAF power respectively, it is obvious that EAF

process goes faster at higher electric power in the given conditions. Meanwhile, “kther”, “2*kther”

and “4*kther” are applied to study the effects of stirring intensity of EMS, and it finds that EAF

process goes faster at higher heat transfer coefficient.

However, this conclusion of the effects of these two factors can only be made in the general

conditions. If the conditions change, the results might have some difference.

6. Future works

When the values of enthalpies of chemical reaction obtained, further researches can be studied on

EAF process. Based on the values of chemical energies, it is possible to investigate the EAF

dynamic model which is helpful to find a way to improve the productivity and reduce energy

waste.

64

7. References

[1] Logar V., Dovžan D. and Škrjanc I.: Modeling and Validation of an Electric Arc Furnace: Part 2, Thermo-

chemistry, ISIJ Int., 52 (2012), No. 3, 413-423.

[2] Narayanan K. V.: A Textbook of Chemical Engineering Thermodynamics, Prentice-Hall of India, New Delhi,

(2006), 62-63

[3] Achuthan M.: Engineering Thermodynamics, PHI learning, New Delhi, (2009), 85-106

[4] Halder G.: Introduction to Chemical Engineering Thermodynamics, PHI learning, New Delhi, (2009), 119

[5] Bekker J. G., Craig I. K. and Pistorius P. C.: Modeling and Simulation of an Electric Arc Furnace Process,

ISIJ Int., 39 (1999), No. 1, 23-32.

[6] Perry R.H. and Green D.W., Perry’s Chemical Engineers’ Handbook, McGraw-Hill, 1997

[7] American Institute of Phy, Nist-janaf Thermochemical Tables, Fourth Edition, 1998

[8] Toulouevski Y. N. and Zinurov I. Y.: Innovation in electric arc furnaces, Chapter 4: Energy (Heat)

Balances of Furnace, Springer Heidelberg Dordrecht London New York, (2010), 75-79

[9] Stål R. and Carlsson C., Electromagnetic stirring in electric arc furnace, Innovation in EAF and in

steelmaking processes Conference, 2009.

[10] Turkdogan E. T. and Frueham R. J.: The Making, Shaping and Treating of Steel, 10th ed., Chapter 2:

Fundamentals of Iron and Steelmaking, The AISE Steel Foundation, Pittsburgh, PA, USA, (1998), 13

[11] U.S. Atomic Energy Commission Report: ANL-5750

[12] Bulletin 542, U.S. Bureau of Mines, Washington DC, 1954

65

Appendix 1 – Abbreviation Index

EAF Electric Arc Furnace

EMS Electromagnetic Stirring

EAF-EMS Electromagnetic stirring in electric arc furnace

EC/HF Enthalpy change by increasing temperature/ Heat of formation

Appendix 2 – Symbol List

p Heat capacity

The total enthalpy of a chemical substance at the temperature T

Σ Ep Internal energy of the products

Σ Er Internal energy of the reactants

Vp Volume of the products

Vr Volume of the reactants

Σ Hp Enthalpy of the products

Σ Hr Enthalpy of the reactants

(T1) Enthalpy of the reaction at T1

(T1) Enthalpy of the reaction at T2

𝑅𝐸𝑆 Resultant thermal effect

Kther Heat transfer coefficient

Kther-ems Heat transfer coefficient when using electromagnetic stirring

Vd Decreasing rate

Vi Increasing rate

Appendix 3 – Heat capacities of the substances

Heat capacities of substances are closely related to the calculation of chemical reaction enthalpies

in “PERRY-NIST-JANAF method”. According to the data of PERRY-NIST-JANAF, the curves

of heat capacities can be generated as following:

𝐶 𝐶 𝑟 𝑛 {2 3 0 002 1

11 00

2 3 11 3

0 000 31 11 3 1 00

66

Fig.A-1 Heat capacity of carbon at the temperature from 273K to 1800K

𝐶 𝐶𝑂 0 0 00120 2 3 2500

Fig.A-2 Heat capacity of CO at the temperature from 273K to 1800K

𝐶 𝐶𝑂2 {10 3 0 002

1 5500

2 3 1200

11 0 0 00133 1200 1 00

67

Fig.A-3 Heat capacity of CO2 at the temperature from 273K to 1800K

𝐶 𝐶𝑟 0 002 5 2 3 1 23

Fig.A-4 Heat capacity of Cr at the temperature from 273K to 1800K

𝐶 𝐶𝑟2𝑂3 2 0 0 00 00 2 3 22 3

68

Fig.A-5 Heat capacity of Cr2O3 at the temperature from 273K to 1800K

𝐶 𝐹𝑒

{

13 0 00 3 2 3 10 1

12 0 0033 10 1 11

11 1

10 0 1 1 00

Fig.A-6 Heat capacity of Fe at the temperature from 273K to 1800K

69

𝐶 𝐹𝑒𝑂 {12 2 0 001 2

200

2 3 11 3

12 50 0 001 3 11 3 1 50 1 3 1 50 1 00

Fig.A-7 Heat capacity of FeO at the temperature from 273K to 1800K

𝐶 𝑀𝑛

{

3 0 00 2 3 110

5 0 0 003 5 110 131

0 0 00 22 131 1 3

11 0 1 3 1 00

Fig.A-8 Heat capacity of Mn at the temperature from 273K to 1800K

70

𝐶 𝑀𝑛𝑂 3 0 0103 0 000003 2 2 3 1 23

Fig.A-9 Heat capacity of MnO at the temperature from 273K to 1800K

𝐶 𝑂2 2 0 00025 1 00

300 5000

Fig.A-10 Heat capacity of O2 at the temperature from 300K to 1800K

71

𝐶 𝑃 {

5 5 2 3 31

30 31 11 0

11 0 1 00

Fig.A-11 Heat capacity of P at the temperature from 273K to 1800K

𝐶 𝑃 𝑂10 {15 2 0 10 2 2 3 31

3 31 1 00

Fig.A-12 Heat capacity of P2O5 at the temperature from 273K to 1800K

72

𝐶 𝑆𝑖 {5 0 000 1

101000

2 3 11

5 3 0 001 11 1 5

5 1 5 1 00

Fig.A-13 Heat capacity of Si at the temperature from 273K to 1800K

𝐶 𝑆𝑖𝑂2 12 0 0 00 302000

2 3 1 3

Fig.A-14 Heat capacity of SiO2 at the temperature from 273K to 1800K

Investigation of Electric Arc Furnace Chemical Reactions ...580469/FULLTEXT01.pdf · From “Perry’s Chemical Engineers’ Handbook” and “NIST-JANAF Thermochemical Tables”,

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