A Mathematical Model for Carbothermic Reduction

of Dust−−−−Carbon Composite Agglomerates

by

Yuki Kuwauchi

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Department of Materials Science and Engineering

Faculty of Applied Science and Engineering

University of Toronto

© Copyright by Yuki Kuwauchi, 2012

ii

A Mathematical Model for Carbothermic Reduction

of Dust−−−−Carbon Composite Agglomerates

Yuki Kuwauchi

Master of Applied Science

Materials Science and Engineering, University of Toronto

July 2012

Abstract

A mathematical model to simulate the reaction kinetics of dust–carbon composite

agglomerates in an RHF was developed. Major chemical, thermal and physical

phenomena taking place during RHF treatment of such agglomerates were formulated

and the corresponding equations were solved to yield the variations with time of solid

composition, temperature and gas composition of the agglomerates. The model was

validated against experimental results and used to predict the reduction behaviour of

dust pellets with bituminous coal and polyethylene plastic. The results demonstrate that

the pellet reduction is accelerated by the reducing gas from high–volatile reductants if

the gas is released after the pellet temperature is sufficiently high for reduction

reactions. The reduction of zinc oxide can also be represented using the proposed

model by implementing its small particle size caused by the inherent vaporization/re–

oxidization process that zinc comes through in a melter. Through the examination of

effect of various parameters on the reduction behaviour of composite agglomerates, it

was demonstrated that the proposed model can be used as an engineering tool to

determine the optimum operating conditions for the RHF process, including pellet

retention time, furnace temperature and pellet properties, to promote recycling a wide

range of waste materials.

iii

Acknowledgement

First and foremost, I would like to thank my supervisor, Professor Mansoor Barati,

who has supported and encouraged me through the fruitful discussion. Without his kind

support and assistance, I would not have been able to complete my project at this

academic standard.

I am also indebted to all of my colleagues in the Sustainable Materials Processing

Research Group, especially Ms. Shaghayegh Esfahani, Ms. Leili Tafaghodikhajavi and

Ms. Samira Sokhanvaran who helped me spend pleasant and informative time during

my project in many aspects from academic to daily life.

I wish to express my profound gratitude to my wife, Ms. Michiko Kuwauchi, for her

support. Her encouragement served as the driving force to move on the right path in

my life at all times.

iv

Table of Contents

Abstract ........................................................................................................................................... ii

Acknowledgement .......................................................................................................................... iii

Table of Contents ........................................................................................................................... iv

List of Tables .................................................................................................................................. vi

List of Figures ............................................................................................................................... vii

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

2 Literature Review ..................................................................................................................... 7

3 Modelling ............................................................................................................................... 10

3.1 Pellet Model .................................................................................................................... 10

3.2 Calculation Procedure..................................................................................................... 11

3.3 Physical and Thermal Properties .................................................................................... 13

3.3.1 Density ........................................................................................................................ 13

3.3.2 Porosity ....................................................................................................................... 14

3.3.3 Specific Heat ............................................................................................................... 15

3.3.4 Effective Thermal Conductivity ................................................................................. 18

3.4 Heat Transfer .................................................................................................................. 21

3.5 Reactions ........................................................................................................................ 22

3.5.1 Reaction Heat .............................................................................................................. 24

3.5.2 Reaction Rate – Volatilization Reactions ................................................................... 26

3.5.3 Reaction Rate – Reduction and Gasification Reactions ............................................. 27

3.5.4 Particle Size Distribution ............................................................................................ 28

3.5.5 Reaction Front Surface Area ....................................................................................... 32

3.5.6 BET Surface Area ....................................................................................................... 33

3.5.7 Surface Area Correction Factor (SACF) ..................................................................... 35

3.6 Gas Transfer ................................................................................................................... 36

3.6.1 Effective Diffusion Coefficient ................................................................................... 37

v

3.6.2 Mass Transfer Coefficient........................................................................................... 40

3.6.3 Modified Hagen–Poiseuille Equation ......................................................................... 40

4 Results and Discussion ........................................................................................................... 42

4.1 Experimental ................................................................................................................... 42

4.1.1 Sample Preparation ..................................................................................................... 42

4.1.2 Pellet Reduction .......................................................................................................... 46

4.2 Model Validation ............................................................................................................ 48

4.2.1 Calculation/Experimental Conditions ......................................................................... 48

4.2.2 Results and Discussion ............................................................................................... 50

4.3 Simulation 1: Use of High Volatile Coal as Reductants ................................................ 53

4.3.1 Calculation/Experimental Conditions ......................................................................... 53

4.3.2 Results and Discussion ............................................................................................... 55

4.4 Simulation 2: Use of Waste Plastic as Reductants ......................................................... 59

4.4.1 Calculation Conditions................................................................................................ 59

4.4.2 Results and Discussion ............................................................................................... 62

4.5 Simulation 3: Zinc Oxide Recovery ............................................................................... 69

4.5.1 Calculation/Experimental Conditions ......................................................................... 69

4.5.2 Results and Discussion ............................................................................................... 71

5 Conclusions and Future Work ................................................................................................ 74

5.1 Summary and Conclusions ............................................................................................. 74

5.2 Future Work .................................................................................................................... 75

6 Nomenclature ......................................................................................................................... 77

7 References .............................................................................................................................. 81

8 Appendix: Publications and Presentations ............................................................................. 87

8.1 Journal Articles ............................................................................................................... 87

8.2 Conference Proceedings ................................................................................................. 87

8.3 Other Presentations ......................................................................................................... 87

vi

List of Tables

Table 1. Typical composition of BF, BOF and EAF dust (wt%) [1–5] .......................................... 1

Table 2. Density of solid (kg·m–3

) [39] ......................................................................................... 13

Table 3. Density of gas (298.15K, 1atm) (kg·m

–3) [39] ................................................................ 13

Table 4. Values of parameters for Equation (2) (solid components) [40]..................................... 15

Table 5. Values of parameters for Equation (2) (solid components) [39]..................................... 16

Table 6. Values of parameters for Equation (2) (gas components) [39, 40] ................................. 17

Table 7. Values of the parameters for Equation (3) (solid components) [40–43] ......................... 19

Table 8. Values of the parameters for Equation (3) (zinc oxide) [44] .......................................... 19

Table 9. Values of the parameters for Equation (3) (gas components) [40, 45] ........................... 20

Table 10. Values of parameters for Equation (27) [39, 40, 52] .................................................... 24

Table 11. Values of parameters for Equation (27) [40] ................................................................ 25

Table 12. Kinetic parameters for volatilization reactions [33, 34]................................................ 26

Table 13. Kinetic parameters for reduction and carbon gasification [33, 53, 54] ......................... 28

Table 14. Apparent minimum diameter after self–agglomeration ................................................ 32

Table 15. BET surface of various types of coal ............................................................................ 34

Table 16. Standard diffusion coefficient Dkl0 (10–4

m2·s

–1) [45, 69–71] ....................................... 38

Table 17. Parameter mkl for calculating diffusion coefficient [45, 69–71] ................................... 38

Table 18. Values of parameters for Equation (55) [72] ................................................................ 41

Table 19. Coal types used in experiments ..................................................................................... 44

Table 20. Parameters for RR distribution function and mass median diameter of the pellet mix

used in the present experiments/simulations ................................................................ 45

Table 21. Parameters for RR distribution function and mass median diameter of zinc oxide used

in the present simulations ............................................................................................. 45

Table 22. Base properties of pellet and furnace ............................................................................ 49

Table 23. Conditions for calculation and experiment ................................................................... 54

Table 24. Calculation conditions ................................................................................................... 60

Table 25. Composition of PE and All–CO imaginary plastic (wt%) [24] .................................... 62

Table 26. Experimental/Calculation conditions ............................................................................ 70

vii

List of Figures

Figure 1. Estimated amount of dust generation in the world .......................................................... 2

Figure 2. Rotary Hearth Furnace (RHF) [5, 17] .............................................................................. 3

Figure 3. RHF process flow sheet ................................................................................................... 4

Figure 4. Schematic representation of the pellet model and the involved phenomena ................. 11

Figure 5. Calculation Procedure .................................................................................................... 12

Figure 6. Effective thermal conductivity of carbon–air system .................................................... 20

Figure 7. Relationship between ln(x) and ln[-ln(1-R(x)/100)] ...................................................... 31

Figure 8. Relationship between ln(x) and ln(R(x)/100) ................................................................ 31

Figure 9. Surface area variations with conversion ratio (Jeddo anthracite coal) [65] ................... 34

Figure 10. Reaction surface area ................................................................................................... 36

Figure 11. Effective diffusion coefficient of CO2 ......................................................................... 39

Figure 12. Particle distribution of the pellet mix used in the present experiments/simulations ... 44

Figure 13. Particle distribution of EAF dust/zinc oxide................................................................ 45

Figure 14. Dust–carbon composite specimen for experiment ....................................................... 46

Figure 15. Stainless steel basket .................................................................................................... 47

Figure 16. Experimental electric furnace ...................................................................................... 47

Figure 17. Calculated pellet temperature at three different positions in pellet (Run 1) ................ 51

Figure 18. Calculated pellet porosity (Run 1) ............................................................................... 51

Figure 19. Calculated effective thermal conductivity (Run 1) ...................................................... 52

Figure 20. Calculated and measured reduction ratio of iron oxides (Run 1) ............................... 52

Figure 21. Calculated and measured pellet compositions (Run 1) ................................................ 53

Figure 22. Calculated and measured reduction ratio against retention time (Runs 1–3) .............. 57

Figure 23. Calculated degree of release of CO from VM against mid–radius pellet temperature

(Runs 1–3) .................................................................................................................... 57

Figure 24. Calculated internal pressure at pellet surface against retention time (Runs 1–3) ........ 58

Figure 25. Calculated reduction ratio against retention time (Runs 1, 4, 5 and 6) ........................ 64

Figure 26. Calculated decomposition ratio of PE against mid–radius pellet temperature

temperature (Run 4–6) ................................................................................................. 65

Figure 27. Calculated pellet porosity against retention time (Runs 1, 4, 5 and 6) ........................ 65

viii

Figure 28. Calculated effective thermal conductivity against retention time (Run 1, 4, 5 and 6) 66

Figure 29. Calculated internal pressure at pellet surface against retention time (Runs 1, 4, 5 and

6)................................................................................................................................... 66

Figure 30. Relationship between maximum internal pressure and PE content in pellet (Run 1, 4, 5

and 6) ............................................................................................................................ 67

Figure 31. Calculated reduction ratio against retention time (Run 1, 4 and 7) ............................. 67

Figure 32. Calculated decomposition ratio of PE against mid–radius pellet temperature (Run 4

and 7) ............................................................................................................................ 68

Figure 33. Calculated internal pressure at pellet surface against reduction time (Run 1, 4 and 7)

...................................................................................................................................... 68

Figure 34. Particle distributions of zinc oxide used for Runs 1, 8 and 9 ...................................... 71

Figure 35. Calculated reduction ratio of iron oxides against retention time (Runs 1, 8 and 9) .... 72

Figure 36. Calculated and measured zinc oxide concentration trend against retention time (Runs

1, 8 and 9) ..................................................................................................................... 73

Figure 37. Relationship between specific surface area and mass median diameter (Runs 1, 8 and

9)................................................................................................................................... 73

1

1 Introduction

Recycling iron–bearing dust from steel works has gained a significant attention from

the steel industry in the past two decades as a method for sustainable steel production.

Dust recycling is expected to be a solution for the mounting pressure on the steel

industry to decrease its environmental impact while reducing raw material

consumption. Dust is an iron oxide–bearing by–product emitted from steelmaking

facilities, such as blast furnaces (BF), basic oxygen furnaces (BOF) and electric arc

furnaces (EAF). The typical composition of dust is shown in Table 1 [1–5].

Considering that 10 to 25 kg of dust is generated for one ton of steel production [6, 7],

it can be estimated from the data published in the references [8, 9] that nearly 25

million tons of dust is estimated to be produced around the world in 2011 (Figure 1).

This dust contains approximately 7.0 million tons of iron and 1.9 million tons of zinc;

hence, it is a promising secondary source for valuable metals. To recover these metals,

a reduction process is used because most of the elements in the dust are in the form of

oxides [10, 11].

Table 1. Typical composition of BF, BOF and EAF dust (wt%) [1–5]

BF dust BOF dust

Sample 1 Sample 2 Sample 1 Sample 2

Total Fe 40.8 31.8 55.4 53.6

Total Zn 0.05 1.2 1.4 2.5

C 20.6 37.6 0.0 0.7

CaO 7.4 3.1 10.6 5.0

SiO2 6.1 4.1 2.3 0.8

EAF dust

Sample 1 Sample 2 Sample 3 Sample 4

Total Fe 17.2 29.8 24.9 49.1

Total Zn 32.2 27.1 23.3 3.5

C 1.7 1.1 – 2.9

CaO 5.2 0.9 4.8 8.4

SiO2 4.0 2.0 1.9 0.9

2

Figure 1. Estimated amount of dust generation in the world

A Rotary Hearth Furnace (RHF) is one of the coal–based reduction processes for dust

recycling (Figure 2) [5, 11–17]. An RHF is a doughnut–shape furnace where its hearth

rotates around at the bottom. The centre–to–centre hearth diameters of the existing

RHFs range from 8 m to 60 m. The typical RHF process flow sheet for dust recycling

is illustrated in Figure 3. Before processing, dust and carbonaceous reductant are

prepared in yards, hoppers or bins. After blending the dust and the reductant, this

mixture is ground into fine particles with desired size distribution. The next step is

agglomeration; the pulverized pellet mix is compacted into a composite agglomerate,

such as a pellet or briquette with the addition of water and organic/inorganic

compounds as binders. The pellet or briquette is then continuously fed onto the rotating

hearth of the furnace and reduced into the final product, direct reduced iron (DRI),

provided with high furnace temperature (1250–1350 °C) and strong reducing

atmosphere. The percent reduction of the DRI can reach up to 90% in 10–15 minutes.

This highly–reduced DRI can be utilized as a feed material for steel production

facilities, including BOFs and EAFs, which decreases the use of scrap in EAFs and the

consumptions of iron ore and coking coal in BF–BOF processes. As will be explained

0

5

10

15

20

25

1981 1991 2001 2011

Es

tim

ate

d D

us

t G

en

era

tio

n (

Mt)

Year

Total

BF & BOF dust

EAF dust

3

later, the process can also recover the zinc contained in the dust. Therefore, the RHF

process decreases the overall consumption of raw materials for both steelmaking and

zinc manufacturing by recovering value of secondary iron and zinc from dust.

Figure 2. Rotary Hearth Furnace (RHF) [5, 17]

4

Figure 3. RHF process flow sheet

The utilisation of low–grade carbonaceous reductants in the RHF process has gained

steelmakers’ attention to further enhance waste recycling, taking into account the

depletion of high–rank coal reserves and the escalation of natural resource prices [18–

24]. High–volatile matter (VM) bituminous and lignite coals can be listed as examples

for the low–rank coals, which have not been fully utilized in steelmaking. Another

prospective reductant is waste plastic because substantial part of the plastic garbage is

currently disposed of without recovering any material or energy from it. The waste

plastic includes polyethylene (PE), polystyrene (PS) and polyethylene terephthalate

(PET) [25, 26]. The utilization of these low–grade carbonaceous reductants would

enable the RHF process to produce metallic iron only from secondary source materials

and enhance the sustainability of steel and chemical industries. Also, several

experimental studies suggested the possibility that the plastic addition to iron oxide

pellet can accelerate the reduction reactions under certain conditions [18, 20, 24]. On

the other hand, the application of the low–grade carbonaceous material as the reductant

for dust has been proved to be a demanding task due to its high volatile content [18, 19,

mixing andgrinding

pelletizing orbriquetting

DRI(direct reduced iron)

RHFdust

dust

reductantaddition

coal

iron ore

coking coal

coking

sintering

BF

scrap

BOF

EAFzinc oxide

5

24–28]. The weight percentage of the volatile matter in bituminous coal, lignite coal

and waste PE can reach up to 30%, 40% and 100%, respectively [18, 29–31]. Hence,

the significant volume of gas is released inside the pellet at relatively low temperature.

The evolved gas may react with iron oxides and play a certain role in the overall

reduction reactions; however, the correlation between the rapid release of volatiles and

its contribution to the reactions is not fully investigated. In addition, the rapid evolution

of gas increases the internal pressure that may lead to the decrepitation of the pellet,

which should be avoided to keep high lump ratio of the product DRI. Therefore, it is of

critical importance to predict the reaction kinetics and the internal gas transfer as well

as the interaction between them to utilize the low–grade carbonaceous material as a

reductant while avoiding the mechanical collapse of pellet.

Another application of the RHF is the utilization of EAF dust as a feed material [5, 17].

EAF dust involves considerable amount of zinc originating from feed scrap as well as

iron. This zinc can be recovered in the RHF process. In the furnace, zinc oxide

contained in dust pellet is reduced into metallic zinc. Then, the zinc metal is

immediately transferred to the gas phase due to its high vapor pressure and re–oxidized

into zinc oxide fume in the furnace atmosphere. After liberated from the pellet, the zinc

oxide fine particles are entrained in the flue gas and collected in a bag house. However,

iron contamination of the collected crude zinc oxide may cause operational issue at the

zinc smelter where the RHF–recovered zinc oxide is refined to metallic zinc. In

addition, the residual zinc in DRI requires additional heat to remove in the steelmaking

facility where the DRI is used. The contaminated DRI may also provoke zinc build–up

on the furnace wall especially if the DRI is fed into BF. Therefore, the detailed kinetic

control over the simultaneous reduction reactions of iron and zinc oxides in pellet is

necessary to recover both of the two metals from EAF dust using the RHF process.

Various applications are considered for the RHF dust recycling process: the utilization

of low–rank coal and waste plastic as reductants and the recovery of zinc from EAF

dust. Since the kinetic interaction between these materials and dust is not well

investigated and the dust pellet itself behaves as a micro reactor where the reducing gas

6

is generated in–situ, it is of critical importance to predict the kinetic and mechanical

behaviour of the pellet to enhance recovering valuable materials from expanded range

of waste materials using the RHF process. Therefore, the present study was undertaken

aiming at creating a mathematical model that describes the reaction behaviour of a

dust–carbon composite agglomerate in an RHF taking into consideration the internal

volatile release and gas transfer as well as the reduction of iron and zinc oxides and

other relevant reactions to promote further recycling using RHFs.

7

2 Literature Review

Several researchers have established models for the reduction of iron ore–carbon or

dust–carbon composite agglomerates and zinc oxide pellets. Ueda et al. [32] developed

a model that describes the reduction of an iron ore–carbon composite in a BF. Their

model was validated against experimental results and predicts the reaction behaviour of

the composite pellet. The outcome of their model has some interesting suggestions for

acceleration of the pellet reduction. They estimated that the gasification of carbon was

the rate controlling step of the overall reduction reaction and found that the reaction

rate is significantly improved by using well–ground coke particles or carbon with low

activation energy. Their simulation, however, is based on the premise that the reduction

reactions take place in a blast furnace, where the governing mechanism is different

from an RHF due to the lower furnace temperature. Thus, their model cannot be

applied directly to the dust recycling using an RHF process. Sun et al. [5, 33–36]

proposed a model for the reduction reaction of iron ore–carbon composite pellets in an

RHF. Considering the high furnace temperature in the RHF, they presumed that heat

transfer plays a governing role in the overall process. Hence, temperature gradients

within the pellet were taken into account in their model. Their model was validated

against experimentally measured reduction degree for various reaction periods. The

model, however, does not include the reactions of hematite (Fe2O3). Hematite is often

contained in dust as well as magnetite (Fe3O4) and wustite (FeO); hence, the hematite–

related reactions should be included in a more comprehensive model. Also, the

parameters for the carbon gasification reactions in the simulation were determined by

fitting the model outputs with the experimental results. Thus, their model may not be

able to provide appropriate predictions when different kinds of reductants are used

because the kinetic parameters for gasification strongly depend on the type of

carbonaceous reductant.

The use of plastic for dust reduction has also been studied through experiments, and it

has been clarified that blending plastic with dust can accelerate the reduction reactions

under certain conditions. Ueki et al. [24] reduced hematite reagent pellets with

polyethylene (PE) and refuse derived fuel (RDF) at 1200 °C. The obtained degree of

8

reduction of the samples with PE and RDF were 63% and 100%, respectively.

Although their experiment confirmed that hematite pellets can be reduced only by PE

without any coal or carbon addition, the reduction ratio of the samples with PE was

much lower compared with that of the RDF–mixed pellets. The weak performance of

PE was attributed to the smaller amounts of solid char generated by decomposition of

PE, whereas RDF contains as much as 15 wt% fixed carbon as well as volatile

reducing gases. Their analysis concluded that plastic containing larger amount of fixed

carbon is more suitable as a reducing agent for iron oxides.

Zhang et al. [20] carried out an experimental study of the reduction of iron oxide–based

mill scale at 1100 °C. After mixing the mill scale and coke powder, they added 1 to 4

wt% of two types of plastic: polycarbonate (PC) and PET. Their results indicated that

the reduction rate was increased by the plastic addition and they discussed that the

acceleration was caused by the enhanced gas transfer due to the tiny pores produced by

the volatilisation of plastic. However, the decrease of reduction ratio was also observed

when 4 wt% PET was added to the sample. In addition, the relatively low ambient

temperature, 1100 °C, seemed to help the plastic behave as an effective reductant in the

mill scale pellet at moderate temperature. The volatile gas contained in the PC and PET

was slowly liberated so that the gas stayed in the pellet for a time long enough for the

reduction of iron oxides. This low temperature reduction, however, cannot be realized

in the RHF as it decreases the productivity of DRI.

Murakami et al. [18, 19] performed the reduction experiment of the pellet made of iron

ore and PE at 1150 °C, and found that the contribution of PE to the reduction is limited

due to the rapid escape of PE–origin gas. Then, they suggested a double–layer pellet,

where the PE concentration is higher in the inner part, to enable the volatile generated

from PE to react with iron oxides in the outer layer. However, it is practically

demanding to produce such complex pellets in commercial scale. Additionally, they

used very fine hematite ore particles (average diameter: 2.6 µm), which is considerably

more reactive than typical larger ground ore/dust particles that also contain wustite and

9

magnetite. Therefore, the plastic–blended dust pellet would demonstrate a different

kinetic behaviour from their results.

Many studies have been performed with respect to the zinc recovery from EAF dust. A

series of research work were carried out by Itoh et al. [37, 38] that included kinetic

analysis of zinc oxide (ZnO) reduction and zinc ferrite (ZnFe2O4) decomposition as

well as the establishment of a simulation model for the simultaneous reductions of

Fe2O3 and ZnO. Their analysis took into account the reductions of zinc oxide and

hematite at the same time; however, they assumed the whole pellet is isothermal. Also,

their model is based on CO–CO2 gas reduction and the carbon gasification inside the

pellet was not taken into account. Thus, their model cannot be applied to an RHF

process, where temperature gradient and gas generation inside the pellet plays a

substantial role in the reduction kinetics.

10

3 Modelling

3.1 Pellet Model

Several simplifying assumptions are made to express the behaviour of a pellet in the

proposed mathematical model. The composite pellet is considered to be a perfect

sphere and the pellet volume and diameter remain constant throughout the reaction.

Then, the pellet is divided into N imaginary concentric layers and a polar coordinate

system is applied. The outermost layer next to the surface is identified by index I=1

and the centre as I=N. Each layer consists of solid and gas phases, with identical

temperatures. When a pellet is placed in an RHF, the outermost layer is heated by

radiation from the hot furnace atmosphere. Then, the temperature of internal layers

gradually increases by heat conduction through the pellet. When a layer reaches

sufficiently high temperature, corresponding reactions are initiated locally in each

layer. At relatively lower temperature, volatile matter in coal or other carbonaceous

reductants starts to be released into the porous space of the pellet. The reducing agents

in the released volatiles initiate the reduction of oxides and the gasification of carbon.

The gas species produced by these reactions are transferred through the pores of pellet,

reacted with other solids in the adjacent layers, and finally exhausted into the furnace

atmosphere. As the reduction reactions proceed, the porosity of pellet increases by the

removal of oxygen from iron oxides and the gasification of carbon, which results in the

decline of the heat conduction rate due to the small thermal conductivity of gas.

11

Figure 4. Schematic representation of the pellet model and the involved phenomena

3.2 Calculation Procedure

Typical calculation procedure in the proposed model is shown in Figure 5. Before

starting the simulation, initial conditions should be set, including retention time and

time step for iteration; pellet composition, weight and diameter; particle size

distribution of each component in pellet; coal type and its reaction front area; and

furnace atmosphere and temperature. The simulation proceeds by performing

calculations in predetermined time steps. First, all physical and chemical temperature–

dependent parameters are determined with the temperature at each layer of the pellet.

Second, the pellet temperature is revised by calculating heat transfer. Then, after

reaction rates are calculated, the solid and gas components of the pellet are updated

with the amounts generated or consumed by the reactions. Consequent temperature

change is derived considering the enthalpy of the reactions. These calculations should

be performed N times from the surface layer to the centre in each iteration. The final

step is gas transfer, which consists of concentration–triggered diffusive flow and

pressure–driven laminar flow. Before calculating flow rates, diffusion coefficients

should be determined as a function of temperature, porosity and composition of gas

Spherical Pellet

Heat radiation

Furnace atmosphere

Exhaust gas

Gas transfer

Heat conduction

Pellet

Rotating hearth

Radiation

RHF

Release of vola tiles

Reaction

Tlayer1

Tlayer2

Tcentre (K)

Furnace temperature, Tfurnace

Imaginary layers

12

phase. The total flow rate is derived from the combined effects of the diffusion and the

laminar flow. At the end of the iteration, the time is incremented by the predetermined

time step. If the retention time is reached, the simulation is terminated. Otherwise, the

simulation proceeds to the next iteration step.

Figure 5. Calculation Procedure

Gas Transfer

- Calculate diffusion coefficients

- Calculate diffusive gas flow

- Determine pressure–triggered gas flow

- Recalculate gas components in each pore

Initialization

- Set simulation conditions

Parameters Setting

- Calculate temperature-dependent

physical and chemical properties

Heat Transfer

- Calculate radiation heat from the furnace

- Calculate heat conduction rate at each layer

- Calculate temperature at each layer

Reaction

- Calculate reaction rates and reaction heats

- Determine solid components of each layer

- Determine gaseous components at each layer

- Recalculate temperature at each layer

considering heat of reaction

Retention time is reached?

- No → Increment time step and continue

- Yes → Finish the calculation

13

3.3 Physical and Thermal Properties

3.3.1 Density

Density of solid constituents remains constant assuming that the influence of

temperature and pressure is negligible. The temperature and pressure dependence of

gas density, however, is taken into account. The values of density of solids and gases

are shown in Tables 2 and 3 (at the standard state for gases).

Table 2. Density of solid (kg·m–3

) [39]

Component Density ρ

(kg·m–3

)

Fe2O3 5242

Fe3O4 5170

FeO 5700

Fe 7874

C 2267

ZnO 5606

CaO 3340

SiO2 2600

MgO 3580

Al2O3 3965

Table 3. Density of gas (298.15K, 1atm) (kg·m

–3) [39]

Component Density ρ

(kg·m–3

)

O2 1.43

N2 1.25

CO 1.23

CO2 1.93

H2 0.09

H2O 0.80

CH4 0.72

C3H8 1.97

C6H6 3.49

14

3.3.2 Porosity

Porosity of pellet is defined as the gas fraction in the pellet, i.e. the fractional volume

which is not occupied with solid components. The volume of each solid component is

calculated by dividing the weight by its density. The porosity, φ, is obtained from

Equation (1). It is worth noting that volatile components in the pellet are not considered

to be solid in the porosity calculation; i.e., the volume of the solid–state volatile matter

is neglected. Once the volatile is released, it occupies large volume as a gas; then, it is

considered as a component of the gas phase.

∑

−=

j j

jC

V

W

ρϕ 1

(1)

15

3.3.3 Specific Heat

The temperature dependence of specific heat is computed by Equation (2) [39, 40]. The

values of parameters, A1 through A5, are listed in Tables 4–6. In Equation (2), M

indicates the molecular weight, which is multiplied to modify the weight basis Cp for

converting the unit from J·mol–1

·°C–1

to J·kg–1

·°C–1

.

MT

ATATATAACp

×+×+×+×+= −−−

2

6

539

4

26

3

3

21

10101010

(2)

Table 4. Values of parameters for Equation (2) (solid components) [40]

Component Temperature

(K)

A1 A2 A3 A4 A5

Fe2O3 T ≤ 960 100.88 75.17 0 0 –1.73

960 < T ≤ 1000 3525.5 –6353.0 2978.29 0 0

1000 < T ≤ 1100 1930.4 –3307.81 1528.20 0 0

T > 1100 132.75 7.30 0 0 0

Fe3O4 T ≤ 850 –72.61 1289.43 –2250.2 1463.48 0

T > 850 609.74 –797.92 494.71 –97.61 0

FeO – 48.79 8.37 0 0 0.28

Fe T ≤ 800 14.38 49.01 –57.47 41.24 0

800 < T ≤ 1000 213.76 –460.60 301.14 0 0

1000 < T ≤ 1040 8.76×103 –1.75×10

4 8.77×10

3 0 0

1040 < T ≤ 1042 –6415.8 6237.5 0 0 0

1042 < T ≤ 1060 1.24×105 –2.34×10

5 1.11×10

5 0 0

1060 < T ≤ 1184 542.91 –816.00 331.48 0 0

T > 1184 24.04 8.30 0.022 0 0

C T ≤ 800 –5.09 55.53 –34.74 5.33 0

T > 800 4.13 31.07 –16.90 3.27 0

16

Table 5. Values of parameters for Equation (2) (solid components) [39]

Component Temperature

(K)

A1 A2 A3 A4 A5

ZnO T ≤ 2250 47.58 3.90 1.28 0 –0.75

T > 2250 5.45 0 0 0 0

CaO T ≤ 298 17.35 122.76 –117.09 0 –0.14

298 < T ≤ 1400 57.75 –10.78 5.33 0 –1.15

1400 < T ≤ 2900 20.39 22.26 –3.12 0 13.84

2900 < T ≤ 3172 –41.56 54.65 –7.86 0 80.32

T > 3172 84.00 0 0 0 0

SiO2 T ≤ 847 58.08 –0.033 28.22 0 –1.43

847 < T ≤ 1079 58.87 10.07 0 0 0.012

1079 < T ≤ 1996 72.74 1.33 –0.013 0 –4.13

T > 1996 85.77 0 0 0 0

MgO T ≤ 1700 47.49 4.65 –0.27 0 –1.03

1700 < T ≤ 3100 78.30 –19.43 5.16 0 –17.10

T > 3100 84.00 0 0 0 0

Al2O3 T ≤ 800 9.78 294.73 –198.17 0 –0.25

800 < T ≤ 2327 115.98 15.65 –2.36 0 –4.43

T > 2327 192.46 0 0 0 0

17

Table 6. Values of parameters for Equation (2) (gas components) [39, 40]

Component Temperature

(K)

A1 A2 A3 A4 A5

O2 T ≤ 1100 49.18 45.83 –18.30 0 –0.75

T > 1100 81.94 0.42 –0.042 0 –6.64

N2 T ≤ 350 29.30 –1.57 3.42 0 –0.001

350 < T ≤ 700 27.75 0.61 4.96 0 0.073

700 < T ≤ 1500 23.53 12.12 –3.08 0 0.12

T > 1500 35.37 1.04 –0.11 0 –4.15

CO T ≤ 800 25.89 6.42 1.11 0 0.11

T > 800 24.72 11.28 –2.84 0 0

CO2 – 22.08 61.42 –37.40 8.35 0

H2 T ≤ 700 32.34 –8.20 6.40 0 –0.15

T > 700 31.30 –7.78 8.81 –2.11 0

H2O – 32.17 1.55 11.29 –3.77 0

CH4 T ≤ 298 33.97 –15.57 70.19 0 0

T ≤ 1000 2.23 96.94 –26.04 0 0.61

T ≤ 2000 47.08 42.36 –7.11 0 –8.60

T > 2000 101.11 5.38 0.14 0 –44.78

C3H8 T ≤ 298 27.84 122.68 101.14 0 0

T > 298 29.93 203.43 –57.58 0 –1.09

C6H6 T ≤ 298 33.46 –49.10 722.54 0 0

T ≤ 1500 55.40 229.65 –70.14 0 –3.19

T > 1500 118.27 116.31 –22.48 0 –6.72

18

3.3.4 Effective Thermal Conductivity

The temperature dependence of the thermal conductivity of each solid or gas element is

calculated by Equation (3) with parameters A1 through A9 which are tabulated in

Tables 7–9 [40–45]. The thermal conductivities of the solid phase and gas phase of

pellet are derived from Equations (4) and (5), respectively [41, 46, 47]. It should be

noted that neither λsolid nor λgas follow a linear dependence on the thermal conductions

of the phase’s constituents. The overall effective thermal conductivity of the pellet is

determined by Equation (6) as a function of the conductivities of the two phases and

the porosity, which consists of three different formulas depending on the value of

porosity [48]. The parameters, α and β, used in the equation are obtained by Equations

(7). Typical examples of the porosity dependence of thermal conductivity are shown in

Figure 6. The conductivity drops quickly at relatively low porosity and continues to

decrease with increasing porosity.

( ) ( )( )TATAA

AT

ATATATAA

loglog

9

5

63

4

2

3218

2710

+⋅++

++++=λ

(3)

∏=j

V

jsolidjλλ

(4)

∑

∑=

k

kk

k

kkk

gasMWP

MWP

31

31

λλ

(5)

( )

( ) ( )( ) ( )( )

( )

( )( )

( )

<−−−+

×

≤<−−

−+−−+−+×

≤−

+×

=

ϕϕϕ

ϕϕ

ϕϕϕ

ϕϕϕ

9011

121

901011

105011.02121

101

21

gas

54323

gas

solid

.β

βλ

..β

e.βββλ

.α

αλ

λβ.

eff

(6)

gassolid

gassolid

solidgas

solidgas

2,

2 λλ

λλ β

λλ

λλ

+

−=

+

−=α

(7)

19

Table 7. Values of the parameters for Equation (3) (solid components) [40–43]

Component Temperature

(K)

A1 A2 A3 A5 A6

Fe2O3 T ≤ 912 0 0 0 0 5.42×103

T > 912 0 0 0 1.11×103 1.20×10

4

Fe3O4 T ≤ 906 0 0 0 0 5.91×103

T > 906 0 0 0 5.08×104 3.37×10

5

FeO T ≤ 825 0 0 0 4.87×102 4.28×10

3

T > 825 0 0 0 –3.75×103 –9.55×10

3

Fe T ≤ 800 62.6 –3.20×10–2

0 0 0

800 < T ≤ 1043 86.4 –6.17×10–2

0 0 0

T > 1043 13.2 8.40×10–3

0 0 0

C – 4.05 2.55×10–3

–1.58×10–6

0 –5.54×102

CaO T ≤ 1173 –0.256 3.47×10–3

–1.38×10–6

0 2.17×102

T > 1173 1.97 1.07×10–4

0 0 0

SiO2 T ≤ 818 2.24 0 0 0 –3.01×102

T > 818 8.95 0 0 0 –5.79×103

MgO T ≤ 1303 –4.88 0 0 0 1.56×104

T > 1303 0 0 0 –1.25×102 7.88×10

3

Al2O3 T ≤ 667 –8.44 0 0 0 1.46×104

T > 667 –1.90 0 0 0 1.02×104

Table 8. Values of the parameters for Equation (3) (zinc oxide) [44]

Component Temperature

(K)

A7 A8 A9

ZnO – –1.05 4.50 4.81×10–4

20

Table 9. Values of the parameters for Equation (3) (gas components) [40, 45]

Component Temperature

(K)

A1 A2 A3 A4 A6

O2 – 1.99×10–2

5.69×10–5

–2.25×10–9

0 –3.05

N2 – 3.55×10–2

2.60×10–5

6.33×10–9

0 –5.43

CO – 1.73×10–2

5.05×10–5

0 0 –2.01

CO2 – –8.58×10–3

9.08×10–5

–1.51×10–8

0 0

H2 – 0.138 2.79×10–4

2.21×10–8

0 –13.0

H2O – –6.12×10–2

1.44×10–4

5.76×10–9

0 10.8

CH4 – –1.72×10–2

1.38×10–4

4.62×10–8

0 1.74

C3H8 – 1.86×10–3

–4.70×10–6

2.18×10–7

–8.41×10–11

0

C6H6 – –8.46×10–3

3.62×10–5

9.80×10–8

–4.06×10–11

0

Figure 6. Effective thermal conductivity of carbon–air system

0.0

0.5

1.0

1.5

2.0

0.1 0.3 0.5 0.7 0.9

Th

erm

al c

on

du

cti

vit

y (

Wm

-1K

-1)

Porosity

25°C

200°C

400°C

Carbon-air system

21

3.4 Heat Transfer

The major heat transfer mechanism within the pellet is conduction while the external

surface is subjected to radiation from the gas phase. Equations (8) – (10) show the heat

conduction equation in a polar coordinate system and two boundary conditions

introduced to the system. Equation (9) describes the radiation heat conveyed from the

furnace onto the pellet surface. Equation (10) corresponds to the energy conservation at

the pellet centre where no heat is exchanged. There may exist substantial temperature

gradient in a dust pellet during reduction in an RHF due to the rapid heating scheme

and the small thermal conductivity of the pellet. In fact, several researchers have

reported that heat transfer is likely to be a rate limiting step in the reduction of iron

oxide–carbon composite at high temperature [33, 49–51]. This temperature gradient is

expressed by Equation (8) using proper effective thermal conductivity depending on

the pellet composition and temperature. ∆Q in Equation (8) is the total heat of

reactions, which is the summation of all endothermic and exothermic heats of the

reactions taking place in the pellet. The calculation of ∆Q is discussed later in Section

3.5.1. ε in Equation (9) is the emissivity at the pellet surface, which may depend on the

composition of pellet (i.e. the colour of pellet surface). However, ε is presumed to be

constant in this model taking into account Sun et al.’s analysis that changing the value

of emissivity does not have significant impact on the overall heat transfer and reactions

of their pellet model due to much slower internal heat conduction [33]. In the present

model, ε=0.85 is used according to their analysis.

Qr

Tr

rrt

TC effp ∆−

∂∂

∂∂

=∂∂

λρ 2

2

1

(8)

( )4

surface

4

furnace

surface

TTr

T

r

eff −=∂∂

=

εσλ

(9)

0centre

=∂∂

=rr

T

(10)

22

3.5 Reactions

The major reactions taking place in a dust–carbon composite pellet are the

volatilization of gaseous compounds contained in coal or other carbonaceous

reductants, the reduction of iron oxides and zinc oxide, and the gasification of carbon.

The chemical formulas representing these reactions are shown in Reactions (11) – (26).

It should be noted that wustite is described as “FetO” in these equations, where

t=0.947. At the initial stage of the RHF reduction, the reactions (16) – (24) are initiated

by CO and H2 gases released from the volatile contents by Reactions (11) and (13).

The carbon gasification reactions (25) and (26) may also take place by CO2 and H2O

from Reactions (12) and (14). Then, the reduction reactions proceed while the reducing

gases are supplied by the volatiles as well as Boudouard reaction (25) and carbon–

steam reaction (26). Since these carbon gasification reactions are strongly endothermic,

sufficient heat must be continuously supplied to the pellet from the furnace

atmosphere. While the required heat is supplied, these reduction reactions keep

proceeding with the reductant gases, CO and H2, provided by the endothermic volatile

evaporation and carbon gasification reactions. Then, the CO2 and H2O generated by the

reduction reactions are recycled to continue to gasify carbon and generate CO and H2.

This cycle is the major driving force for the reduction of dust–carbon composite pellet.

In addition to the reactions listed above, the reduction by solid carbon might occur in a

real pellet. However, it is difficult to estimate the extent of this reaction and the share

of the solid state reduction is minimal considering much larger contact area between

gas–solid and faster diffusion. Therefore, no solid–solid reaction is taken into account

in the present model. Gas–gas interactions are also neglected for the sake of model

simplicity. The metallic zinc produced by Reaction (24) is evaporated immediately into

gas due to its high vapor pressure. However, the vapor zinc metal is quickly re–

oxidized in the environment and removed from the pellet system. Therefore, the

interactive reactions between gas–phase metallic zinc and other components are also

neglected.

23

CO in coal or reductant � CO (11)

CO2 in coal or reductant � CO2 (12)

H2 in coal or reductant � H2 (13)

H2O in coal or reductant � H2O (14)

CmHn in coal or reductant � CmHn (15)

3Fe2O3 + CO � 2Fe3O4 + CO2 (16)

3Fe2O3 + H2 � 2Fe3O4 + H2O (17)

1.202Fe3O4 + CO � 3.807FetO + CO2 (18)

1.202Fe3O4 + H2 � 3.807FetO + H2O (19)

0.25Fe3O4 + CO � 0.75Fe + CO2 (20)

0.25Fe3O4 + H2 � 0.75Fe + H2O (21)

FetO + CO � 0.947Fe + CO2 (22)

FetO + H2 � 0.947Fe + H2O (23)

ZnO + CO � Zn(g) + CO2 (24)

C + CO2 � 2CO (25)

C + H2O � CO + H2 (26)

24

3.5.1 Reaction Heat

The reaction heat can be calculated with Equation (27), where the values of A1 through

A5 used in the equation are shown in Tables 10 and 11. The total heat generated or

absorbed is the summation of all these reaction heats considering the amount reacted.

The pellet temperature is updated according to the net heat generated/consumed by all

relevant reactions.

T

ATATATAAH

3

539

4

26

3

3

21

10101010

×+×+×+×+=∆ −−−

(27)

Table 10. Values of parameters for Equation (27) [39, 40, 52]

Reaction Temperature

(K)

A1 A2 A3 A4

C + CO2 = 2CO T ≤ 900 165.39 37.05 –50.73 19.02

T > 900 175.56 1.13 –7.63 1.51

C + H2O = CO + H2 T ≤ 900 124.57 29.83 –27.13 8.61

T > 900 128.29 16.31 –10.54 1.78

ZnO + CO = Zn(g) + CO2 – 201.66 –13.72 3.95 –1.48

Loosely bound CO in volatile = CO – 22.72 0 0 0

Tightly bound CO in volatile = CO – 22.72 0 0 0

CO2 in volatile = CO2 – 35.69 0 0 0

H2 in volatile = H2 – 1.64 0 0 0

H2O in volatile = H2O – 14.61 0 0 0

CH4 in volatile = CH4 – 13.01 0 0 0

C3H8 in volatile = C3H8 – 35.76 0 0 0

C6H6 in volatile = C6H6 – 63.35 0 0 0

25

Table 11. Values of parameters for Equation (27) [40]

Reaction Temperature

(K)

A1 A2 A3 A4 A5

3Fe2O3 + CO T ≤ 600 –47.17 0 0 7.25 0

= 2Fe3O4 + CO2 600 < T ≤ 850 –213.54 793.08 –1265.5 683.49 0

850 < T ≤ 970 –202.97 408.89 –247.10 0 0

970 < T ≤ 1050 0 243.20 –584.77 301.85 0

1050 < T ≤ 1300 –104.75 116.97 –52.62 0 0

T > 1300 –21.22 0 –21.99 7.68 0

3 Fe2O3 + H2 T ≤ 600 –5.47 0 –4.82 2.11 0

= 2Fe3O4 + H2O 600 < T ≤ 850 –165.01 767.91 –1244.6 673.84 0

850 < T ≤ 975 436.00 –265.30 0 0 –176.91

975 < T ≤ 1045 0 299.54 –586.12 281.63 0

1045 < T ≤ 1300 144.47 –72.87 0 0 –77.32

T > 1300 18.43 0 –29.13 9.62 0

1.202Fe3O4 + CO T ≤ 850 53.43 –46.41 127.21 –127.94 0

= 3.807FetO + CO2 T > 850 165.11 –324.13 236.20 –54.00 0

1.202Fe3O4 + H2 T ≤ 850 94.17 –38.05 101.31 –116.08 0

= 3.807FetO + H2O T > 850 212.02 –338.36 238.31 –54.06 0

0.25Fe3O4 + CO T ≤ 850 2.80 –30.01 39.51 –26.61 0

= 0.75Fe + CO2 850 < T ≤ 900 26.02 –87.77 62.18 –11.23 0

900 < T ≤ 1045 34.34 –76.05 6.48 24.80 0

1045 < T ≤ 1184 34.34 –168.37 191.00 –67.23 0

T > 1184 26.53 –72.69 49.95 –11.23 0

0.25Fe3O4 + H2 T ≤ 850 43.59 –22.71 15.71 –16.05 0

= 0.75Fe + H2O 850 < T ≤ 900 68.12 –85.17 44.20 –3.15 0

900 < T ≤ 1045 44.10 23.90 –108.16 64.45 0

1045 < T ≤ 1184 44.10 –83.07 104.40 –40.98 0

T > 1184 72.97 –86.19 51.27 –11.24 0

FetO + CO T ≤ 900 –10.51 –25.71 16.49 0 0

= 0.947Fe + CO2 900 < T ≤ 1045 0 –10.91 –53.86 45.50 0

1045 < T ≤ 1184 0 –127.50 179.18 –70.72 0

T > 1184 –9.87 –6.67 1.04 0 0

FetO + H2 T ≤ 900 30.34 –18.69 –6.77 10.22 0

= 0.947Fe + H2O 900 < T ≤ 1045 0 119.07 –199.19 95.60 0

1045 < T ≤ 1184 0 –16.04 69.25 –37.55 0

T > 1184 36.47 –19.97 2.71 0 0

26

3.5.2 Reaction Rate – Volatilization Reactions

The gas release from volatile matter is presumed to be a self–degradation reaction.

Hence, the rate of volatilization reaction is considered to be proportional to the

remaining amount of each volatile component shown in Equation (28). The rate

constant can be derived from Equation (29) as its temperature dependence is assumed

to follow the Arrhenius equation. The parameters in Equation (29) solely depend on the

gas species; the source material of volatile (i.e. coal, plastic or other carbonaceous

waste) does not affect the gas behaviour. The frequency factors and activation energies

required for these volatilization reactions are summarized in Table 12. The parameters

for the release of CO are taken from Sun et al.’s data [33]. They classified CO in

volatile into “loosely bound CO” and “tightly bound CO” without providing details in

the standard of classification. Thus, in the present model, the first half of the volatile

CO is presumed to be loosely bound CO and the remaining to be tightly bound CO.

VMi

VMiVV

M

Wkn =

(28)

−=RT

Ekk a

VV exp0

(29)

Table 12. Kinetic parameters for volatilization reactions [33, 34]

Reactions component

of VM

kV0

(s–1

)

Ea

(10–3

J·mol–1

)

(11) loosely bound CO 583 86.2

(11) tightly bound CO 742 100.4

(12) CO2 0.5 33.5

(13) H2 450 106.3

(14) H2O 1.5 41.4

(15) CH4 383 81.2

(15) C2H4 383 81.2

(15) C3H8 383 81.2

(15) C6H6 125 66.9

27

3.5.3 Reaction Rate – Reduction and Gasification Reactions

As the reduction reactions of iron and zinc oxides are also assumed to be Arrhenius–

type first–order reactions with respect to the relevant gas concentration, the reaction

rates are obtained by Equations (30) and (31). The equations for the rates of carbon

gasification by CO2 and H2O are described in the same manner as shown in Equations

(32) and (33). The values of parameters used in Equations (30) – (33) are listed in

Table 13. For the surface area, indicated by Sreactant, Sproduct or Scarbon in Equations (30)

and (32), the total area of reaction front of each solid component is used. The reaction

front of the oxides is the total surface area of their particles; thus, the area has strong

dependence on the particle size distribution. On the other hand, a carbon particle itself

involves very porous structure which has much larger area than its apparent external

surface area. Therefore, the BET surface area measured by liquid N2 adsorption is used

as the reaction front area for the carbon gasification reactions. The parameters fS and

fSC in Equations (31) and (33) are defined as the surface area correction factors

(SACF), which are introduced to adjust the surface area based on the difference

between the assumptions made in the present model and the experimental conditions

where the published frequency factors were measured.

⋅−⋅⋅=

E

OHCO

HCOK

CSCSkn 22

2

orproduct

orreactant

(30)

−⋅=RT

Ekfk a

S exp0

(31)

OHCOCC CSkn22 orcarbon ⋅⋅=

(32)

−⋅=RT

Ekfk a

CSCC exp0

(33)

28

Table 13. Kinetic parameters for reduction and carbon gasification [33, 53, 54]

Reactions k0

(m·s–1)

Ea

(10–3

J·mol–1

)

KE

fS, fSC

(16) 2700 113.8 exp(4.91 + 6235/T) 2.3

(17) 160 92.0 exp(8.384 + 2547/T) for T<848 (K)

exp(8.102 + 2065/T) for T ≥848 (K)

2.3

(18) 25 73.6 exp(1.52 – 623/T) 2.3

(19) 23 71.1 exp(5.19 – 4685/T) 2.3

(20) 16 73.6 exp(–0.84 + 949/T) 2.3

(21) 6.5 68.6 exp(3.95 – 3931/T) 2.3

(22) 17 69.4 exp(–2.82 + 2376/T) 2.3

(23) 30 63.6 exp(1.01 – 1858/T) 2.3

(24) 18 86.2 exp(14.310 – 22871/T) 4.0

(25) 1.87×108 221.8 exp(32.80 – 20766/T)/(RT) 116.5

(26) 6.05×105 172.7 exp(28.61 – 16142/T)/(RT) 116.5

3.5.4 Particle Size Distribution

The particle size distribution plays a critical role in determining the reaction front area

of oxide particles. Two major distribution functions have been proposed by Rosin and

Rammlar, and Gates, Gaudin and Schumann to represent the particle diameter

distribution of ore, dust and coal [55–58]. Equations (34) and (35) show Rosin–

Rammlar (RR) distribution and Gates–Gaudin–Schumann (GGS) distribution,

respectively; R(x) is the weight percentage of particles with diameter under x, and the

parameters, mR, kR, mG and kG, determine the shape and width of the distribution.

Rearranging Equations (34) and (35), the relationships between R(x) and x of RR and

GGS functions can be obtained as shown in Equations (36) and (37). Figures 7 and 8

show ln[-ln(1-R(x)/100)] and ln(R(x)/100) plotted against ln(x) for the mixture of dust

and anthracite coal used in the present experiment. Straight lines are obtained in Figure

7, which demonstrates RR equation is suitable to express the particle size distribution

of dust and coal. Two characteristic parameters, mR and kR, in Equation (34) can be

determined when the information for two sets of diameter x and weight percentage

R(x) is available. Equations (38) and (39) show the formulas to calculate kR and mR

29

from these data. Once the RR distribution function is obtained, mass median diameter,

d50, can be derived from Equation (40) as an indicator of the fineness of particles.

A different distribution scheme is applied for zinc oxide particles in dust. The zinc

oxide particle is formed through the oxidation of zinc fume which is evaporated from

molten iron bath in a melter such as BOF or EAF. The particle formation mechanism

of zinc oxide is different from the other particles (i.e. iron oxides and carbon), most

part of which is originated from physical entrapment of the feed materials and bubble

bursting of the iron bath. Thus, the zinc oxide particles are much smaller than the

others; applying uniform size distribution to all elements in dust would lead to

unrealistic kinetic behaviour of the pellet reduction. For zinc oxide, two separate RR

equations, Equation (41), are applied to better express the particle diameter

distribution, considering that the shape of size distribution of zinc oxide changes at a

threshold particle size (e.g. 10 µm in Figure 13). Determining these two RR equations

requires the measured sets of data on diameter, x, and percent passing, R(x), at the

threshold point in addition to other two points.

( ) [ ]passing-%100exp1RR ×

−−=

Rm

Rk

xxR

(34)

( ) [ ]passing-%100GGS ×

=

Gm

Gk

xxR

(35)

( )

( )x

xR

kmxmxR

RR

RRRRR

ln100

1lnln

lnln100

1lnln

∝

−−

−=

−−

(36)

30

( )

( )x

xR

kmxmxR

GGGGGS

ln100

ln

lnln100

ln

GGS ∝

−=

(37)

( ) ( )

( ) ( )

−−

−

×

−−×

−=

1001

1lnln

1001

1lnln

ln1001

1lnlnln

1001

1lnln

exp

21

1

2

2

1

xRxR

xxR

xxR

k

RRRR

RRRR

R (38)

( ) ( )21

21

lnln

1001

1lnln

1001

1lnln

xx

xRxRm

RRRR

R −

−−

−=

(39)

( )

= Rm

Rkd1

50 2ln

(40)

( ) ( )

( ) ( )a

m

R

a

m

R

xxk

xxR

xxk

xxR

R

R

≥×

−−=

<×

−−=

100exp1

100exp1

2

1

2

RR2

1

RR1

(41)

31

Figure 7. Relationship between ln(x) and ln[-ln(1-R(x)/100)]

Figure 8. Relationship between ln(x) and ln(R(x)/100)

-3

-2

-1

0

1

2

-4 -3 -2 -1 0 1

ln[-

ln(1

-R(x

)/1

00

)]

ln(x)

-3

-2

-1

0

1

2

-4 -3 -2 -1 0 1

ln(R

(x)/

10

0)

ln(x)

32

3.5.5 Reaction Front Surface Area

The total surface area of all particles is of interest to determine the reduction rate of the

oxides. The area is obtained by Equation (42), summing up the surface area of the

particles having different diameters between two threshold sizes, xmin and xmax. The

existence of fine particles dramatically increases the total area due to their large

specific area. However, the fine particles in ore or dust are often spontaneously

agglomerated to one another and behave as one particle, and the surface of smaller

particles under the threshold minimum diameter does not contribute to the reaction

front area. Several researchers suggested through the experimental observations that it

is reasonable to consider that the particles having less than 0.5 µm diameters are likely

to clump together and act as larger agglomerates (Table 14) [6, 59, 60]. Accordingly, in

the present model, the apparent minimum diameter after the self–agglomeration of the

fine particles, xmin in Equation (42), is set as 0.5 µm. On the other hand, xmax = 10 mm

is used considering the typical size distribution of ore or dust.

( ) ( )∑

−+=

max

min

6jtotal,

x

x j

j

x

xRdxxRWS

ρ

(42)

Table 14. Apparent minimum diameter after self–agglomeration

Researcher Minimum

diameter

(µm)

Notes

Guezennec et al. [6] 5 Fine EAF dust particles (< 2~3 µm) are often found

agglomerated into 5~20 µm large particles.

0.3 Size of film drops, which are generated when a gas

bubble emerging from inside iron bath of an EAF

ruptures at the surface, ranges from 0.3 to 500 µm.

0.2 EAF dust particles consist of two categories:

- Large part: 20 ~ few hundred µm

- Fine part: 0.2 ~ 20 µm

Sekula et al. [59] 1 5%–passing diameter of an EAF dust measured by dry

dispersion is 1 µm.

0.5 Fine EAF dust particles (< 0.05~0.5 µm) are often

found in bigger agglomerates.

33

3.5.6 BET Surface Area

BET method is used here to determine the total surface area of the carbonaceous phase.

Two major experimental options have been proposed using two different adsorption

conditions: liquid nitrogen at 77K and carbon dioxide gas at room temperature, which

hereafter are referred as SBET (N2) and SBET (CO2), respectively [31, 61]. The examples

of the two SBET values for several types of coal are shown in Table 15. Although SBET

(CO2) seems to be appropriate for dust reaction model, several researchers have

concluded that SBET (N2) better represents the active surface area for carbon

gasification reactions [62, 63]. The possible reason for this, according to Hurt et al., is

that the surface of micropores (<2.0 nm) in a carbon particle, which is counted only by

CO2 method, may not contribute to the gasification reactions because it is chemically

less active [64]. They also suggested that the catalytic elements required for the

gasification reactions mainly exist on larger pores. Liu et al. experimentally discovered

the direct correlation between gasification rate and SBET (CO2) surface area only at

1200–1300 °C, and concluded that the micropores do not play an important role in

reaction at lower temperature [63]. Therefore, SBET (N2) is used for the reaction front

area of carbon particles in the proposed model. Furthermore, Zondlo et al.’s

experimental results indicate that the surface area of coal changes with increasing its

conversion ratio [65]. According to their analysis, the surface area increases with

increasing conversion at the beginning due to the pore formation. Then, it decreases

when approximately 40% of coal is gasified because of the widening and collapse of

the pore walls. The typical behaviour is shown in Figure 9. This relationship between

surface area and coal conversion is introduced in the present dust reaction model to

precisely express the reactivity of coal mixed in pellet.

34

Table 15. BET surface of various types of coal

Coal type Origin Brand %C %VM SBET (N2) SBET (CO2) Reference

(daf) (dry) (m2·g–1

) (m2·g–1

)

Lignite Australia Yallourn 69.8 45.4 411.8 488.6 Adschiri et al. [66]

Canada Onakawara 70.2 39.6 134.0 279.0 Ng et al. [29]

Canada Bienfait 70.5 44.1 38.2 246.0 Ng et al. [29]

Bituminous Indonesia Baiduri 71.3 42.8 228.2 356.5 Adschiri et al. [66]

Australia Blair Athol 81.9 27.8 91.0 104.0 Haga et al. [67]

Canada Tulameen 75.7 32.4 41.1 212 Ng et al. [29]

Anthracite Canada Mt. Klappan 88.5 9.1 6.7 121.0 Ng et al. [29]

Viet Nam Hongei 92.7 6.6 4.6 92.7 Adschiri et al. [66]

Figure 9. Surface area variations with conversion ratio (Jeddo anthracite coal) [65]

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0

Su

rafc

e a

rea

/ I

nit

ial s

urf

ac

e a

rea

Conversion ratio

900

950

975

Temperature (°C)

Anthracite, Jeddo (WV, USA)

35

3.5.7 Surface Area Correction Factor (SACF)

The frequency factors measured in the references [33, 34, 53, 54] were determined

based on a shrinking core model where the cross–sectional area of the reactant particles

was considered to be the reaction front. In the present model, however, the total area of

the particles at the reaction front is used in the rate equations (Figure 10). Therefore,

the SACF is introduced to obtain an appropriate pre–exponential factor for the present

pellet model from the published data. Equation (43) and (44) show the reaction rate

equations derived from both the shrinking core model and the present model,

respectively. Sf is a variable called a surface factor, which is defined in the shrinking

core model. Rearranging Equation (43) and (44), the SACF, fS = k0SCM/k0, can be

obtained by Equation (45). For a coal gasification reaction, the frequency factor is an

apparent factor including the effect of reaction surface and usually measured in terms

of the conversion ratio of coal. Thus, the SACF for coal gasification, fSC, can be

defined as the surface area itself of the coal sample used in the experiment measuring

its gasification rate.

model) core shrinking(crossSCM0 exp SRT

EkSn a

f

−=

(43)

model)(present total0 exp SRT

Ekn a

−=

(44)

ff

SCMS

SSS

S

k

kf

4

cross

total

0

0 =⋅

==

(45)

36

Figure 10. Reaction surface area

3.6 Gas Transfer

The internal gas transfer is triggered by two factors: concentration difference and

pressure gradient between adjacent layers in pellet. The concentration–driven gas

diffusion is described with Fick’s law using the effective diffusion coefficient

(Equation (46)). Equation (47) and (48) show two boundary conditions; Equation (47)

describes the gas exchange at the pellet surface whereas Equation (48) indicates the

pellet centre where no gas is exchanged. The effective diffusion coefficient, Deff, is the

overall diffusivity of gas in pellet taking its porosity into account. The calculation

method for the coefficient is explained later.

The pressure–triggered gas flow plays a more important role than the diffusive gas

movement in RHF reduction of dust [12]. Noting that the reaction rates are not uniform

throughout the dust pellet due to the substantial temperature gradient and that the

release of volatiles takes place at low temperature, there may exist a significant internal

pressure gradient within the pellet. This internal pressure curve creates the intense gas

flow in the porous pellet. A modified Hagen–Poiseuille equation (49) is applied to

determine this flow rate [68].

shrinking core model proposed model

particle particle

cross–sectional surface total particle surface

37

∂

∂∂∂

=∂

∂r

CDr

rrt

C kkeff

k,

2

2

1

(46)

( )1,,

surface

, kfkg

r

kkeff CCk

r

CD −=

∂∂

=

(47)

0centre

=∂

∂

=r

k

r

C

(48)

r

PPd

RT

dNG k

k

kcchk ∆

∆=

µπ

264

3

(49)

3.6.1 Effective Diffusion Coefficient

The effective diffusion coefficient inside the pellet depends on the gas composition in

pores, temperature, pressure and porosity. The diffusion coefficient of a gas element is

usually measured in a two–phase system. The coefficient of gas k in gas ℓ follows

Equation (50) when the surrounding temperature and pressure are changed. The values

of Dkℓ0 and mkℓ are summarized in Tables 16 and 17 [45, 69–71]. The diffusion

coefficient of gas component k in multi–phase atmosphere is derived by Equation (51)

[45]. The porosity dependence of the diffusion coefficient is expressed in Equation

(52), where the overall effective diffusion coefficient is determined [68]. As an

example, Figure 11 shows the diffusion coefficient of CO2 in pellet at 298.15 K and 1

atm as a function of its porosity. The coefficient almost linearly decreases with

decreasing porosity towards 0 at φ=0.

×

⋅=t

m

klklP

TDD

kl 5

0

1001325.1

273

(50)

38

∑=

l kl

l

tk

D

P

PD

(51)

kkeff DDϕ

ϕ−

=3

2, (52)

Table 16. Standard diffusion coefficient Dkl0 (10–4

m2·s

–1) [45, 69–71]

Gas species l

O2 N2 CO CO2 H2 H2O CH4 C6H6

k O2 0.186 0.181 0.188 0.138 0.661 0.240 0.185 0.078

N2 0.181 0.178 0.192 0.144 0.689 0.251 0.185 0.082

CO 0.188 0.192 0.175 0.137 0.651 0.251 0.185 0.081

CO2 0.138 0.144 0.137 0.097 0.575 0.146 0.153 0.053

H2 0.661 0.689 0.651 0.575 1.285 0.734 0.625 0.321

H2O 0.240 0.251 0.251 0.146 0.734 0.277 0.216 0.185

CH4 0.185 0.185 0.185 0.153 0.625 0.216 0.200 0.185

C6H6 0.078 0.082 0.081 0.053 0.321 0.185 0.185 0.185

Table 17. Parameter mkl for calculating diffusion coefficient [45, 69–71]

Gas species l

O2 N2 CO CO2 H2 H2O CH4 C6H6

k O2 1.92 1.75 1.68 1.80 1.89 1.73 1.75 2.00

N2 1.75 1.90 1.75 1.73 1.72 1.75 1.75 2.00

CO 1.68 1.75 1.75 1.75 1.75 1.75 1.75 1.75

CO2 1.80 1.73 1.75 1.90 1.76 1.84 1.75 2.00

H2 1.89 1.72 1.75 1.76 1.75 1.82 1.75 1.75

H2O 1.73 1.75 1.75 1.84 1.82 1.75 1.75 1.75

CH4 1.75 1.75 1.75 1.75 1.75 1.75 1.69 1.75

C6H6 2.00 2.00 1.75 2.00 1.75 1.75 1.75 1.75

39

Figure 11. Effective diffusion coefficient of CO2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.1 0.3 0.5 0.7 0.9

Eff

ec

tive

Dif

fus

ion

Co

eff

icie

nt

of

CO

2(1

0–4

m2�s

–1)

Porosity

25 °C

400 °C

800 °C

40

3.6.2 Mass Transfer Coefficient

The mass transfer coefficient, kg, determines the rate of gas transfer between furnace

atmosphere and pellet surface. The coefficient can be derived from Frössling equation

(Equations (53) and (54)). It should be noted that Df, Scf and Ref indicate the diffusion

coefficient, Schmidt number and Reynolds number with respect to the furnace gaseous

atmosphere. vC in Equation (54) is the gas velocity surrounding the pellet. For an

experimental furnace, vC can be determined by the flow rate of purging inert gas and

the internal cross–sectional area of the furnace tube. For an RHF simulation, vC can be

estimated from the volume of furnace exhaust gas.

( )21

31

ReSc6.00.2Sh ff

f

f

f

gd

D

d

Dk +==

(53)

f

fC

f

ff

f

f

dv

D µ

ρ

ρ

µ== Re,Sc

(54)

3.6.3 Modified Hagen–Poiseuille Equation

The modified Hagen–Poiseuille equation (49) is introduced to determine the internal

gas flow caused by pressure gradient with several assumptions. The pore part in each

pellet layer is divided into Nh imaginary straight cylinders with length of ∆r (thickness

of the layer) and uniform diameter dc. Then, the pressure–triggered gas transfer taking

place in the tube is presumed to be a laminar flow. Based on these premises, Equation

(49) can be derived from the well–known Hagen–Poiseuille equation for straight

cylinders to represent the gas flow in the pellet’s porous part. The viscosity of gas in

the equation can be obtained by Sutherland’s equation (55) with the parameters listed

in Table 18 [72]. The calculation of the number and diameter of the imaginary

cylinders, Nh and dc, requires additional assumptions. Presuming that all solid particles

are distributed randomly and uniformly in each layer of pellet, it is reasonable to

consider the same number of the tubes and particles is present from the axial direction

41

onto the surface of the layer. This assumption leads to Equations (56) and (57)

determining the number of cylinders, Nh, and the diameter dc.

5.1

0

00

++

=T

T

ST

ST

u

ukk µµ

(55)

∑ ∆=

j

jp

j

h Nr

dN ,

,50

(56)

rN

Vd

h

c ∆=

πϕ4

(57)

Table 18. Values of parameters for Equation (55) [72]

Component µk0

(µPa·s)

T0

(K)

Su

(K)

O2 18.7 273 127

N2 16.6 273 109

CO 16.2 273 100

CO2 13.8 273 277

H2 8.6 273 79

H2O 32.0 866 1100

CH4 10.4 273 215

C6H6 9.2 273 272

42

4 Results and Discussion

4.1 Experimental

4.1.1 Sample Preparation

The dust–carbon composite pellet was made of BOF dust and reductant coal. The BOF

dust was obtained from the feedstock yard of an RHF dust recycling process in Japan.

For the reductant, one type of coal was chosen for each experiment depending on its

composition. The two coal types used in the present experiments are listed in Table 19.

The volatile content and its composition were determined by gasifying the two types of

coal, anthracite A and bituminous B. The coal samples were heated up to 900 °C in

nitrogen atmosphere with an electric furnace. They are kept until all volatile content in

the coal are released and no concentration change was observed in the exhaust gas.

After cooling the specimen in inert atmosphere, the sample weight was measured and

the weight decrease was attributed to the volatile matter. The chemical composition of

the released gas was also measured, and then, the constituents of volatile were

determined. On the other hand, the BET surface of the coal was determined based on

the published literature since the measured data was not available. For the anthracite

coal A, 4.6 (m2·g

–1) was used according to the measured surface area of the anthracite

from the same mine in the same country, Viet Nam. SBET (N2) of the bituminous coal B

was presumed to be 228.2 (m2·g

–1) based on the measured value of the Indonesian

bituminous coal with similar volatile content [66].

The dust and coal were first dried in air for more than eight hours to remove the

moisture contained in them. The temperature of the dryer was controlled to be 105 ± 5

°C. After the desiccation process, the pellet mix was prepared by blending the two. The

mixture ratio was determined so that the weight percent of total carbon in the pellet

becomes approximately 14–17 wt%. Then, the pellet mix was crushed with laboratory–

scale muddler and mortar. The crushing time was controlled so that 80%–passing

diameter of the pulverized mixture exists in the range of 200–250 µm. After crushing,

the particle size distribution of the blended composite was measured by sieving.

43

Figure 12 shows the measured particle size distribution of the pellet mix and the

corresponding RR distribution function determined by two measured points. The two

parameters for the RR function and the mass median diameter, d50, for the pellet mix

are summarized in Table 20. For zinc oxide particles in the pellet mix, they are

assumed to follow the size distribution of EAF dust, taking into consideration the fact

that major component of EAF dust is zinc oxide and that particle size of the zinc oxide

contained in dust is not easily measurable. The published particle diameter distribution

of typical EAF dust is shown in Figure 13. In the present model, the zinc oxide

particles in dust are presumed to follow the size distribution of this EAF dust with

d50=5.9 µm. The parameters for RR distribution functions for zinc oxide were

determined with three known sets of diameter and percent passing, which are listed in

Table 21. The two RR curves are also graphically indicated in Figure 13.

For agglomeration of the mix into pellets, 8.7 wt% of water and 1.8 wt% of organic

and inorganic binder were added. The blend was agglomerated into a cylindrical shape

pellet using hydraulic pressure. For producing one pellet specimen, 32.6 g of the dust–

carbon mixture was compacted into a cylindrical die with internal diameter of 30 mm

under a pressure of 3.8 MPa. The height of the agglomerated pellet sample became

approximately 12–18 mm depending on its constituents. The desiccation of the pellet

then followed; the remained moisture in the pellet specimen was removed in air. The

temperature of this pellet dryer was set to be 105 ± 5 °C. The chemical composition

and weight of the sample were measured after it was kept in the dryer for more than

eight hours. The desiccated sample weight showed in the range between 29.8 and 30.2

g. An image of the pellet sample is shown in Figure 14.

44

Table 19. Coal types used in experiments

Code Type Origin SBET (N2)

(m2·g

–1)

VM

(wt%)

Composition of VM

(wt%)

A anthracite Viet Nam 4.6 8.2 CO 10.0

H2 12.7

CO2 12.2

CH4 65.1

B bituminous Indonesia 228.2 39.8 CO 17.6

H2 3.0

CO2 11.7

CH4 67.7

Figure 12. Particle distribution of the pellet mix used in the present experiments/simulations

0

20

40

60

80

100

0 200 400 600 800 1000

% P

as

sin

g (

wt%

)

Particle diameter (µm)

Pellet mix (measured)

Pellet mix (RR distribution)

45

Table 20. Parameters for RR distribution function and mass median diameter of the pellet mix

used in the present experiments/simulations

Parameter Value

mR – 1.083

kR (µm) 131.1

d50 (µm) 93.5

Figure 13. Particle distribution of EAF dust/zinc oxide

Table 21. Parameters for RR distribution function and mass median diameter of zinc oxide used

in the present simulations

Parameter Value

xa (µm) 10.0

mR1 – 0.639

kR1 (µm) 10.5

mR2 – 0.290

kR2 (µm) 11.2

d50 (µm) 5.9

0

20

40

60

80

100

0 20 40 60 80 100

% P

as

sin

g (

wt%

)

Particle diameter (µm)

EAF dust (measured)

RR distributions (calculated)

46

Figure 14. Dust–carbon composite specimen for experiment

4.1.2 Pellet Reduction

The reduction was carried out using a laboratory–scale vertical electric furnace with a

graphite tube heater. After the furnace interior reached the predetermined temperature,

the sample was inserted into the furnace core from the top. The sample was placed at

the bottom of a basket container, and then the container was suspended at the furnace

centre. The wall and bottom parts of the basket were made of stainless steel mesh to

facilitate heat and gas transfer between the pellet sample and the furnace atmosphere

(Figure 15). During the reduction, an inert atmosphere was maintained inside the

furnace by purging nitrogen gas. After the prescribed retention time, the reactions were

arrested by quenching the pellet to ambient temperature in a nitrogen atmosphere while

preventing it from re–oxidation. After cooling, its chemical composition was

determined. The experimental electric furnace is shown in Figure 16.

47

Figure 15. Stainless steel basket

Figure 16. Experimental electric furnace

48

4.2 Model Validation

4.2.1 Calculation/Experimental Conditions

The reduction of a BOF dust pellet was simulated using the proposed model and

compared with experimental results. The pellet was made of BOF dust and the

anthracite coal and the reduction experiment was performed according to the procedure

described in Section 4.1. The simulation was executed with the same condition as the

experiment. The properties of the pellet specimen and the calculation/experimental

conditions are summarized in Table 22. Because the shape of pellet used in the

experiment (a cylinder) is different from that in the simulation (a sphere), the pellet

diameter for the simulation was determined assuming the spherical pellet has the same

weight and density as those of the experimental cylinder–shape sample.

49

Table 22. Base properties of pellet and furnace

Parameter Unit Run 1

Pellet temperature* (°C) 25

Pellet weight* (g) 30.0

Pellet composition*

Total Fe (wt%) 52.5

Metallic Fe (wt%) 1.0

FeO (wt%) 37.9

Fe2O3 (wt%) 31.4

Total C (wt%) 14.3

ZnO (wt%) 2.4

VM (wt%) 0.8

Composition of VM*

CO (wt%) 10.0

H2 (wt%) 12.7

CO2 (wt%) 12.2

CH4 (wt%) 65.1

Added Coal**

Type – A (anthracite)

BET surface area (N2)* (m2·g

–1) 4.6

Emissivity of pellet surface – 0.85

Mass median diameter***

Zinc oxide (µm) 5.9

Others (µm) 93.5

Furnace condition

Atmosphere – N2 100%

Flow rate of N2 (m·s–1

) 0.1

Temperature (°C) 1250

Retention time (sec) 900

* Initial value (before reduction)

** See Table 19

*** See Figures 12 and 13

50

4.2.2 Results and Discussion

Figure 17 shows the calculated temperature with time at different positions of the

pellet. The temperature at the surface reaches over 1100 °C in 100 seconds while the

core temperature remains around 500 °C until the end of the simulation, 15 minutes.

Figure 17 clearly shows that the large temperature gradient continues to exist in a pellet

throughout the reduction period. Figures 18 and 19 show the calculated pellet porosity

and effective thermal conductivity, respectively. As the reactions proceed, the porosity

increases due to the gas release from volatile matter and the oxygen removal from iron

and zinc oxides. Then, decline of the thermal conductivity is resulted. In Figure 20, the

calculated percent reduction with respect to iron oxides is presented with the

corresponding experimental results. The definition of the reduction ratio is described in

Equation (58). The reduction reached 82% in 900 seconds, indicating that the present

experiment/simulation well represents the pellet reduction process in an RHF, where a

similar degree of reduction is achieved within comparable time and ambient

temperature. Figure 21 shows the calculated and measured values for total Fe, metallic

Fe, FeO, Fe2O3 and residual carbon in the pellet. Iron oxides are reduced into metallic

iron consuming carbon as a reductant. Although some discrepancies are recognized,

reasonable agreement is seen between the model outputs and the experimental

measurements for the composition trends shown in Figures 20 and 21. In fact, the

difference between calculated and measured reduction ratios is less than 2.0%.

Therefore, the simulated information of pellet composition, temperature and other

properties by the proposed model is useful to design the RHF dust recycling process

and optimize its operating conditions especially in the case where a new raw material

or reductant is used.

( ) 100

2

3

34

1%

.

red32

32

43

43

×

++

−=

Fe

OFeT

OFe

OOFe

OFe

OOFe

OFe

OOFe

M

MW

M

MW

M

MW

M

MW

wtR t

t

(58)

51

Figure 17. Calculated pellet temperature at three different positions in pellet (Run 1)

Figure 18. Calculated pellet porosity (Run 1)

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000

Pell

et

tem

pera

ture

(°C

)

Retention time (sec)

Surface

Mid–radius

Centre

0.4

0.5

0.6

0.7

0.8

0.9

0 200 400 600 800 1000

Po

ros

ity

Retention time (sec)

52

Figure 19. Calculated effective thermal conductivity (Run 1)

Figure 20. Calculated and measured reduction ratio of iron oxides (Run 1)

0

50

100

150

200

250

0 200 400 600 800 1000

Eff

ec

tive

th

erm

al c

on

du

cti

vit

y

(10

–3

J�m

–1s

–1°C

–1)

Retention time (sec)

0

20

40

60

80

100

0 200 400 600 800 1000

Re

du

cti

on

ra

tio

(w

t%)

Retention time (sec)

measured

calculated

53

Figure 21. Calculated and measured pellet compositions (Run 1)

4.3 Simulation 1: Use of High Volatile Coal as Reductants

4.3.1 Calculation/Experimental Conditions

Three sets of calculations and experiments were carried out to examine the impact of

volatile matter contained in coal on the reduction behaviour of dust pellet. The

conditions and parameters of the three runs are listed in Table 23. The conditions of

Run 1 were discussed in the previous section. In Runs 2 and 3, the high–VM

bituminous coal B (as described in Table 19) was added as the reductant instead of the

anthracite coal A. The volatile content is increased from 0.8 wt% to 4.1 wt% and 6.1

wt% in Runs 2 and 3, respectively. In addition, it should be remembered that increased

BET surface, 228.2 (m2·g

–1), is used for the bituminous coal whereas the surface of the

anthracite is 4.6 (m2·g

–1). Other conditions including pellet weight, emissivity, particle

size and furnace conditions remain same as described in Table 22 in the previous

section.

0

20

40

60

80

0 200 400 600 800 1000

Co

nc

en

tra

tio

n i

n p

ell

et

(wt%

)

Retention time (sec)

Total Fe (calculated)

Metallic Fe (calculated)

FeO (calculated)

Fe2O3 (calculated)

C (calculated)

Total Fe (measured)

Metallic Fe (measured)

FeO (measured)

Fe2O3 (measured)

C (measured)

Fe2O3 (measured)

Fe2O3 (calculated)

54

Table 23. Conditions for calculation and experiment

Parameter Unit Run 1 Run 2 Run 3

Pellet temperature* (°C) 25 25 25

Pellet weight* (g) 30.0 30.0 30.0

Pellet composition*

Total Fe (wt%) 52.5 52.0 48.5

Metallic Fe (wt%) 1.0 1.0 0.9

FeO (wt%) 37.9 40.3 37.9

Fe2O3 (wt%) 31.4 28.1 25.9

Total C (wt%) 14.3 14.2 17.0

ZnO (wt%) 2.4 2.4 2.2

VM (wt%) 0.8 4.1 6.1

Composition of VM*

CO (wt%) 10.0 17.6 17.6

H2 (wt%) 12.7 3.0 3.0

CO2 (wt%) 12.2 11.7 11.7

CH4 (wt%) 65.1 67.7 67.7

Added coal**

Type – A (anthracite) B (bituminous) B (bituminous)

BET surface area (N2)* (m2·g

–1) 4.6 228.2 228.2

Emissivity of pellet surface – 0.85 0.85 0.85

Mass median diameter***

Zinc oxide (µm) 5.9 5.9 5.9

Others (µm) 93.5 93.5 93.5

Furnace condition

Atmosphere – N2 100% N2 100% N2 100%

Flow rate of N2 (m·s–1

) 0.1 0.1 0.1

Temperature (°C) 1250 1250 1250

Retention time (sec) 900 900 900

* Initial value (before reduction)

** See Table 19

*** See Figures 12 and 13

55

4.3.2 Results and Discussion

Figure 22 shows the calculated reduction ratio of the pellet samples with the

corresponding experimental measurements for Runs 1–3. The calculated and measured

results indicate that the reduction rate is increased with increasing content of volatile

component in the pellet. The average difference between calculated and measured

reduction degree is 4.0%, which is within acceptable level, noting that all kinetics

constants used in the present simulations are taken from published literatures. Thus, it

can be concluded that the proposed model is also applicable to the reduction of dust

pellet containing high volatile matter.

The acceleration of reduction reactions is attributed to the following two factors: the

reducing gases generated from the volatile matter during heating process, and the larger

BET surface area of the bituminous coal. Figure 23 illustrates the released amount of

CO from VM plotted against the pellet temperature at the mid–radius. It should be

remembered that the weighted average temperature of pellet is much higher than the

mid–radius temperature considering that only one–fourth of the pellet volume exists

between this point and the centre. As seen in Figure 23, substantial part of the CO gas

is liberated after the pellet temperature becomes high enough for the reduction

reactions of iron oxides. This results in the early initiation of the reactions and the

higher reduction ratio at the end of retention time.

A rapid gas release at the initial stage of simulation is also recognized in Figure 23.

This volatile release is mainly triggered by the fast temperature increase at pellet

surface by the radiation heating, which leads to the sharp increase of the internal

pressure as depicted in Figure 24. This figure shows that the internal pressure at the

surface can reach 2.5 atm when the volatile content is 6.1 wt%. This pressure rise may

cause the decrepitation of the pellet, which should be avoided to keep the lump ratio of

product DRI because the fragmented piece of DRI is easily re–oxidized. Therefore,

increasing volatile content in dust pellet by using high–volatile coal has two effects on

the dust reduction. The positive effect is to accelerate the reduction reaction and carbon

gasification by providing the reducing gases. The downside is that when the excessive

56

amounts are used, it can cause fracture of the pellet by raising the internal pressure.

Consequently, there is an optimum volatile concentration which gives the maximum

reduction ratio of the pellet while avoiding its decrepitation. The exact value of this

concentration cannot be determined using a mathematical model because it depends on

various operation–specific properties, most importantly being the physical properties of

the pellet such as porosity, raw strength, and pore size. However, the maximum value

and the trend of internal pressure obtained with the proposed simulation model provide

decisive information to determine the optimum volatile content.

In addition to the volatile matter, the larger BET surface of the bituminous coal used in

Runs 2 and 3 may also play a considerable role in the acceleration of the reduction

reactions by promoting the gasification reactions of carbon. As several researchers

have suggested, the two carbon gasification reactions, the Boudouard reaction (25) and

the carbon–steam reaction (26), are likely to be the rate–controlling step for the

reduction of dust–carbon composites due to their strong endothermic nature (∆H=

172.43 and 131.28 kJ·mol–1

at room temperature for Equations (25) and (26),

respectively). Thus, it is reasonable to consider that using the coal with larger reaction

front area is beneficial to increasing the overall reaction rate of the dust pellet. On the

other hand, since the two reactions have significantly large activation energies (Ea =

221.8 kJ·mol–1

for Equation (25) and 172.7 kJ·mol–1

for Equation (26)), pellet

temperature plays a more critical role than the surface area to increase the rate of

gasification. For example, the exponential terms of Equation (33) for the Boudouard

reaction (25) becomes 1011

times larger when the temperature increases from 200 °C to

600 °C, although the BET surface of bituminous coal is only 50 times larger than that

of anthracite. Therefore, between the mechanisms, the release of volatiles will have a

stronger effect on the reduction reactions than the larger surface area. Consequently,

using high–volatile coals is more effective than using reactive coal with large BET

surface to accelerate the overall rate of dust reduction reactions.

57

Figure 22. Calculated and measured reduction ratio against retention time (Runs 1–3)

Figure 23. Calculated degree of release of CO from VM against mid–radius pellet temperature

(Runs 1–3)

0

20

40

60

80

100

0 200 400 600 800 1000

Red

uc

tio

n r

ati

o (

wt%

)

Retention time (sec)

Run 1 VM0.8% (measured)

Run 2 VM4.1% (measured)

Run 3 VM6.1% (measured)

Run 1 VM0.8%

Run 2 VM4.1%

Run 3 VM6.1%

0

20

40

60

80

100

0 200 400 600 800

% o

f C

O R

ele

as

ed

fro

m V

M

Mid–radius temperature (°C)

Run 1: VM0.8%

Run 2: VM4.1%

Run 3: VM6.1%

58

Figure 24. Calculated internal pressure at pellet surface against retention time (Runs 1–3)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 200 400 600 800 1000

Inte

rna

l p

res

su

re a

t I=

2 (

atm

)

Retention time (sec)

Run 1: VM0.8%

Run 2: VM4.1%

Run 3: VM6.1%

59

4.4 Simulation 2: Use of Waste Plastic as Reductants

4.4.1 Calculation Conditions

Polyethylene (PE) was used as a waste plastic reductant considering its vast

availability. Table 24 shows the five simulation conditions to evaluate the use of PE as

a reductant. The pellet compositions in Runs 4–6 were calculated based on a blend of

2.5, 5.0 and 10 wt% of PE and the pellet mix in Run 1. Table 25 shows the estimated

constituents of volatiles which will be released from the PE when heated. The increase

of volatile content and the change of its composition can be seen as more PE is blended

to the pellet. It should be noted that only reducing gas generated from PE is hydrogen,

and that the physical and chemical properties of C2H2 and C2H4 are presumed to be the

same as those of CH4 since no reaction involving these heavier hydrocarbons is

considered in the present model. In addition, Run 7 was carried out to investigate the

effect of volatiles with different constituents on the reactions. The pellet composition

of Run 7 was created based on a blend of 2.5 wt% of an “imaginary plastic” that

consists of 100% volatile CO. The composition of VM resulting from the mix of coal

and this imaginary plastic is also shown in Table 25. In Runs 4–7, the fractional weight

of the base anthracite coal in the pellet remains unchanged; consequently, the total

carbon percent increases with increasing PE addition.

60

Tab

le 2

4. C

alcu

lati

on c

ondit

ions

Par

amet

er

Unit

R

un 1

R

un 4

R

un 5

R

un 6

R

un 7

Pel

let

tem

per

ature

*

(°C

) 25

25

25

25

25

Pel

let

wei

ght*

(g

) 30.0

30.0

30.0

30.0

30.0

Pel

let

com

posi

tion

*

T

ota

l F

e (w

t%)

52.5

51.1

49.8

47.4

51.1

M

etal

lic

Fe

(wt%

) 1.0

1.0

1.0

0.9

1.0

F

eO

(wt%

) 37.9

37.0

36.0

34.3

37.0

F

e 2O

3

(wt%

) 31.4

30.6

29.8

28.4

30.6

T

ota

l C

(w

t%)

14.3

15.6

16.9

19.2

14.9

Z

nO

(w

t%)

2.4

2.4

2.3

2.2

2.4

V

M

(wt%

) 0.8

3.2

5.5

9.8

3.2

Com

posi

tion o

f V

M*

C

O

(wt%

) 10.0

2.5

1.4

0.8

77.8

H

2

(wt%

) 12.7

8.3

7.6

7.2

3.1

C

O2

(wt%

) 12.2

3.0

1.7

0.9

3.0

C

H4

(wt%

) 65.1

86.3

89.3

91.1

16.1

Added

coal

**

T

ype

–

A (

anth

raci

te)

A (

anth

raci

te)

A (

anth

raci

te)

A (

anth

raci

te)

A (

anth

raci

te)

B

ET

surf

ace

area

(N

2)*

(m

2·g

–1)

4.6

4.6

4.6

4.6

4.6

PE

addit

ion

(wt%

) 0

2.5

5.0

10.0

2.5

****

61

Tab

le 2

4. C

alcu

lati

on c

ondit

ions

(conti

nued

)

Par

amet

er

Unit

R

un 1

R

un 4

R

un 5

R

un 6

R

un 7

Em

issi

vit

y o

f pel

let

surf

ace

–

0.8

5

0.8

5

0.8

5

0.8

5

0.8

5

Mas

s m

edia

n d

iam

eter

***

Z

inc

oxid

e (µ

m)

5.9

5.9

5.9

5.9

5.9

O

ther

s (µ

m)

93.5

93.5

93.5

93.5

93.5

Fu

rnac

e co

ndit

ion

A

tmosp

her

e –

N2 1

00%

N

2 1

00%

N

2 1

00%

N

2 1

00%

N

2 1

00%

F

low

rat

e of

N2

(m·s

–1)

0.1

0.1

0.1

0.1

0.1

T

emper

ature

(°

C)

1250

1250

1250

1250

1250

R

eten

tion t

ime

(sec

) 900

900

900

900

900

* I

nit

ial

val

ue

(bef

ore

red

uct

ion)

** S

ee T

able

19

*** S

ee F

igure

s 12 a

nd 1

3

**** I

mag

inar

y p

last

ic (

all

CO

)

62

Table 25. Composition of PE and All–CO imaginary plastic (wt%) [24]

Composition PE

(wt%)

Imaginary plastic

(wt%)

H2 6.8 –

CH4 42.3 –

C2H2 9.0 –

C2H4 41.9 –

CO – 100.0

4.4.2 Results and Discussion

The calculated reduction ratios for Runs 1, 4, 5 and 6 are compared in Figure 25. In

contrast to the simulation using high–volatile bituminous coal (Figure 22), the overall

reduction rate is not improved with the PE addition. On the contrary, slowing down of

reduction is observed in the pellet with 10 wt% PE, Run 6. These simulation results

demonstrate that the dust reduction cannot be accelerated by PE addition under the

given conditions. This may be related to the low temperature release of PE volatiles, as

depicted in Figure 26. In this figure, the decomposition ratio of PE is plotted against

mid–radius temperature of the pellet. Unlike the CO release from high–VM coal

illustrated in Figure 23, significant portion of PE is volatilized when the pellet

temperature is not sufficient for reduction of iron oxide. This results in early escape of

the released volatiles without their effective contribution in reduction. Although the

energy content of the PE may be partially utilized by combustion in the furnace

freeboard, this would only improve the energy balance and not the reduction kinetics.

In fact, as seen in Figure 25, large amounts of PE may even hinder the later stage

reduction of pellet. This is attributed to the substantial increase in the pellet porosity,

leading to reduced thermal conductivity, which in turn slows down the thermally

activated reactions. Figures 27 and 28 show the trends of porosity and effective thermal

conductivity of pellet, respectively. The porosity rises with the evaporation of volatiles

from PE, and a corresponding decline in thermal conductivity is resulted. Figures 29

and 30 show the sharp increase of internal pressure at the early stages and the linear

relationship between the maximum pressure and the percentage of PE, respectively.

63

These pressure trends also indicate that almost all volatiles contained in PE are released

during a short period and that the generated hydrogen gas, which is the only reducing

agent contained in the PE, is exhausted immediately from the pellet. In addition, Figure

31 compares the reduction ratio trends for Runs 1, 4 and 7. As seen, Run 7 gives a

faster reduction rate than Run 4. The difference between these simulations is the

composition of the plastics blended to the pellets: PE in Run 4 and all–CO imaginary

plastic in Run 7. Figure 32 illustrates that the decomposition of the plastic in Run 7

takes place more slowly and, in turn, the CO gas is released at higher pellet

temperature. As a result, the initial pressure increase is mitigated in Run 7 as depicted

in Figure 33.

It can be concluded from the obtained simulation results that the dust reduction rate

cannot be enhanced by the simple PE addition to the pellet. The major factor

preventing the plastic from acting as a reductant is that its only reducing volatile is

hydrogen, which is rapidly released at low temperatures and transferred outside the

pellet very quickly. It should be noted, however, that the findings here pertain to a

specific type of waste plastic, with low–temperature volatiles. Clearly, the composition

of the plastic and the temperature dependence behaviour of the volatiles release will

play key roles in how the addition to pellet affects reduction kinetics, pellet physical

properties and furnace energy balance.

It is thus essential that for each type of waste plastic, characterisation be carried out

with respect to constituents and the kinetic parameters, to predict its effects. A proper

mix of waste plastics and coal may be engineered that the volatiles are released at the

time and position that serve the reduction process best. One solution would be the use

of waste materials containing less hydrogen and more CO. The waste plastics whose

carbon to hydrogen ratio is larger than PE, such as polystyrene and polyethylene

terephthalate, may be more suitable candidates as reductants, although their availability

is limited compared to PE. Another option suggested by Ueki et al. is refuse–derived

fuel (RDF), which is produced from regular solid waste through shredding and

desiccating [24]. The RDF used in their experiments contains 11.5 wt% of fixed carbon

64

as well as 75.2 wt% of volatile elements. They performed iron oxide pellet reduction

using RDF as a reductant, and concluded that RDF is more effective than PE due to

RDF’s high fixed carbon content. The better performance of RDF is also attributed to

its slower volatilization rate. However, because the production process of RDF itself

requires considerable amounts of energy, the total energy balance of the whole process

including the dust reduction and the RDF manufacture should be examined when its

use for this purpose is considered.

Figure 25. Calculated reduction ratio against retention time (Runs 1, 4, 5 and 6)

0

20

40

60

80

100

0 200 400 600 800 1000

Red

uc

tio

n r

ati

o (

wt%

)

Retention time (sec)

Run 1 PE 0%

Run 4 PE 2.5%

Run 5 PE 5.0%

Run 6 PE 10.0%

65

Figure 26. Calculated decomposition ratio of PE against mid–radius pellet temperature

temperature (Run 4–6)

Figure 27. Calculated pellet porosity against retention time (Runs 1, 4, 5 and 6)

0

20

40

60

80

100

0 200 400 600 800

De

co

mp

osit

ion

ra

tio

of

PE

(w

t%)

Mid–radius temperature (°C)

Run 4 PE 2.5%

Run 5 PE 5.0%

Run 6 PE 10.0%

0.4

0.5

0.6

0.7

0.8

0 200 400 600 800 1000

Po

ros

ity

Retention time (sec)

Run 1 PE 0%

Run 4 PE 2.5%

Run 5 PE 5.0%

Run 6 PE 10.0%

66

Figure 28. Calculated effective thermal conductivity against retention time (Run 1, 4, 5 and 6)

Figure 29. Calculated internal pressure at pellet surface against retention time (Runs 1, 4, 5 and

6)

10

20

30

40

50

60

0 200 400 600 800 1000

Eff

ec

tive

th

erm

al c

on

du

cti

vit

y

×1

0–3

(c

al�

m–

1s

–1°C

–1)

Retention time (sec)

Run 1 PE 0%

Run 4 PE 2.5%

Run 5 PE 5.0%

Run 6 PE 10.0%

0

1

2

3

4

0 200 400 600 800 1000

Inte

rnal p

res

su

re a

t I=

2 (

atm

)

Retention time (sec)

Run 1 PE 0%

Run 4 PE 2.5%

Run 5 PE 5.0%

Run 6 PE 10.0%

67

Figure 30. Relationship between maximum internal pressure and PE content in pellet (Run 1, 4, 5

and 6)

Figure 31. Calculated reduction ratio against retention time (Run 1, 4 and 7)

0

1

2

3

4

0 2 4 6 8 10 12

Ma

xim

um

in

tern

al p

ress

ure

(a

tm)

PE addition (wt%)

0

20

40

60

80

100

0 200 400 600 800 1000

Red

uc

tio

n r

ati

o (

wt%

)

Retention time (sec)

Run 1 PE 0%

Run 4 PE 2.5%

Run 7 All-CO 2.5%

68

Figure 32. Calculated decomposition ratio of PE against mid–radius pellet temperature (Run 4

and 7)

Figure 33. Calculated internal pressure at pellet surface against reduction time (Run 1, 4 and 7)

0

20

40

60

80

100

0 200 400 600 800

De

co

mp

os

itio

n r

ati

o o

f P

E (

wt%

)

Mid–radius temperature (°C)

Run 4 PE 2.5%

Run 7 All-CO 2.5%

0

1

2

3

4

0 200 400 600 800 1000

Inte

rna

l p

ress

ure

at

I=2

(a

tm)

Retention time (sec)

Run 1 PE 0%

Run 4 PE 2.5%

Run 7 All-CO 2.5%

69

4.5 Simulation 3: Zinc Oxide Recovery

4.5.1 Calculation/Experimental Conditions

Three simulations of dust pellet reductions, Run 1, 8 and 9, as well as the experimental

results corresponding to Run 1 were compared to investigate the kinetic behaviour of

zinc oxide reduction in dust. The pellet composition is same for the three simulations,

containing 2.4 wt% of zinc oxide. Zinc is considered to be entirely in the form of zinc

oxide (ZnO), assuming the rapid decomposition rate for zinc–ferrite (ZnFe2O4), which

is the other major compound of zinc in dust [37]. The calculation conditions for the

three simulations are summarized in Table 26. The difference among these conditions

lies in the particle size of zinc oxide while the other components follow the identical

particle distribution where the mass median diameter (d50) is 93.5 µm. As mentioned

before, a smaller distribution is used for zinc oxide in Run 1, taking into consideration

the generation mechanism of zinc oxide in steelmaking furnaces. In the other two

simulations, Runs 8 and 9, larger ZnO particle size was presumed. In Run 8, the

particle diameter of the zinc oxide is assumed to follow the same distribution of the

other elements. In Run 9, the ZnO particle size is set in the middle between Runs 1 and

8. The particle distributions of zinc oxide used for Runs 1, 8 and 9 are illustrated in

Figure 34.

70

Table 26. Experimental/Calculation conditions

Parameter Unit Run 1 Run 8 Run 9

Pellet temperature* (°C) 25 25 25

Pellet weight* (g) 30.0 30.0 30.0

Pellet composition*

Total Fe (wt%) 52.5 52.5 52.5

Metallic Fe (wt%) 1.0 1.0 1.0

FeO (wt%) 37.9 37.9 37.9

Fe2O3 (wt%) 31.4 31.4 31.4

Total C (wt%) 14.3 14.3 14.3

ZnO (wt%) 2.4 2.4 2.4

VM (wt%) 0.8 0.8 0.8

Composition of VM*

CO (wt%) 10.0 10.0 10.0

H2 (wt%) 12.7 12.7 12.7

CO2 (wt%) 12.2 12.2 12.2

CH4 (wt%) 65.1 65.1 65.1

Added coal**

Type – A (anthracite) A (anthracite) A (anthracite)

BET surface area (N2)* (m2·g

–1) 4.6 4.6 4.6

Emissivity of pellet surface – 0.85 0.85 0.85

Mass median diameter***

Zinc Oxide (µm) 5.9 93.5 21.6

Others (µm) 93.5 93.5 93.5

Furnace condition

Atmosphere – N2 100% N2 100% N2 100%

Flow rate of N2 (m·s–1

) 0.1 0.1 0.1

Temperature (°C) 1250 1250 1250

Retention time (sec) 900 900 900

* Initial value (before reduction)

** See Table 19

*** See Figures 12, 13 and 34

71

Figure 34. Particle distributions of zinc oxide used for Runs 1, 8 and 9

4.5.2 Results and Discussion

Figures 35 and 36 compare the calculated trends of reduction ratio (with respect to iron

oxides as defined in Equation (58)) and zinc oxide concentration in pellet, respectively.

Figure 35 indicates that the kinetic behaviour of the iron oxide reduction is not affected

by the particle size of zinc oxide for these simulations. In contrast, Figure 36 clearly

illustrates that the calculated ZnO concentration using smaller particle size agrees with

the experimental result better than the output assuming that ZnO and the other

constituents follow the same particle size distribution. These results confirm that the

specific surface area of zinc oxide is 7.5 times larger than that of other oxides and

carbon due to the fine particle size of zinc oxide (Figure 37).

This is attributed to the inherent generation mechanism of zinc oxides in dust. The

major regimes of dust generation are bubble bursting and entrainment of particles,

where relatively large metal droplets ejected from the melting iron bath of a BOF or an

EAF by oxygen blowing or arc discharging are entrained into the exhaust gas. On the

0

20

40

60

80

100

0 200 400 600 800

% P

as

sin

g (

wt%

)

Particle diameter (µm)

Run 1: d50=5.9µm

Run 8: d50=93.5µm

Run 9: d50=21.6µm

d50

d50

d50

72

other hand, metallic zinc, which originates mainly from galvanized steel scrap,

vaporizes in the melter due to its high vapour pressure, and then re–oxidizes in the

furnace atmosphere [6, 73]. Therefore, it is reasonable to consider that the zinc oxide

particle has smaller diameter. Determining the diameter distribution of ZnO particles

and applying it to the model would improve the reliability and viability of the proposed

model for EAF dust recycling. It would be also beneficial for the further enhancement

of the model accuracy to obtain the different particle distribution data pertaining to

each component taking its generation mechanism into account.

Figure 35. Calculated reduction ratio of iron oxides against retention time (Runs 1, 8 and 9)

0

20

40

60

80

100

0 200 400 600 800 1000

Red

ucti

on

rati

o (

wt%

)

Retention time (sec)

Run 1:

Run 8:

Run 9:

d50 = 5.9µm

d50 = 93.5µm

d50 = 21.6µm

73

Figure 36. Calculated and measured zinc oxide concentration trend against retention time (Runs

1, 8 and 9)

Figure 37. Relationship between specific surface area and mass median diameter (Runs 1, 8 and

9)

0

1

2

3

4

0 200 400 600 800 1000

Zn

O i

n p

ell

et

(wt%

)

Retention time (sec)

Run1 (measured)

Run 1:

Run 8:

Run 9:

d50 = 5.9µm

d50 = 93.5µm

d50 = 21.6µm

0.0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120

Sp

ec

ific

su

rfa

ce

are

a (

m2�g

–1)

Mass median diameter (µm)

74

5 Conclusions and Future Work

5.1 Summary and Conclusions

A mathematical model to predict the reaction behaviour of the dust–carbon composite

agglomerate in an RHF was developed. The proposed comprehensive model simulates

heat transfer, gas transfer and reactions in the dust pellet at the same time. The

reactions taken into account include volatile release from coal or other carbonaceous

reductants and zinc oxide reduction as well as iron oxide reduction and carbon

gasification. Reduction experiments were carried out in a laboratory–scale electric

furnace to validate the model under several conditions. The calculated results showed

good agreement with the experimental measurement with respect to the degree of pellet

reduction and the concentration of major components. The following important

conclusions were drawn.

• The simulation of the pellet reduction with anthracite and bituminous coals

demonstrated that the reduction reaction is accelerated when high–volatile coal is

used as a reductant. The liberated reducing gases from the coal initiate the iron

oxide reductions at moderate temperature before the strong endothermic carbon

gasification reactions start providing CO and H2 gases, although the calculation

results also indicate that the released gas increases the internal pressure which

could lead to the decrepitation of the pellet.

• Hindering of reduction reactions was observed in the simulation of polyethylene

(PE)–blended dust pellets. In this case, volatile matter is released from the plastic

at much lower temperature compared with the bituminous coal–added pellet. Thus,

the evaporated reducing gas, mainly H2, escapes out of the pellet without

contributing to the reduction as the pellet temperature is not sufficiently high for

the reactions.

• The comparison of the calculated reduction trend of zinc oxide with the

experimental result revealed that zinc oxide particles in dust follow smaller size

distribution and have larger reaction front area than other major constituents. This

finer particle size of zinc oxide is attributed to its inherent generation pathway to

the dust from iron bath or feed scrap at a melter. Metallic zinc fed into a melting

75

furnace is vaporized due to its high vapor pressure and re–oxidized in the furnace

atmosphere. Thus, the produced zinc oxide particles are much smaller than other

elements in dust which are generated through bubble bursting or physical

entrapment.

Through these three series of simulations, the proposed model was confirmed to be a

powerful tool to design the process and determine the optimum operating conditions

for recycling an expanded range of dust and waste materials using the RHF process.

5.2 Future Work

• The simulation results with high–volatile coal and PE show the increase of internal

pressure of pellet during reduction; however, the exact pressure at which a pellet

breaks into small parts cannot be determined only by the model outputs since it

depends much on the physical and mechanical properties of the pellet. This

threshold pressure could be predicted through the careful comparison of the

model–derived maximum internal pressure and the experimentally observed pellet

behaviour as a function of pellet properties including porosity, composition,

apparent density and compressive strength. This information on the pressure limit

would be very useful to utilize high–volatile carbonaceous reductants to accelerate

the reduction reactions while avoiding the pellet decrepitation.

• Although calculation outputs discovered that PE cannot behave as a reductant for

dust pellet due to its low decomposition temperature, the released gas from PE

would combust outside the agglomerate. This combustion heat can contribute to

keeping the furnace temperature and, in turn, saving the fuel gas consumption

injected into the RHF. An overall materials and energy balance on the furnace

should be carried out for the cases where plastic is mixed into a dust pellet to

demonstrate the benefit of partially substituting the furnace fuel gas. Essentially, if

waste plastic replaces the furnace fuel, then the furnace acts as an effective

incinerator or gasifier. The gas generation rate from a plastic–mixed pellet

76

determined by the proposed pellet model can be used in the heat balance

examination.

• In addition to PE, there are several alternatives for non–coal reductants including

other plastic (PS, PET, polycarbonate, polyvinyl chloride, acrylonitrile butadiene

styrene), RDF, used tire, waste rubber and biomass. These may provide a more

important role in reduction than the studied PE because of their higher volatile

release temperature. The proposed model would be a beneficial tool to evaluate

how effectively a newly proposed waste plastic or reductant contributes to the dust

reduction reactions prior to the laboratory experiment or pilot–scale test. For that,

one needs to obtain the kinetic parameters of such materials and feed the data into

the model to investigate their effectiveness in reduction.

• The present model is able to simulate the reduction behaviour of zinc oxide in dust

by providing its proper particle size distribution. There are several constituents that

also come through different paths than the process of iron oxide particles when

they are entrained into dust in a melter. Such constituents include lead, potassium,

sodium, chlorine and fluorine, which play important roles in the dust recycling

process. Lead can be recovered in RHF in the same manner as zinc. On the

contrary, alkali metals and halogens have negative impacts on the process. They

will also be evaporated from a dust pellet into the furnace freeboard during

reduction. The released alkali metals would be absorbed into the furnace refractory

and could affect its stability. On the other hand, halogens could contaminate and

degrade the crude zinc oxide recovered from the exhaust gas of RHF. Including

relevant reactions in the model enables its use in investigating the behavior of these

constituents during RHF treatment.

77

6 Nomenclature

Ai coefficient for time–dependence equation of physical property

Cj fractional weight of solid component j

Ck concentration of gaseous component k (mol·m–3

)

Ck,f concentration of gas component k in furnace atmosphere (mol·m–3

)

Ck,1 concentration of gas component k in the first layer of pellet (mol·m–3

)

Cp specific heat (J·kg–1

·K–1

)

d diameter of pellet (m)

dc average diameter of imaginary tubes (m)

d50, j mass median diameter of solid component j (m)

Dk diffusion coefficient of gas component k (m2·s

–1)

Dkl diffusion coefficient of gas in two–phase system (m2·s

–1)

Dkl0 standard–state diffusion coefficient of gas in two–phase system (m2·s

–1)

Deff, k effective diffusion coefficient of gas component k in porous media (m2·s

–1)

Df diffusion coefficient of furnace atmosphere (m2·s

–1)

Ea activation energy (J·mol–1

)

fS surface adjustment factor

fSC surface adjustment factor for carbon gasification

Gk internal flow rate of gas component k (mol·s–1

)

∆H reaction heat (enthalpy) (kJ·mol–1

)

k reaction rate constant (m·s–1

)

k0 frequency factor (m·s–1

)

kC reaction rate constant for carbon gasification (m·s–1

)

kC0 frequency factor for carbon gasification (m·s–1

)

kV reaction rate constant for volatilization (s–1

)

kV0 frequency factor for volatilization (s–1

)

k0SCM frequency factor determined in a shrinking core model (m·s–1

)

kg mass transfer coefficient between furnace and pellet surface (m·s–1

)

kG coefficient in RGGS(x) equation (m)

kR coefficient in RRR(x) equation (m)

KE equilibrium constant

78

mkl coefficient in the equation for gas diffusion coefficient

mG coefficient in RGGS(x) equation

mR coefficient in RRR(x) equation

M molecular weight (kg·mol–1

)

MFe molecular weight of Fe, 55.845×10–3

(kg·mol–1

)

MFetO molecular weight of FetO, 68.885×10–3

(kg·mol–1

)

MFe3O4 molecular weight of Fe3O4, 231.535×10–3

(kg·mol–1

)

MFe2O3 molecular weight of Fe2O3, 159.690×10–3

(kg·mol–1

)

MO molecular weight of O, 16.000×10–3

(kg·mol–1

)

MVMi molecular weight of volatile matter i (kg·mol–1

)

n reaction rate (mol·s–1

·m–3

)

nC reaction rate of carbon gasification (mol·s–1

·m–3

)

nV reaction rate of volatilization (mol·s–1

·m–3

)

N the number of concentric layers

Nh the number of imaginary tubes

Np, j the number of solid particles of solid component j

Pt total pressure (Pa)

Pk internal partial pressure of gas component k (Pa)

∆Q rate of heat generated by reactions (J·s–1

·m–3

)

r pellet radius (m)

∆r thickness of each concentric layer (m)

R gas constant, 8.314 (J·K–1

·mol–1

)

RGGS percent passing calculated from Gates–Gaudin–Schumann equation (wt%)

RRR percent passing calculated from Rosin–Rammlar equation (wt%)

Rred reduction ratio of pellet with respect to iron oxides (wt%)

SBET BET surface area (m2·g

–1)

Sf surface factor used in a shrinking core model

Scross cross–sectional area of a partcile (m2)

Stotal total surface area of a partcile (m2)

Stotal, j total surface area of solid component j (m2)

Sreactant reaction front area of solid reactant (m2·m

–3)

79

Sproduct reaction front area of solid product (m2·m

–3)

Scarbon reaction front area of carbon (m2·m

–3)

Su Sutherland coefficient (K)

t retention time (s)

T temperature (K)

Tcentre temperature of pellet centre (K)

Tfurnace temperature of furnace (K)

Tsurface temperature of pellet surface (K)

T0 standard temperature for Sutherland equation (K)

vC velocity of gas in furnace atmosphere (m·s–1

)

V pellet volume (m3)

Vj volumetric fraction of solid component j in the solid portion of pellet

W pellet weight (kg)

Wj weight of solid component j in pellet (kg)

WVMi weight of remaining volatile matter i in pellet (kg)

x particle size (m)

xa threshold particle size for two RR equations (m)

xmin minimum particle size to calculate the total surface area (m)

xmax maximum particle size to calculate the total surface area (m)

Scf Schmidt number with respect to furnace atmosphere

Shf Sherwood number with respect to furnace atmosphere

Ref Reynolds number with respect to furnace atmosphere

α, β coefficients in the equation for effective thermal conductivity

ε emissivity of pellet surface

λ thermal conductivity (J·s–1

·m–1

·K–1

)

λj thermal conductivity of solid component j (J·s–1

·m–1

·K–1

)

λk thermal conductivity of gas component k (J·s–1

·m–1

·K–1

)

λsolid thermal conductivity of solid part of pellet (J·s–1

·m–1

·K–1

)

λgas thermal conductivity of gas part of pellet (J·s–1

·m–1

·K–1

)

80

λeff effective thermal conductivity (J·s–1

·m–1

·K–1

)

µf viscosity of gas in furnace atmosphere (kg·m-1

·s-1

)

µk viscosity of gas component k (kg·m-1

·s-1

)

µk0 standard viscosity of gas component k at temperature T0 (kg·m-1

·s-1

)

ρ density of solid (kg·m–3

)

ρf density of gas in furnace atmosphere (kg·m–3

)

ρj density of solid component j (kg·m–3

)

σ Stefan–Boltzmann constant, 5.670×10–8

(J·s–1

·m–2

·K–4

)

φ porosity

81

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8 Appendix: Publications and Presentations

8.1 Journal Articles

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Carbothermic Reduction

of Dust–Carbon Composite Agglomerates,” submitted to ISIJ Int., 2012.

8.2 Conference Proceedings

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Carbothermic Reduction

of Dust–Carbon Composite Agglomerates,” Proceedings of the 50th

Conference of

Metallurgists of the Metallurgy and Materials Society of the Canadian Institute of

Mining, Metallurgy and Petroleum, Montreal, Canada, October 2–5, 2011.

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Carbothermic Reduction

of Dust–Carbon Composite Agglomerates,” Proceedings of the AISTech 2012,

Atlanta, USA, May 7–10, 2012.

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Reduction Kinetics of

Zinc and Iron Oxides in Dust–Carbon Composite Agglomerates,” Proceedings of

the 4th

International Conference on Process Development in Iron and Steelmaking

(Scanmet IV), Luleå, Sweden, June 10–13, 2012.

8.3 Other Presentations

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Carbothermic Reduction

of Dust-Carbon Composite Agglomerates,” presented at the 23rd

Canadian

Materials Science Conference, Kelowna, Canada, June 22–24, 2011.

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Carbothermic Reduction

of the Dust–Carbon Composite Agglomerates,” presented at GMSI–COSM–UT2

Graduate Student Workshop, Toronto, Canada, June 9–10, 2011.

• Y. Kuwauchi and M. Barati, “A Mathematical Model for Carbothermic Reduction

of Dust–Carbon Composite Agglomerates,” presented at Graduate Research

Seminar, Department of Materials Science and Engineering, University of

Toronto, Toronto, Canada, October 20, 2011.