Seetharaman S. Fundamentals of metallurgy

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



 ÿD



rE C





v 7:132

A corresponding equation to equatio n 7.131 exists for the anode, but in this case

there are presumably no mass transfer effects, since there are no gradients for the

reactant Zn:

j

j 



2:3  log

 

7:133

The Ohmic resistances consist of the resistance to electrons in leads and contacts

and the resistance to ions in the electrolyte:

ohm

 R

lead

 R

contact

 R

electrolyte

7:134

The electrolyte resistance can be evaluated from the mobility of all ions present

and the geometry and size of the electrolyte. By solving equations 7.128 to

7.134, a short circuit current will be found and this current corresponds to the

corrosion current. From the corrosion current, the loss of Zn due to dissolution

can be readily computed, using Faraday's law.

Electrolytic Al production

Hall, an American, and Herault, a Frenchman, simultaneously engineered a

process to produce metallic aluminum from a molten salt based on cryolite

and alumina (Na

AlF

-Al

). This mixture forms a low melting eutectic

(approx. 1000 ëC) salt mixture as opposed to pure alumina, which melts above

2000 ëC.

At the cathode, Al is produced according to:

AlF

3ÿ

 3e  Al  6Fÿ (7.135)

At the anode:

2Al

2ÿ

 C

(s)

 12Fÿ   4 AlF

3ÿ

 CO

 4e (7.136)

and the overall cell reaction is:

2Al

 3C  4Al  3CO

(7.137)

In this case the net cell potential (E

cathode

ÿ E

anode

) is negative  ÿ1.2 V and

thus, external power is needed to drive the reaction. Examining Fig. 7.16b and

using Kirkhoff's law one obtains for this electrolysis cell:

imposed

 ÿE

cell

 j

anode

j  j

cathode

j  i 

ohmic

7:138

At the cathode, the mass transfer of ions is suggested to cause the overpotential

of approximately 0.46 V (Hayes, 1993). At the anode the step:

(s)

 2O

2ÿ

! CO

2(g)

4e (7.139)

is sluggish and causes an overpotential of 0.41 V.

316 Fundamentals of metallurgy

Ohmic losses, including electrolyte resistance contribute to 1.9 V. The

imposed cell potential thus amounts to about 4.4 V. When computing the energy

needed to produce a tonne of Al, this corresponds to about 250 GJ per tonne of

Al. This can be compared to the production of steel through the blast furnace

route, which cost s only roughly 30 GJ/tonne.

7.7 Gas±liquid reactions

There are several important cases where molten metals react with a gas phase

such as:

1. Metal droplets in reacting gases (e.g. during atomization).

2. Gas bubbles in melts (e.g. during purging during steelmaking).

3. Reaction between continuous gas and a metal phase (vacuum de-gassing or

reoxidation).

In general, the mass transfer depends on the flow in the two fluid phases and the

reaction kinetics depends on the nature of the interface.

7.7.1 Melt reoxidation

Reoxidation of a molten steel surface as a result of unwanted reaction between

reactive elements in melt with air is a cause of exogenous inclusions that can get

entrained into the melt and lead to lowering product quality (Farrell et al., 1970).

Melt reoxidation with air can take place at a number of locations in the

steelmaking process where the melt is temporarily expose d to the atmosphere. It

is likely to happen primarily (Lindenberg and Vorwerk, 1981) at melt surfaces

that happen to be uncovered in the ladle furnace, tundish or continuous casting

mold, or at refractory joints and nozzles between these three vessels. In the latter

case, reoxidation occurring at or near nozzles due to air aspiration can lead to

deposits on the walls that results in clogs that prevent a uniform steel melt flow

which degrades process control (Rastogi and Cramb, 2001). Sasai (Sasai, 2001;

Sasai and Mizukami, 2001) studied how reoxidation cause d by air leads to

build-up in the tundish nozzle, and found that during stable casting

modest reoxidation resulted solely from oxidation by air on the tundish bath

surface, whereas during teeming the reoxidation increased fivefold and was

caused primarily by oxidation at the tundish inlet.

The reoxidation process involves: (i) transport of oxygen to the melt, (ii)

mass transport in the melt (iii) precipi tation of the oxide phase and growth of the

oxide precipitate into a macro-inclusion.

Gas phase mass transfer to a melt has been extensively studied and

documented in the literature (e.g. Fruehan, 1998). Sasai and Mizukami (2000)

developed models based on experimental results (Sasai and Mizukami, 1996,

1998) to predict the melt reoxidation rates in the tundish based on gas phase

mass transfer through the tundish inlet and top covering tundish powder.

The kinetics of metallurgical reactions 317

Precipitation of the oxide phase follows a chemical reaction between metallic

elements in the melt (unreacted deoxidation reactants such as Al, Si or Ca and/or

Fe) and oxygen dissolved in the melt, and the thermodynamic basis of this

reaction is essentially similar to the much studied (Turkdogan, 1996)

deoxidation equilibrium that takes place in the ladle. It should, however, be

mentioned that, unlike deoxidation that occurs under isothermal conditions (at

about 1600 ëC) where thermodynamic data are abundant, reoxidation occurs

more often under significantly lower and often changing temperatures where

published interaction coefficient data are more scarce.

7.7.2 Melt evaporation

The evaporation of a solute, such as Mn, under near vacuum conditions, from a

melt can be controlled by one or a combination of the following factors:

1. Mass transfer from the melt to the surface:

J  k

C

ÿ C

 7:140

where, k

is the mass transfer coefficient and C

and C

are the solute

concentrations in bulk and interface respectively.

2. Evaporation kinetics (Richardson, 1974, p. 486):

J 

44  33A



C

ÿ p

ÿ 

7:141

where, M is the molecular mass,  is the vaporization constant,  is the

activity coefficient, p

is the vapor pressure over the pure solute and p

is the

impurity vapor pressure near the interface.

3. Gas phase mass transfer:

J 

ÿ p

ÿ 

7:142

where k

is the gas phase mass transport coefficient, and p

is the pressure

of the solute in the bulk gas.

7.7.3 Gas bubbles rising in metals

During gas purging, bubbles rise through a molten metal bath and react during

their ascent with solutes in the melt. The rate is determined by either mass

transport in the gas or melt or chemical reaction.

In the case of inert gas purging, where rising Ar bubbles absorb impurit ies, it

is possible that mass transfer inside the bubble can be the rate controlling step.

According to Bradshaw and Richardson (1970) the mass transfer coefficients in

the gas phase, for the case of N and H in ste el, were estimated to be half of the

mass transfer coefficients in the melt phase. In the cases of H or N where the gas

partial pressure in equilibrium with the melt is very low, this could result in a

318 Fundamentals of metallurgy

slow mass transport kinetics whereas for gases which have a higher equilibrium

pressure (CO), the concentration difference term will result in gas phase mass

transfer being less important.

Mass transfer in the melt phase

Gas bubbles encountered during purging in metallurgical processes are usually

larger than 1 cm in diameter. For such bubbles, if mass transport is assumed to

occur only across the cap of a rising cap-shaped bubble, the mass transfer

coefficient has been developed for the case of laminar flow over the cap (Baird

and Davidson, 1962):

k  0:975  d

ÿ1=4

1=2

1=4

7:143

Here, d is the equivalent spherical diameter, D is the diffusion coefficient in the

melt and g is gravity.

The resulting transf er rate of gas into the bubble is:

J  kC

ÿ C

 7:144

Here, C

and C

are the concentrations of the solute in the bulk melt and in the

melt at the bubble surface, respectively.

7.7.4 Foaming

Foams are widely used in the iron- and steelmaking processes since they provide

rapid refining of metal droplets held in the foam due to the enormous (surface

area/mass) ratio. Foaming slags are also used in electric arc furnaces (EAF) to

stabilize the arc and improve energy efficiency.

There is a general agreement (e.g., Cooper and Kitchener, 1959) that the

principal factors promoting foaming are:

· a low surface tension of slag (

) (P

, Na

O, oxide additions cause a

decrease in 

);

· high bulk and surface viscosities which retard draining of the slag film (P

and SiO

are both surface active and will congregate preferentially at the

surface and will tend to increase the surface viscosity);

· the presence of solids in the slag (since this will increase viscosity and tend to

lock the bubbles and prevent their escape);

· low temperature since this will increase slag viscosity and encourage the

formation of solids (a high solidification temperature of the slag would also

be beneficial);

· high surface elasticity.

Although there is a general agreement on the factors affecting foam stability

there is still some disagreement about the relative importance of the various

factors.

The kinetics of metallurgical reactions 319

7.7.5 Sulfide smelting and converting reactions

These reactions take place at sufficiently high temperatures, where the chemical

reactions are very rapid. Thus, the overall rate of the process is determined by

mass transfer between the gas and the molten phase. Further, in most operations,

the process is designed and operated under the conditions in which mass transfer

is also very rapid. Therefore, the overall rate is often determined by the supply

rate of the oxygen-containing process gas, which is dependent on other factors

such as heat generations and removal, erosion of refractory and gas injectors,

melt splashing and sloshing, etc.

The major reactions in sulfide smelting and converting steps are the oxidation

of sulfur and iron, as discussed in Section 7.2. Another critical factor is the

removal and distribution of minor elements. The rates of their removal also

depend on the injection rate of the process gas, but an important addi tional factor

in this respect is the equilibrium relationships that describe the distribution ratios

of the minor elements among the gas, slag, and matte or metal phases. The minor

element removal stops with the gas injection at the end of the iron and sulfur

removal. In the case of the fire-refining process in which the removal of the

impurities is the main objective, the process continues until the impurity

concentrations become sufficiently low. In both cases, the rate of impurity

removal is largely dependent on the gas supply rates and the thermodynamics of

impurity distribution. Much work has been done in this respect, and the reader is

referred to the literature for details (Nagamori and Sohn, 2000; Kim and Sohn,

1998a, 1998b, 1997, 1996; Chaubal and Nagamori, 1988; Nagamori and

Chaubal, 1982; Nagamori and Mackey, 1978).

7.8 Comprehensive process modeling

In traditional metallurgical process modeling, it was possible to incorporate only

the simplified aspects of fluid flow, mixing, and mass/heat transfer into the

analysis of process rates and reactor design. As a result, accurate and realistic

incorporation and simulations of many aspects of complex processes have not

been possible. With the advent of high-speed, high-capacity computing devices

and technologies, complex processes have become amenable to analysis and

modeling. This has also resulted in the merging of various disciplines in

formulating detailed descriptions of complex processes. Developments that

exemplify this in the field of metal lurgical process modeling are discussed in

this section.

7.8.1 Flash smelting process

The flash smelting process is important in the production of non-ferrous metals

from sulfide minerals. A schematic diagram of this process is given in Fig. 7.17.

In this process, fine, dried mineral particles and fluxes are injected into the

320 Fundamentals of metallurgy

furnace with industrial oxygen or oxygen-enriched air. The sulfide particles are

ignited and burn in the turbulent gas jet. The design and operation of a flash-

smelting furnace has largely remained an art, despite the fact that the process has

been in commercial use for a long time and is currently the dominant sulfide-

smelting process. This is mainly due to the difficulty of quantifying the comple x

interactions of the individual sub-processes, i.e. the turbulent fluid flow,

convective heat and mass transfer, chemical reactions, and radiative heat transfer.

A reliable mathematical model starts with good understanding of identifiable

component processes followed by assembling them into the overall description

of the process. The model equations are written based on the continuity of mass

and the conservation of momentum and energy for the gas and the particle

phases (Hahn and Sohn, 1990a; Perez-Tello et al., 2001b). The time-averaged

equations for the conservation of fluid prope rties can be expressed in the

following general form:

r  

v ÿ r  ÿ



r  S



7:145

where  is the dependent variable, ÿ



is the coefficient for the diffusive transfer,

and S



is the source term. Table 7.1 shows all the gas phase governing equations.

The particle phase is often described using the Lagrangian framework, the

governing equation being listed in Table 7.2. Further details of the model equations

can be found elsewhere (Hahn and Sohn, 1990a; Perez-Tello et al., 2001b).

The next sub-process to include is the gas±particle reactions, i.e. the oxida-

tion of sulfur and iron in the mineral particles. To describe the ignition transient

as well as the main combustion period following the ignition, information on the

intrinsic kinetics of the mineral particle oxidation is needed. This information is

preferably obtained by carrying out separate experiments (Chauba l and Sohn,

1986). Appropriate measures must be taken to ensure the determination of the

intrinsic kinetics.

The ability of the com puter model to describe the dispersion of the particles

in the turbulent gas jet of a flash-smelting furnace shaft was verified by the use

of a non-reacting model system (Yasuda and Sohn, 1995). Sohn and co-workers

7.17 Schematic diagram of a flash smelting process.

The kinetics of metallurgical reactions 321

Table 7.1

Gas phase equations





























ÿ



@

 



@

 



@

 

 S



Equation



Continuity

1 0

(A-1)

x-Momentum







 





 





 







k 





 S

(A-2)

y-Momentum







 





 





 







k 





 S

(A-3)

z-Momentum







 





 





 







k 





 S

(A-4)

Turbulent kinetic energy



=

G ÿ







(A-5)

Dissipation rate

 

=



=kC

G ÿ C







(A-6)

Sulfur mass fraction



=

(A-7)

Reacted oxygen ratio

 

=



(A-8)

Enthalpy



=

 Q















(A-9)

where:

G 



 





 





 









 









 









 

(

)

(A-10)



 

 

(A-11)



 C





=

(A-12)

 S

ÿ S



(A-13)

(Perez-Tello et al., 2001a; Sohn and Seo, 1990; Sohn et al., 1988) carried out

experiments in a laboratory flash furnace under various operating conditions

and compared the results with the experimental data (Hahn and Sohn, 1990a;

Perez-Tello et al., 2001b). They also verified their model results against the

independent measurements obtained in a pilot plant by Outokumpu personnel

(Hahn and Sohn, 1990a), providing further evidence of the reliability of the

mathematical model. The mathematical model provides a realistic

representation of the process because it is built based on either first principles

or well-established correla tions for i ndividual sub-processes de velope d

independently. One can thus use the mathematical model with much greater

confidence to describe, analyze, and design the sulfide-smelting proce sses. An

example is the application of this mathematical model to the description of

minor-element behavior (Seo and Sohn, 1991), which is an important problem

in any smelting process.

Figure 7.18 shows a typical comparison between the model predictions and

laboratory measurements in terms of the SO

concentration in the gas and sulfur

content in the particles at various axial positions along the centerline of the

furnace shaft (Hahn and Sohn, 1990a). The discrepancy toward the bottom of the

furnace is due to the air leaking into the furnace through an opening through

which the sample probe is inserted. It is particularly noteworthy that the model

adequately predict s the particle ignition point, after which the reaction is very

fast. A similar comparison between the model predictions and measurements

obtained by Outokumpu Co. in their pilot plant is shown in Fig. 7.19. The top

figure shows the SO

and O

concentrations along the central axis from the

burner, as well as the amount of oxygen used in the oxidation of metal contents.

The second graph is for the case in which the feed gas was preheated.

Considering the complexity of the process and the fact that the pilot-plant

measurements were made completely independently from our computation, the

agreement is noteworthy. The botto m graph compares the temperature profiles

for these two cases.

Table 7.2 Particle phase equations

Motion m

dhVi

 m



jhUi ÿ hVijhUi ÿ hVi  m

ÿ m

g (B-1)

Particle

dispersion 

t  2

t

i

ddt

(B-2)

(cloud

model)

Species

mass



jq

j1

i;j

ÿ R

(B-3)

balance

Energy

m

  H

 Q

ÿ Q

ÿ H

(B-4)

The kinetics of metallurgical reactions 323

7.8.2 Fluidized-bed reactors for gas±solid reactions

In a fluidized-bed reactor, the solid particles are dragged upward as clouds or

wakes by the gas bubbles and descend by gravity in the emulsion phase, as

shown in a schematic representation in Fig. 7.20. Fresh particles may be fed

continuously to the bed and discharged either through an overflow pipe or by

entrainment of gases. Particle size and density may change, and particles of the

same size have different residence time in the bed. All of these must be

accounted for in order to predict and control the behavior of the solids in a

fluidized-bed process.

Zhou and Sohn (1996) investigat ed the fluidized-bed chlorination of rutile by

CO±Cl

mixtures, using the bubble assemblage model to describe the bed

behavior with sever al new features. An experimentally determined, particle-

size-dependent reaction-rate expression of the chlorination kine tics was

incorporated to calculate the concentration profile of reactant gases in the

bed. This rate expression is more realistic than those previously used (Youn and

Park, 1989; Fuwa et al., 1978). The particle-size distribution in the bed was

7.18 Comparison of the computed and measured results along the centerline of

a laboratory flash furnace shaft. (Conditions for the tests are given in Hahn and

Sohn (1990a).)

324 Fundamentals of metallurgy

calculated by a population balance. The model assumes that the solid particles

are well mixed throughout the bed, but the gas concentrations vary with the bed

height. This makes the model applicable to industrial application where the

concentrations of reactant gases may change substantially along the bed height.

The gases flow through the bubble and emulsion phases, while exchanging

mass between the phase s. The gas-phase mass balances in these two phases can

be expressed as follows:

ÿf

g;b

 K

C

ÿ C

  f

g;b

ÿr

g;b

 7:146

ÿf

g;e

 K

C

ÿ C

  f

g;e

ÿr

g;e

 7:147

where f

g;j

is the fraction of the bed volume occupied by gas in phase j; K

is the

interchange coefficient for gas between the bubble and the emulsion phases

based on the bubble volume; and r

i;j

is the consumption rate of reactant gas i per

7.19 Comparison of the computed and measured results along the centerline of

an Outokumpu pilot flash furnace shaft. (O

(Me

) denotes the percent of

input O

consumed to produce metal oxides. Conditions for the tests are given

in Hahn and Sohn (1990a).)

The kinetics of metallurgical reactions 325