Application of Gibbs Energy minimization to Oxygen Steelmaking Process

Ajay Kumar ShuklaDepartment of Metallurgical and Materials EngineeringIndian Institute of Technology, MadrasChennai 600036

Prof. Brahma DeoDepartment of Materials and Metallurgical EngineeringIndian Institute of Technology, Kanpur 208016

Variation of metal composition duringBOF steelmaking process

Variation of metal composition duringQ-BOP steelmaking process

FeO level in the slag for (1) Top blown BOF steelmaking process and(2) blown Q-BOP steelmaking process

Variations of Oxygen Steelmaking top vs Bottom blowingCourtesy: Steelmaking by V. Kudrin

Sequence of reactions in an oxygen steelmaking system

Liquid metal

Slag +metal droplets+ gas bubbles

Emulsion of metal and slag+ gas bubbles

Gas + droplets of metal + droplets of slag

Gas bubbles

Oxygen supply

Let the metal phase contain[C], [Si],[P] and [O] in dissolved state.

The slag phase contains CaO, FeO,SiO2 and P2O5.

The gas phasecontains CO,CO2and O2.

)1(.

..

..

..

...

..

2222

5252

22

COCO

OOCOCO

CaOCaOOPOP

FeOFeOSiOSiO

OOPPFeFe

SiSiCC

Gn

GnGn

GnGn

GnGn

GnGnGn

GnGnG

Representation of BOF steelmaking process as fully mixed freeenergy minimization system

Annn COCOC 2Bnn SiOSi 2

Cnn FeOFe Dnn OPP 52.2

EnCaO

(2)

Total Gibbs freeenergy of the systemIs given as:

It is subject to the following mass conservation constraints:

(3)

(4) (5)

(6)

)7(22

.522

52

22

OXYOOP

FeOSiOCO

CO

Nnn

nnn

n

In a fully mixed system, the equation (1) has to be minimized subject to the constraints (2) – (7). Let a function G’ be defined such that all the equality constraints are added to equation (1)by using Lagrange multipliers:

OXYOOPFeO

SiOCOCO

CaO

OPP

FeOFe

SiOSi

COCOC

COCOOOCOCO

CaOCaOOPOP

FeOFeOSiOSiO

OOPPFeFeSiSiCC

Nnnn

nnn

EnDnn

CnnBnn

AnnnGnGnGn

GnGn

GnGn

GnGnGnGnGnG

22.5

2

2.

).().2.(

).().(

).(...

..

..

.....

52

22

6

5

524

3

22

21

2222

5252

22

(8)

In order to have minima for G, the following conditions should be satisfied:

0

inG 0

i

G

This, in turn, results in the following equations:

01 CG

02 SiG

03 FeG

04 PG

05 CaOG 0622 SiOG

026

3 FeOG 0

2.5.2 6

452 OPG

026

1 COG 0612 COG

026

OG

(9) (10)

(11)(12)

(13) (14)

(15)(16)

(17)(18)

(19)

Equations (9) to (14) give:CG1 SiG2

FeG3 PG4

CaOG5 26 SiOSi GG

Plugging these values in Equations (15)-(19),

0.21

2 SiOSiFeFeO GGGG

0.25.2 252 SiOSiPOP GGGG

0.21

2 SiOSiCCO GGGG

022 SiOSiCCO GGGG

0.21

2 SiOSiO GGG

Equations (20)-(24) imply that ΔG 0 for the following chemical reactions while the system marches towards minimum free energy:

(FeO) + 0.5[Si] = 0.5 SiO2 + [Fe] (A) (P2O5 )+ 2.5[Si] = 2.5 SiO2 + 2 [P] (B){CO} + 0.5[Si] = 0.5 SiO2 + [C] (C) {CO2} + [Si] = SiO2 + [C] (D) 0.5 [Si] + [O] = 0.5 (SiO2) (E)

(20)

(21)

(22)

(23)

(24)

Similarily ΔG 0 for the following reactions also:

[Fe] + [O] = (FeO) (F) [C] + [O] = {CO} (G) [C] + 2[O]={CO2} (H) {CO2} + [C] = 2{CO} (I) (FeO) + [C] = {CO} + [Fe] (J) 2.5 (FeO) + [P] = 0.5 P2O5 + 2.5 [Fe] (K)

Suppose that oxygen is added to the metal bath. The free energy of reactions (E),(F) and (G) before supplying oxygen is given as:

)25(0].[.].[

.ln 5.0

5.022

eqoSi

SiOSiO

oSiSi

OfSifX

RT

GG

After supply of little bit oxygen the free energy of reaction (E) becomes:

)][].([.].[.

ln 5.0

5.022

SieqoSi

SiOSiO

oSiSi

OOfSifX

RT

GG

(26)

From Equations (25) and (26), the following equation is derived:

1exp][][

RTG

OO Si

eq

Si

The oxygen dissolved in excess of equilibrium amount will be consumed andfree energy of reaction (26) will tend towards zero.

Similarly, if we consider reactions (F) and (G),

1exp][][

RTG

OO Fe

eq

Fe

1exp][][

RTG

OO C

eq

C

(27)

(28)

(29)

From equations (27),(28) and (29)it turns out that supplied oxygenWill distribute itself in the ratio of :

1exp

RTGreac

RTGifRTG

reacreac

Or,

Metal Reactor

Reactions occurs under jet impact zone:

(a) Dissolution of oxygen under jet impact zone

O2 = 2 [O] [A]

[C] + [O] = {CO} [B][Fe] + [O] = (FeO) [C][Si] +2 [O] = (SiO2) [D]

(b) Oxidation of impurities by dissolved oxygen in previous step

Steps of calculations in partially mixed reactor

Free energies of reactions B,C and D are defined as:

OC

o

aaPCORTCGGC

.ln.11

O

FeOo

aa

RTFeGGFe ln.11

2

2

.ln.11

OSi

SiOo

aaa

RTSiGGSi

12111

11

GSiGFeGC

GCxC

12111

121

1

GSiGFeGC

GSixSi

Distribution of oxygen occurs in the ratio of the free energies:

1.22400

2..2.100

_][C

C

C

xFO

MHMWt

dtCd

1.22400

2..2.100

_][2 SiSi

Si

xFO

MHMWt

dtSid

Finally rate equations for the removal of [C] and [Si] become as:

Slag-metal ReactorIron oxide in slag is reduced by following reactions:

[C] + (FeO) = {CO} + [Fe] [E][Si] + 2(FeO) = (SiO2) + 2[Fe] [F]

Free energies of reactions E and F are defined as:

FeOC

o

aaPCORTCGGC.

ln.22

2

2

.ln.22

FeOSi

SiOo

aaa

RTSiGGSi

Distribution of FeO occurs in the ratio of the free energies:

2212

22

GSiGC

GCxC

2212

221

2

GSiGC

GSixSi

Rate equations for the removal of [C] and [Si] by above mechanism:

2.22400

2..2.100

_][C

C

C

xFO

MHMWt

dtCd

2.22400

2..2.100

_][2 SiSi

Si

xFO

MHMWt

dtSid

SiC ,Efficiency factors ( ) are assumed to vary as a function of total mixingenergy of the bath as follows: no

totalSiC Efactorefficiency ),(

Slag-metal-gas (emulsion) Reactor

{CO} + (FeO) = [Fe] + {CO2} [G]

Formed by metal droplets, rising gas bubbles and liquid slag:

FeOCO

COFeOCO aP

PK

.2

Post combustion ratio (PCR) inside the vessel is defined as:

Lime dissolution

FeOCaOcao aAkdt

dCaO ..

Rate of lime dissolution depends upon activity of FeO in slag:

Scrap dissolution

Figure 1.2 :Schematic diagram of temperature and composition profile in scrap and metal

Solves coupled heat transfer and mass transfer (of carbon) to predict the velocity of moving boundary

0

)(

xdX

dTTiTbhHv

ttxT

xtxT scsc

),(),(2

2

v(Ci-Cs)=k(Ci-Cb)

Accuracy of the model is validated by fundamental Green’s function approach

Calculations steps using FactSage

Calculation results using FactSage 6.2The Equilibrium module was used for the open system where a feed equivalentto the oxygen, lime and scrap equivalent to one second is given for 1000 steps.FTOxid database was used for slag solution, FTmisc was used for liquid metal and Fact53 was used for gaseous phase.

Decarburization rate vs blowing time

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 200 400 600 800 1000 1200

Blowing time (sec)

Dec

arbu

rizat

ion

rate

(%/m

in)

Slag composition vs blowing time

0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1000 1200

Blowing time (sec)

(%)

% FeO% CaO% SiO2

C% vs blowing time

0

0.51

1.5

22.5

3

3.5

44.5

5

0 200 400 600 800 1000 1200

Blowing time (sec)

C (%

)

Si% vs blowing time

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 100 200 300 400 500

Blowing time (sec)

Si (%

)

P% vs blowing time

0

0.010.02

0.030.04

0.05

0.060.07

0.080.09

0.1

0 200 400 600 800 1000 1200

Blowing time (sec)

P (%

)

C% vs O%

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5

C (%)

O (%

)

Calculation Results using FactSage 6.2 (continued)

Results of partially mixed reactor

The calculations are done for a fully mixed system with the following initial conditions:Hot metal = 150 tons, Si_HM = 0.8%, C_HM=4.5%, P_HM = 0.1%, Temperature of hot metal = 1300 C. Oxygen flow rate = 500 NM3/min, Lime dissolution rate = 1 ton/min and scrap dissolution rate = 1 ton/min.

Decarburization rate for different levels of oxygen supersaturation in the bath

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 200 400 600 800 1000 1200

Blowing time (sec)

d[C

]/dt

(%/m

in)

10 ppm 50 ppm100 ppm 200 ppm300 ppm 500 ppm1000 ppm 2000 ppm

FeO level in the slag for different level of oxygen supersaturation in the bath

0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1000 1200

Blowing time (sec)

FeO

(%)

10 ppm 50 ppm100 ppm 200 ppm300 ppm 500 ppm1000 ppm 2000 ppm

FeO level in the slag for different levels of oxygen supersaturation for fully mixed system

Predictions for a partially mixed oxygen steelmaking reactor

% decarburization due to droplets for different levels of oxygen supersaturation in the bath

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700 800

Blowing time (sec)

% d

ecar

buriz

atio

n du

e to

dro

plet

s

100 ppm 200 ppm300 ppm 600 ppm1500 ppm 2000 ppm

FeO level in the slag for different level of oxygen supersaturation in the bath

0

5

10

15

20

25

30

35

40

45

50

50 250 450 650 850

Blowing time (sec)

FeO

(%)

100 ppm 200 ppm300 ppm 600 ppm1500 ppm 2000 ppm

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 200 400 600 800 1000 1200

Blowing time (sec)

d[C

]/dt (

%/m

in)

d[C]/dt (%/min) -directd[C]/dt (%/min)-indirectd[C]/dt(total)

Time vs %FeO

0102030

40506070

0 200 400 600 800 1000 1200time(s)

% F

eO

0% heavy scrap10% heavy scrap25% heavy scrap50% heavy scrap75% heavy scrap90% heavy scrap100% heavy scrap

%FeO for different scrap ratios

Time vs PCR waste gas

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000 1200time(s)

PCR

was

te g

as 0% heavy scrap10% heavy scrap25% heavy scrap50% heavy scrap75% heavy scrap90% heavy scrap100% heavy scrap

PCR for different scrap ratios

Time vs size of heavy scrap

0

0.05

0.1

0.15

0.2

0 200 400 600 800 1000 1200time (s)

Hal

f Thi

ckne

ss (m

) 10% heavy scrap25% heavy scrap50% heavy scrap75% heavy scrap90% heavy scrap100% heavy scrap

Heavy scrap size for different scrap ratios

Light scrap size for different scrap ratios

Temperature for different scrap ratios

Decarburization rate for different Scrap ratios

700

900

1100

1300

1500

1700

1900

0 1 2 3 4 5

0% heavy scrap10% heavy scrap25% heavy scrap50% heavy scrap75% heavy scrap90% heavy scrap100% heavy scrap

C-T trajectory for different ratios of heavy vs light scrap.

CONCLUSIONSA fundamental study of oxygen steelmaking process based upon Gibb’senergy minimization technique, and also through FactSage, has been done for the case of a fully mixed reactor.

The trend of results of free energy minimization are similar to an actualprocess in the middle blow period, implying that both BOF and OBM processes are close to equilibrium during the middle part of blow.

The difference of results (based upon Gibb’s energy minimization) and theactual process can be attributed to the lack of mixing and gradual changein extent of mixing during initial and final part of the process.

The predicted indirect decarburization (due to droplets) is of the order of10-25% during middle blow period and approximately 30% during endblow period.

Dephosphorization process cannot be explained adequately by free energycalculations because mass transfer in slag phase is important in that case. Mixing in metal phase cannot do much however extended surface area ofslag-metal due to droplets thrown in slag phase help this to a great extent.

Good agreement with the practical observations on the shopfloor. The model is integrated with the scrap dissolution model which is based uponcoupled heat and mass transfer. The computed results are similar to thepractical observations.

The model can be used as a simulation tool to study the effectof various parameters. Further testing on extensive plant data required.

AcknowledgementsNational Metallurgical Laboratory for Fact-Sage thermodynamic software

Thanks….