A Thermodynamic Model of Phosphate Capacity 2 O -MnO-Al O -P …student.sut.ac.th/sakhob/DeP/fulltext.pdf · 2011-07-23 · literatures. The results from the IMCT phosphate capacity

A Thermodynamic Model of Phosphate Capacityfor CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 SlagsEquilibrated with Molten Steel during a Top–BottomCombined Blown Converter Steelmaking Process Basedon the Ion and Molecule Coexistence Theory

XUE-MIN YANG, CHENG-BIN SHI, MENG ZHANG, JIAN-PING DUAN,and JIAN ZHANG

A thermodynamic model for predicting the phosphate capacity of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags at the steelmaking endpoint during an 80-ton top–bottom combinedblown converter steelmaking process has been developed based on the ion and moleculecoexistence theory (IMCT). The phosphate capacity has a close relationship with the phosphatecapacity index, whereas the logarithm of phosphate capacity is 12.724 greater than that ofphosphate capacity index at 1873 K (1600 �C). The developed phosphate capacity predictionmodel can be also used to predict the phosphate capacity index with reliable accuracy comparedwith the measured and the predicted phosphate capacity index of the slags by other models inliteratures. The results from the IMCT phosphate capacity prediction model show that thecomprehensive effects of iron oxides and basic components control the dephosphorizationreaction with an optimal ratio of (pct FeO)/(pct Fe2O3) as 0.62. The determined contributionratio of FetO, CaO+FetO, MgO+FetO, and MnO+FetO to the phosphate capacity orphosphate capacity index of the slags is approximately 0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct,respectively. The generated 2CaOÆP2O5, 3CaOÆP2O5, and 4CaOÆP2O5 as products of dep-hosphorization reactions accounts for 0.016 pct, 96.01 pct, and 3.97 pct of the phosphatecapacity or phosphate capacity index of the slags, respectively.

DOI: 10.1007/s11663-011-9527-0� The Minerals, Metals & Materials Society and ASM International 2011

I. INTRODUCTION

IN a conventional steelmaking process arrangement,dephosphorization is an important metallurgical func-tion of a top–bottom combined blown converterbecause the subsequent secondary refining processcannot provide additional phosphorus removal. The

phosphorus distribution ratio LP ¼ ðpct P2O5Þ�½pct P]2;

L0 0P ¼ ðpct PO3�

4 Þ�½pct P]; or L000P ¼ ðpct P2O5Þ=½pct P] has

been widely used to express the phosphorus removalability of a slag because of its simple meaning and

because it can be calculated easily. The dephosphoriza-tion potential of a slag has been defined by Wagner[1] inthe 1970s as phosphate capacity CPO3�

4or phosphide

capacity CP3� based on slag–gas equilibrium; similarly,the phosphate capacity index CPO3�

4 ;index has been also

proposed by Yang et al.[2,3] in the 1990s and applied bymany researchers based on slag–metal equilibrium. Itshould be emphasized that the phosphate capacity indexCPO3�

4 ;index can be easily confused with phosphate capacity

CPO3�4: Therefore, the phosphate capacity index CPO3�

4 ;index

is used to distinguish phosphate capacity CPO3�4

and

phosphate capacity index CPO3�4 ;index in this article.

Large amounts of phosphate capacity CPO3�4

data forvarious slags have been measured based on slag–gasequilibrium reaction since the 1970s after it was pro-posed by Wagner[1]; meanwhile, a lot of phosphatecapacity index CPO3�

4 ;index data have been also measuredbased on slag–metal equilibrium reaction, althoughsome researchers did not distinguish the concept ofphosphate capacity CPO3�

4and phosphate capacity index

CPO3�4 ;index.

[4–9] Some prediction models for calculatingphosphate capacity CPO3�

4and phosphate capacity index

CPO3�4 ;index had been developed, such as Selin’s model[10]

for CaO-SiO2-CaF2 slags, Mori’s model[11] forCaO-MgO-SiO2-FetO slags, Suito’s model[6,12] for

XUE-MIN YANG, Research Professor, is with the State KeyLaboratory of Multiphase Complex Systems, Institute of ProcessEngineering, Chinese Academy of Sciences, Beijing 100190, P. R.China. Contact e-mail: [email protected] CHENG-BINSHI, Ph.D. Candidate and Joint-Training Student, and MENGZHANG, Master Degree Student and Joint-Training Student, arewith the School of Metallurgical and Ecological Engineering,University of Science and Technology Beijing, Beijing 100083, P. R.China, and with the Institute of Process Engineering, ChineseAcademy of Sciences. JIAN-PING DUAN, Senior Engineer, is withthe Technology Center, Shanxi Taigang Stainless CorporationLimited, Taiyuan 030003, P. R. China. JIAN ZHANG, Professor, iswith the School of Metallurgical and Ecological Engineering,University of Science and Technology.

Manuscript submitted March 5, 2011.

METALLURGICAL AND MATERIALS TRANSACTIONS B

CaO-MgO-FetO-SiO2 slags, Young’s models[13] forCaO-SiO2-MgO-MnO slags, and Kunisada’s model[14]

for soda-based slags. It should be emphasized that theoriginal meaning of the applied CP3�;index ¼ ðpct P)=½pct P] � ½pctO]5=2 in Suito’s model as well as in Young’smodel is different from the defined phosphate capacityCPO3�

4by Wagner[1] or phosphate capacity index

CPO3�4 ;index by Yang et al.[2,3] All these prediction mod-

els were developed from mathematical regression ofexperimental data rather than based on the dephosph-orization reaction according to metallurgical physico-chemistry. Thus, developing a universal model isimportant and interesting to the presentation of phos-phate capacity CPO3�

4or phosphate capacity index

CPO3�4 ;index for various slags.

The ion and molecule coexistence theory (IMCT) hasbeen developed to express the reaction ability ofcomponents in a slag by the defined mass actionconcentration Ni according to the mass action law, likethe traditionally applied activity ai of component i.[15–21]

The meaning of mass action concentration of a struc-tural unit or an ion couple is defined[22–30] as the molefraction under the equilibrium condition of a slagsystem. To expand the application fields, IMCT[22–30]

has been successfully used to predict sulfur distributionratio LS between CaO-SiO2-MgO-Al2O3 blast furnaceironmaking slags and hot metal,[22] the sulfide capacityCS2� of CaO-SiO2-MgO-Al2O3 blast furnace ironmakingslags,[23] the sulfur distribution ratio LS between CaO-SiO2-MgO-FeO-MnO-Al2O3 ladle refining slags andmolten steel,[28] the sulfide capacity CS2� of CaO-SiO2-MgO-FeO-MnO-Al2O3 ladle refining slags,[29] and thephosphorus distribution ratio LP between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 converter steelmak-ing slags and molten steel.[30] Under these circumstances,a thermodynamic model for predicting phosphatecapacity CPO3�

4of CaO-SiO2-MgO-FeO-Fe2O3-MnO-

Al2O3-P2O5 slags at the steelmaking endpoint during atop–bottom combined blown converter steelmakingprocess has been developed according to IMCT[22–30]

based on the previously mentioned investigation accu-mulations on IMCT.[22–30]

To clarify the difference between phosphate capacityand phosphate capacity index, the relationship betweenphosphate capacity and phosphate capacity index wasfirst deduced, the relationship between the phosphatecapacity or phosphate capacity index and the phospho-rus distribution ratio LP ¼ L

0P ¼ ðpct P2O5Þ

�½pct P]2; or

L0 0P ¼ ðpct PO3�

4 Þ�½pct P]; or L000P ¼ ðpct P2O5Þ=½pct P] has

been also established. The predicted phosphate capacityor phosphate capacity index of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags at the steelmaking end-point during a top–bottom combined blown convertersteelmaking process by the developed IMCT CPO3�

4prediction model was compared with the measuredphosphate capacity or phosphate capacity index, as wellas the calculated phosphate capacity or phosphatecapacity index by other models, such as Selin’s model,[10]

Mori’s model,[11] Suito’s model,[6,12] and Young’smodel.[13] The contribution ratio of each structural unitcontaining P2O5 to the total phosphate capacity C

PO3�4

or phosphate capacity index CPO3�4 ;index of the slags was

also determined from the developed IMCT CPO3�4model.

The influences of mass percent for components or massaction concentrations for structural unit or ion couples,ratio of mass percent, or mass action concentration ofiron oxides to that of basic components, slag basicityincluding binary basicity as well as complex basicity,and optical basicity on phosphate capacity CPO3�

4or phos-

phate capacity index CPO3�4 ;index for the slags were also

discussed. The ultimate aim of this study is to develop auniversal phosphate capacity CPO3�

4or phosphate capac-

ity index CPO3�4 ;index prediction model for various slags in

different metallurgical reactors or processes; further-more, it provides the theoretical fundamentals to opti-mize chemical compositions of metallurgical slags withthe maximum dephosphorization potential.

II. PHOSPHATE CAPACITY DATA OFCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

STEELMAKING SLAGS

The industrial tests were carried out in a routine 80-ton top–bottom combined blown steelmaking converterat the No. 2 Steelmaking Plant of Shanxi TaigangStainless Steel Corporation Limited. The detailed oper-ation parameters have been briefly introduced in aprevious paper.[30] The total charged metallic rawmaterial is approximately 89 tons containing 83 tonsof the pretreated hot metal, i.e., by desiliconization,dephosphorization, and desulphurization, and 6 tons ofscraps. The average mass of slag-forming materialsincludes about 4900-kg lime, 2800-kg light-burneddolomite, 360-kg laterite, and 500-kg pellets of converterred mud in each heat. The samples of both slag andmetal were sampled at the steelmaking endpoint duringsteelmaking of typical low-carbon steel. The normalizedchemical compositions of both slags and metal with thedefinite temperature T for 27 heats are listed in Table Ias that reported elsewhere.[30] The measured phosphatecapacity CPO3�

4 ;measured of the slags is calculated from themeasured phosphorus distribution ratio between theslags and molten steel at the steelmaking endpoint of the80-ton top–bottom combined blown steelmaking con-verter, i.e., LP;measured ¼ ðpct P2O5Þ

�½pct P]2; through the

relationship between CPO3�4

and LP described in detail inSection III–B.

III. FUNDAMENTAL THEORY OF PHOSPHATECAPACITY AND PHOSPHATE CAPACITY

INDEX OF SLAGS

A. Relationship between Phosphate Capacityand Phosphate Capacity Index

Phosphorus will exist as phosphate PO3�4

� �or phos-

phide P3�� in slags according to oxygen potential of

slags. A large enough oxygen potential of slags will

promote the formation of phosphate PO3�4

� �in slags;

otherwise, phosphide P3�� will account for most of

phosphorus in slags. The formation reaction of


phosphate PO3�4

� �or phosphide P3��

in slags can bepresented as follows:

1

2P2 gð Þ þ 5

4O2 gð Þ þ 3

2O2��

¼ PO3�4

� �pO2

>10�13Pa

½1�

1

2P2 gð Þ þ 3

2O2��

¼ P3�� þ 3

4O2 gð Þ pO2

<10�13Pa

½2�

The concept of phosphate capacity CPO3�4

was firstdefined and proposed by Wagner[1] based on gas–slagreaction shown in Eq. [1] as

CPO3�4� ðpct PO3�

4 ÞpO2

=pHð Þ5=4 pP2=pHð Þ1=2

�ð Þ ½3�

Similar to the defined phosphate capacity CPO3�4; the

phosphide capacity CP3� can be defined and proposedaccording to gas–slag reaction in Eq. [2] as[2,31]

CP3� �ðpct P3�Þ pO2

�pH

� �3=4

pP2=pHð Þ1=2

ð�Þ ½4�

The oxygen potential of slags at the endpoint during atop–bottom combined blown converter steelmakingprocess is controlled by [Fe]–(FetO) equilibrium

reaction, whereas the equilibrium oxygen potential of[Fe]–(FetO) is much greater than 10�13 Pa. Therefore,most phosphorus in converter steelmaking slags exists asphosphate PO3�

4

� �.

The dephosphorization reaction at slag–metal inter-face is usually described as

P½ � þ 5

2O½ � ¼ 1

2P2O5ð Þ

DrGHm;P2O5

¼ �352721:753þ 278:253T½32� J=molð Þ [5a]

The equilibrium constant KHP2O5

of reaction in Eq. [5a]can be presented as

KHP2O5¼

a1=2P2O5

aPa5=2O

�ð Þ ½5b�

Replacing P2O5 activity aP2O5by the definition of

mass action concentration NP2O5¼ nP2O5

=P

ni ¼ðpct P2O5Þ= MP2O5

Pnið Þð Þ according to IMCT,[22–30]

the formula of KHP2O5

in Eq. [5b] can be rewritten as

KHP2O5¼

N1=2P2O5

aPa5=2O

¼ ðpct P2O5Þ1=2

½pct P�fP½pctO�5=2f5=2O M1=2P2O5

Pnið Þ1=2

�ð Þ [5c]

Table I. Chemical Compositions of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags and Molten Steel at the Steelmaking

Endpoint during an 80-Ton Top–Bottom Combined Blown Converter Steelmaking Process for 27 Heats

TestNo.

Chemical Composition of Slags (mass pct)Chemical Composition of Molten Steel (mass

pct)

T K (�C)CaO SiO2 MgO FeO Fe2O3 MnO Al2O3 P2O5 [C] [Si] [Mn] [P] [S] [O]

1 40.02 12.12 6.20 14.23 23.04 0.73 2.41 1.25 0.061 <0.01 0.025 0.006 0.018 0.045 1949 (1676)2 36.20 10.17 6.19 16.47 27.15 0.67 2.14 1.01 0.028 <0.01 0.015 0.007 0.017 0.097 1951 (1678)3 42.28 11.53 6.37 13.56 21.93 0.82 2.09 1.42 0.044 <0.01 0.030 0.008 0.014 0.062 1953 (1680)4 36.24 9.10 6.57 15.48 27.59 0.97 2.72 1.34 0.021 <0.01 0.029 0.011 0.016 0.130 1986 (1713)5 49.17 10.22 9.25 10.11 16.31 0.81 2.79 1.34 0.035 0.015 0.037 0.011 0.015 0.078 1949 (1676)6 43.30 12.02 8.03 11.87 19.28 0.96 3.00 1.54 0.030 <0.01 0.040 0.012 0.013 0.091 1943 (1670)7 46.86 16.22 7.50 9.76 14.87 0.82 2.31 1.66 0.042 0.014 0.057 0.019 0.010 0.065 1949 (1676)8 46.07 15.36 6.50 10.86 16.18 0.96 2.37 1.70 0.032 <0.01 0.044 0.014 0.021 0.085 1948 (1675)9 48.96 16.75 7.49 9.06 13.65 0.86 1.70 1.53 0.130 0.017 0.074 0.018 0.014 0.021 1963 (1690)10 49.39 15.55 7.71 8.63 14.11 0.89 2.16 1.57 0.096 0.011 0.076 0.024 0.013 0.028 1963 (1690)11 47.38 13.69 7.59 10.35 16.05 0.95 2.38 1.62 0.063 0.023 0.065 0.018 0.016 0.043 1953 (1680)12 45.88 14.64 7.36 10.60 16.78 1.00 2.26 1.48 0.083 0.020 0.079 0.025 0.015 0.033 1963 (1690)13 43.18 15.22 7.39 13.54 16.56 0.86 1.98 1.27 0.088 0.033 0.073 0.022 0.014 0.031 1973 (1700)14 45.45 14.51 6.60 10.43 17.00 1.18 3.26 1.57 0.037 0.013 0.049 0.022 0.039 0.074 1929 (1656)15 39.14 9.89 7.51 14.49 24.20 0.74 2.60 1.43 0.024 <0.01 0.022 0.011 0.021 0.113 1976 (1703)16 42.91 11.90 7.14 12.42 21.16 0.96 2.15 1.35 0.024 <0.01 0.029 0.009 0.022 0.113 1955 (1682)17 40.71 14.54 6.72 13.30 20.58 1.10 1.92 1.13 0.026 <0.01 0.046 0.016 0.028 0.105 1974 (1701)18 53.02 19.21 9.03 5.56 8.81 1.09 2.12 1.17 0.110 0.043 0.140 0.046 0.014 0.025 1969 (1696)19 48.34 17.67 7.51 8.45 12.55 0.99 3.08 1.42 0.140 <0.01 0.070 0.017 0.022 0.019 1943 (1670)20 46.43 17.15 7.25 9.37 14.08 1.12 3.14 1.45 0.070 0.020 0.060 0.016 0.025 0.039 1954 (1681)21 46.98 18.52 7.10 6.73 14.61 1.21 3.26 1.58 0.090 <0.01 0.060 0.017 0.021 0.030 1943 (1670)22 44.89 17.50 6.82 8.83 16.06 1.14 3.24 1.51 0.040 <0.01 0.040 0.012 0.022 0.068 1973 (1700)23 41.47 15.03 8.13 10.43 18.05 1.17 4.34 1.38 0.060 <0.01 0.050 0.015 0.019 0.045 1940 (1667)24 42.77 15.11 8.20 11.59 16.25 1.01 3.79 1.28 0.120 <0.01 0.100 0.033 0.019 0.023 1953 (1680)25 46.26 17.33 8.59 7.32 14.52 1.18 3.34 1.46 0.080 <0.01 0.070 0.018 0.021 0.034 1955 (1682)26 47.98 17.16 7.94 7.63 13.88 1.02 2.98 1.40 0.130 0.023 0.090 0.024 0.024 0.021 1951 (1678)27 46.79 17.49 7.60 8.02 14.01 1.28 3.51 1.30 0.080 <0.01 0.090 0.016 0.015 0.034 1945 (1672)


The phosphorus in metallurgical slags is usuallyanalyzed as P2O5 by the routine chemical analysismethod. The mass percent of PO3�

4 can be transferredfrom mass percent of P2O5 by

ðpctPO3�4 Þ ¼ 2� ðpctP2O5Þ

MP2O5

MPþ 2� ðpctP2O5ÞMP2O5

4MO

¼ ðpctP2O5Þ2MP þ 8MO

MP2O5

¼ 1:3382ðpctP2O5Þ

½6�

The gas–slag reaction in Eq. [1] can be also presentedby a slag–metal reaction as follows:

P½ � þ 5

2O½ � þ 3

2O2��

¼ PO3�4

� �½7a�

The equilibrium constant K0HPO3�

4

of Eq. [7a] can bewritten as

K0HPO3�

4¼

aPO3�4

aPa5=2O a

3=2

O2�

¼NPO3�

4

aPa5=2O N

3=2

O2�

�ð Þ ½7b�

Comparing Eqs. [1] and [7], the gas–metal reaction ofphosphorus or oxygen can be presented as follows:

1

2P2 gð Þ ¼ P½ �

DrGHm;P ¼ �157700þ 5:4T½33� J=molð Þ

½8a�

KHP ¼

aP

pP2=pHð Þ1=2

;

pP2

�pH

� �1=2 ¼ aP

KHP

¼ aP

exp 18968:0T � 0:6495

� � �ð Þ½8b�

1

2O2 gð Þ ¼ O½ �

DrGHm;O ¼ �117110� 3:39T 33½ � J=molð Þ

½9a�

KHO ¼

aO

pO2=pHð Þ1=2

;

pO2

�pH

� �5=4 ¼ a5=2O

KHO

� �5=2 ¼a5=2O

exp 14085:9T þ 0:4077

� �� 5=2 �ð Þ

½9b�

By considering the relationship between mass percentof P2O5 and PO3�

4 in Eq. [6], the concept of phosphatecapacity index CPO3�

4 ;index proposed by Yang et al.[2,3]

can be presented based on slag–metal dephosphoriza-tion reaction in Eq. [7] as

CPO3�4 ;index �

ðpct PO3�4 Þ

aPa5=2O

¼ 1:3382ðpct P2O5ÞaPa

5=2O

�ð Þ ½10�

Combining Eqs. [8b], [9b], [10], and [3], the definedCPO3�

4by Wagner[1] in Eq. [3] can be rewritten as

CPO3�4� ðpctPO3�

4 ÞpO2

=pHð Þ5=4 pP2=pHð Þ1=2

¼ ðpctPO3�4 Þ

a5=2O aP

KHO

� �5=2KH

P

¼ CPO3�4 ;index KH

O

� �5=2KH

P �ð Þ [11a]

Equation [11a] shows the relationship between CPO3�4

and CPO3�4 ;index of a slag. The relationship between CPO3�

4and CPO3�

4 ;index in Eq. [11a] can be expressed in logarith-mic form as

lgCPO3�4¼ lgCPO3�

4 ;index þ5

2lgKH

O þ lgKHP

¼ lgCPO3�4 ;index þ

23531:25

Tþ 0:1606 �ð Þ [11b]

It can be obtained from Eq. [11b] that the phosphatecapacity CPO3�

4of a slag is much greater than phosphate

capacity index CPO3�4 ;index: The value of lgCPO3�

4is 12.724

greater than lgCPO3�4 ;index of a slag at 1873 K (1600 �C).

Obviously, the phosphate capacity index CPO3�4 ;index is

more practical than the widely applied phosphatecapacity CPO3�

4: Therefore, some researchers[4–9] mea-

sured the phosphate capacity index CPO3�4 ;index of some

slags, but they nominated the measured or studiedCPO3�

4 ;index as phosphate capacity CPO3�4: It is certainly

inaccurate and may lead to misunderstanding themagnitude scale of CPO3�

4and CPO3�

4 ;index for a fixedslag. Equation [11] can be used to transfer valuesbetween CPO3�

4and CPO3�

4 ;index of the slags.

B. Relationship Between LP and CPO3�4

or CPO3�4 ;index

1. Relationship Between LP and CPO3�4

or CPO3�4 ;index

for Dephosphorization Reaction with Product as P2O5

The presentation of KHP2O5

in Eq. [5c] can be rearrangedeven more by inserting the definition of phosphatecapacity index CPO3�

4 ;index in Eq. [10] and the relationshipbetween phosphate capacity index CPO3�

4 ;index and phos-phate capacity CPO3�

4in Eq. [11a] as

KHP2O5

� �2

¼ ðpctP2O5Þ½pctP�2f2P½pctO�

5f5OMP2O5

Pni

¼ ðpctPO3�4 Þ

1:3382½pctP�2f2P½pctO�5f5OMP2O5

Pni

¼CPO3�

4 ;index

1:3382½pctP�fP½pctO�5=2f5=2O MP2O5

Pni

¼CPO3�

4

1:3382 KHO

� �5=2KH

P ½pctP�fP½pctO�5=2f

5=2O MP2O5

Pni�ð Þ

[5d]

Consequently, the relationship between LP andCPO3�

4 ;index or CPO3�4

can be established by inserting thedefinition of phosphorous distribution ratio LP = (pctP2O5)/[pct P]2 and relationship between mass percentof P2O5 and PO3�

4 in Eq. [6] into Eq. [5d] as


LP �ðpct P2O5Þ½pct P�2

¼ KHP2O5

� �2f2Pf

5O½pctO�

5MP2O5

Xni

¼CPO3�

4 ;index

1:3382½pct P� fPf5=2O ½pctO�

5=2

¼CPO3�

4

1:3382 KHO

� �5=2KH

P ½pct P�fPf

5=2O ½pctO�

5=2 �ð Þ ½12�

The relationship between LP and CPO3�4

or CPO3�4 ;index

based on slag–metal dephosphorization reaction withproduct as P2O5 in Eq. [5a] can be expressed inlogarithmic form as

lgCPO3�4¼ lgLP þ lg½pct P� � lg fP �

5

2lg aO

þ lgKHP þ

5

2lgKH

O þ lg 1:3382

¼ lgLP þ lg½pct P� � lg fP �5

2lg aO

þ 23531:25

Tþ 0:2871 �ð Þ [13a]

lgCPO3�4 ;index ¼ lgLP þ lg½pct P� � lg fP �

5

2lg fO

� 5

2lg½pctO� þ 0:1265 �ð Þ [13b]

Obviously, the phosphate capacity CPO3�4of a slag can be

determined by LP with the known chemical compositionof molten steel, especially [pct O] and [pct P] under slag–metal equilibrium and temperature T using Eq. [13a];whereas the phosphate capacity index CPO3�

4 ;index can be

calculated with the known chemical composition ofmolten steel, especially [pct O] and [pct P] under slag–metal equilibrium as well as LP using Eq. [13b]. Hereby,the measured phosphate capacity CPO3�

4 ;measured or phos-

phate capacity index CPO3�4 ;index;measured of a slag can be

calculated from the measured phosphorus distributionratio LP,measured by Eq. [13]. The measured CPO3�

4 ;measured

or CPO3�4 ;index;measured of the slags for 27 heats has been

summarized in Table II.

2. Relationship between LP and CPO3�4

or CPO3�4 ;index

for dephosphorization reaction with product as PO3�4

The presentation of K0HPO3�

4

in Eq. [7b] can be rear-

ranged by inserting the definition of phosphate capacityindex CPO3�

4 ;index in Eq. [10] and the relationship betweenphosphate capacity index CPO3�

4 ;index and phosphatecapacity CPO3�

4in Eq. [11a] as

K0HPO3�

4¼ ðpct PO3�

4 Þ½pct P�fP½pctO�5=2f5=2O N

3=2

O2�MPO3�4

Pni

¼CPO3�

4 ;index

N3=2

O2�MPO3�4

Pni¼

CPO3�4

KHO

� �5=2KH

PN3=2

O2�MPO3�4

Pni

[7c]

Thus, the relationship between L00P and CPO3�4

orCPO3�

4 ;index can be deduced by inserting the definition of

phosphorous distribution ratio L00P ¼ ðpct PO3�4 Þ�½pct P]

into Eq. [7c] as

L00P �ðpctPO3�

4 Þ½pctP� ¼K0H

PO3�4fP½pctO�5=2f5=2O N

3=2

O2�MPO3�4

Xni

¼CPO3�4 ;indexfP½pctO�

5=2f5=2O

¼CPO3�

4

KHO

� �5=2KH

P

fP½pctO�5=2f5=2O �ð Þ

or in logarithmic form as

lgCPO3�4¼ lgL00P� lg fP �

5

2lgaOþ

23531:25

Tþ 0:1606 �ð Þ

½14b�

lgCPO3�4 ;index ¼ lgL00P � lg fP �

5

2lg½pctO� � 5

2lg fO �ð Þ

½14c�

Equation [14] can be rewritten by inserting therelationship between mass percent of P2O5 and PO3�

4in Eq. [6] as

L000P �ðpct P2O5Þ½pct P� ¼

ðpct PO3�4 Þ

1:3382½pct P�

¼K0H

PO3�4

fP½pctO�5=2f5=2O N3=2

O2�MPO3�4

Pni

1:3382

¼CPO3�

4 ;indexfP½pctO�5=2f

5=2O

1:3382

¼CPO3�

4

1:3382 KHO

� �5=2KH

P

fP½pctO�5=2f 5=2O �ð Þ [15a]

Therefore, the relationship between L000P ¼ ðpct P2O5Þ=½pct P� and CPO3�

4 ;index or CPO3�4

based on slag–metaldephosphorization reaction with product as PO3�

4 inEq. [7a] can be established in logarithmic form as

lgCPO3�4¼ lgL000P � lg fP �

5

2lg½pctO� � 5

2lg fO

þ 5

2lgKH

O þ lgKHP þ 0:1265

¼ lgL000P � lg fP �5

2lg aO þ

23531:25

T

þ 0:2871 �ð Þ [15b]

lgCPO3�4 ;index ¼ lgL000P � lg fP �

5

2lg½pctO� � 5

2lg fO

þ 0:1265 �ð Þ [15c]

The equation group ofEq. [13]–Eq. [15] depict the estab-lished universal relationship between LP ¼ ðpct P2O5Þ

�

½pct P]2 � L0P or L00P ¼ ðpct PO3�

4 Þ�½pct P] or L000P ¼

ðpct P2O5Þ=½pct P] and CPO3�4or CPO3�

4 ;index of a slag.


Table

II.

MeasuredLP;m

easured,L00 P;m

easured,andL000 P;m

easured;Calculated½pctO�in

terface

ðFe tOÞ�½O�,MeasuredC

PO

3�4;m

easured,andC

PO

3�

4;index;m

easuredfrom

MeasuredLP;m

easured;Calculated

CIM

CT

PO

3�4;calculatedandC

IMCT

PO

3�

4;index;calculatedbyIM

CTModel;

lgCIM

CT

PO3�

4;cal:

lgCPO3�

4;m

eas:

and

lgCIM

CT

PO3�

4;index;cal:

lgCPO3�

4;index;m

eas:

forCaO-SiO

2-M

gO-FeO

-Fe2O

3-M

nO-A

l 2O

3-P

2O

5SlagsatTop–Bottom

Combined

Blown

Converter

SteelmakingTem

peraturesfor27Heats

Test

No.

LP;m

eas:

(–)

L00 P;m

eas:

(–)

L000 P;m

eas:

(–)

½pct

O�in

terface

ðFe tOÞ�½O�*

(–)

Measured

Calculatedfrom

IMCT

Model

lgC

IMCT

PO3�

4;cal:

lgC

PO3�

4;m

eas:

(–)

lgCIM

CT

PO3�

4;index;cal:

lgCPO3�

4;index;m

eas:

(–)

lgC

PO

3�4;m

eas:

(–)

lgC

PO

3�4;index;m

eas:

(–)

lgC

IMCT

PO

3�

4;cal:

(–)

lgC

IMCT

PO

3�

4;index;cal:

(–)

140,556

326

243

0.155

16.758

4.524

16.639

4.937

1.025

1.091

225,102

235

176

0.190

16.379

4.158

16.259

5.106

1.058

1.228

325,781

276

206

0.131

16.842

4.633

16.720

5.018

1.023

1.083

413,306

196

146

0.198

16.039

4.030

15.895

4.780

1.047

1.186

512,231

180

135

0.063

17.465

5.231

17.346

4.939

0.983

0.944

612,014

193

144

0.102

17.020

4.749

16.905

5.144

1.023

1.083

75125

130

97

0.090

16.940

4.706

16.821

5.010

1.018

1.064

89694

182

136

0.102

16.955

4.715

16.837

5.036

1.019

1.068

95216

126

94

0.082

16.933

4.785

16.805

4.738

0.997

0.990

10

2969

95

71

0.075

16.917

4.769

16.788

4.868

1.006

1.021

11

5586

135

101

0.084

17.002

4.793

16.880

5.070

1.016

1.058

12

2624

88

66

0.101

16.556

4.408

16.427

5.049

1.039

1.145

13

3037

89

67

0.133

16.209

4.122

16.073

4.899

1.048

1.189

14

3492

103

77

0.094

16.914

4.555

16.809

5.514

1.057

1.210

15

13,967

206

154

0.153

16.397

4.328

16.260

4.833

1.031

1.117

16

19,136

230

172

0.119

16.851

4.654

16.728

4.944

1.017

1.062

17

5117

110

82

0.162

16.075

3.994

15.939

4.803

1.050

1.203

18

572

35

26

0.047

16.949

4.837

16.816

4.513

0.981

0.933

19

5294

120

90

0.077

17.111

4.840

16.996

4.871

1.002

1.007

20

6172

132

99

0.095

16.861

4.657

16.738

4.761

1.006

1.022

21

5813

132

99

0.085

17.056

4.784

16.940

4.742

0.998

0.991

22

11389

183

137

0.118

16.649

4.562

16.514

4.335

0.986

0.950

23

6800

136

102

0.114

16.764

4.473

16.651

5.008

1.032

1.120

24

1331

59

44

0.113

16.328

4.118

16.206

5.213

1.067

1.266

25

4784

115

86

0.081

16.964

4.767

16.840

4.593

0.990

0.964

26

2604

84

63

0.076

16.911

4.690

16.791

4.871

1.011

1.039

27

5469

117

88

0.084

17.002

4.743

16.886

4.773

1.002

1.006

Average

1.020

1.076

*½pct

O�in

terface

ðFe tOÞ�½O�isthemass

percentofdissolved

oxygen

inmolten

steelatslag–metalinterface

basedon(Fe tO)–[O

]equilibrium

withreplacingaFe tObyN

Fe tOto

express

slagoxidizationabilityor

Fe tO

activity.


IV. PHOSPHATE CAPACITY MODELOF CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

STEELMAKING SLAGS BASED ON IMCT

A. Phosphorous Distribution Ratio Prediction ModelBased on IMCT

Besides the presentation of dephosphorization reac-tions with product as P2O5 or PO

3�4 in Eqs. [5a] or [7a]

described in Section III–A, the dephosphorizationreactions between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags and molten steel can be also presentedby ion couples (Fe2++O2�), (Ca2++O2�), (Mg2++O2�), and (Mn2++O2�) in the slags, in which the slagoxidization ability can be described by FetO, to formnine dephosphorization products as P2O5, 3FeOÆP2O5,4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5,2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5 accordingto IMCT[22–30] as follows[30]:

2 P½ � þ 5 FetOð Þ ¼ P2O5ð Þ þ 5t Fe½ �

KHP2O5¼ aP2O5

a5tFea5FetOa

2P

¼ðpct P2O5ÞP2O5

=MP2O5

.P

ni

� �

N5FetO½pct P�2f2P

½16a�

2 P½ �þ5 FetOð Þþ3ðFe2þþO2�Þ¼ 3FeO �P2O5ð Þþ5t Fe½ �

KH3FeO�P2O5

¼ a3FeO�P2O5a5tFe

a5FetOa3FeOa

2P

¼ðpct P2O5Þ3FeO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N3FeO½pct P�

2f2P[16b]

2 P½ �þ5 FetOð Þþ4ðFe2þþO2�Þ¼ 4FeO �P2O5ð Þþ5t Fe½ �

KH4FeO�P2O5

¼ a4FeO�P2O5a5tFe

a5FetOa4FeOa

2P


=MP2O5

.P

ni

� �

N5FetO

N4FeO½pct P�

2f2P[16c]

2 P½ �þ5 FetOð Þþ2ðCa2þþO2�Þ¼ 2CaO �P2O5ð Þþ5t Fe½ �

KH2CaO�P2O5

¼ a2CaO�P2O5a5tFe

a5FetOa2CaOa

2P

¼ðpct P2O5Þ2CaO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N2CaO½pct P�

2f2P[16d]


KH3CaO�P2O5


a5FetOa3CaOa

2P


=MP2O5

.P

ni

� �

N5FetO

N3CaO½pct P�

2f2P[16e]


KH4CaO�P2O5


a5FetOa4CaOa

2P


=MP2O5

.P

ni

� �

N5FetO

N4CaO½pct P�

2f2P[16f]

2 P½ �þ5 FetOð Þþ2ðMg2þþO2�Þ¼ 2MgO�P2O5ð Þþ5t Fe½ �

KH2MgO�P2O5

¼ a2MgO�P2O5a5tFe

a5FetOa2MgOa

2P

¼ðpct P2O5Þ2MgO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N2MgO½pct P�

2f2P[16g]

2 P½ �þ5 FetOð Þþ3ðMg2þþO2�Þ¼ 3MgO �P2O5ð Þþ5t Fe½ �

KH3MgO�P2O5

¼ a3MgO�P2O5a5tFe

a5FetOa3MgOa

2P


=MP2O5

.P

ni

� �

N5FetO

N3MgO½pct P�

2f2P16h

2 P½ �þ5 FetOð Þþ3ðMn2þþO2�Þ¼ 3MnO �P2O5ð Þþ5t Fe½ �

KH3MnO�P2O5

¼ a3MnO�P2O5a5tFe

a5FetOa3MnOa

2P

¼ðpct P2O5Þ3MnO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N3MnO½pct P�

2f2P[16i]

Therefore, the prediction model of phosphorous distri-bution ratio LP ¼ ðpct P2O5Þ

�½pct P]2 using mass ac-

tion concentration NFetOof FetO to present the slag

oxidation ability as well as NP2O5¼ nP2O5

=P

ni ¼ðpct P2O5Þ= MP2O5

Pnið Þð Þ to define the mass action

concentration of NP2O5based on IMCT[22–30] can be

deduced as[30]


LP ¼ LP;P2O5þ LP; 3FeO�P2O5

þ LP; 4FeO�P2O5þ LP; 2CaO�P2O5

þ LP; 3CaO�P2O5þ LP; 4CaO�P2O5

þ LP; 2MgO�P2O5

þ LP; 3MgO�P2O5þ LP; 3MnO�P2O5

¼ðpct P2O5ÞP2O5

½pct P�2þðpct P2O5Þ3FeO�P2O5

½pct P�2

þðpct P2O5Þ4FeO�P2O5

½pct P�2þðpct P2O5Þ2CaO�P2O5

½pct P�2

þðpct P2O5Þ3CaO�P2O5


½pct P�2

þðpct P2O5Þ2MgO�P2O5

½pct P�2þðpct P2O5Þ3MgO�P2O5

½pct P�2

þðpct P2O5Þ3MnO�P2O5

½pct P�2

¼MP2O5N5

FetOf2PðKH

P2O5þ KH

3FeO�P2O5N3

FeO

þ KH4FeO�P2O5

N4FeO þ KH

2CaO�P2O5N2

CaO

þ KH3CaO�P2O5

N3CaO þ KH

4CaO�P2O5N4

CaO

þ KH2MgO�P2O5

N2MgO þ KH

3MgO�P2O5N3

MgO

þ KH3MnO�P2O5

N3MnOÞ

Xni �ð Þ [17a]

The relationship of slag oxidization ability presentedby FetO and the oxidization ability of molten steel atslag–metal interface can be developed by

t Fe½ � þ O½ � ¼ FetOð ÞDrG

Hm;FetO

¼ �116100þ 48:79T½34� J=molð Þ [18a]

KHFetO¼ aFetO

aOatFe

¼ NFetO

aO � 1�ð Þ ½18b�

Thus, the activity or content of oxygen of molten steelat slag–metal interface can be determined by

ainterfaceO; ðFetOÞ�½O� ¼ ½pctO�interfaceðFetOÞ�½O�fO ¼ NFetO

.KH

FetO;

½pctO�interfaceðFetOÞ�½O� ¼ NFetO

.KH

FetOfO

� ��ð Þ [18c]

The dephosphorization reactions in Eq. [16] can berewritten by replacing NFetO with ainterfaceO;ðFetOÞ�½O�

(abbrevi-

ated as aO) presented in Eq. [18c] as follows:

2 P½ � þ 5 O½ � ¼ P2O5ð Þ

K0HP2O5¼ aP2O5

a5Oa2P

¼ðpctP2O5ÞP2O5

=MP2O5

.P

ni

� �

a5O½pctP�2f2P

�ð Þ

½19a�

2 P½ � þ 5 O½ � þ 3ðFe2þ þO2�Þ ¼ 3FeO � P2O5ð Þ

K0H3FeO�P2O5¼ a3FeO�P2O5

a5Oa3FeOa

2P


=MP2O5

.P

ni

� �

a5ON3FeO½pct P�

2f2P�ð Þ

[19b]

2 P½ � þ 5 O½ � þ 4ðFe2þ þO2�Þ ¼ 4FeO � P2O5ð Þ

K0H4FeO�P2O5¼ a4FeO�P2O5

a5Oa4FeOa

2P


=MP2O5

.P

ni

� �

a5ON4FeO½pct P�

2f2P�ð Þ

[19c]

2 P½ � þ 5 O½ � þ 2ðCa2þ þO2�Þ ¼ 2CaO � P2O5ð Þ

K0H2CaO�P2O5¼ a2CaO�P2O5

a5Oa2CaOa

2P


=MP2O5

.P

ni

� �

a5ON2CaO½pct P�

2f2P�ð Þ

[19d]



a5Oa3CaOa

2P


=MP2O5

.P

ni

� �

a5ON3CaO½pct P�

2f2P�ð Þ

[19e]



a5Oa4CaOa

2P


=MP2O5

.P

ni

� �

a5ON4CaO½pct P�

2f2P�ð Þ

[19f]

2 P½ � þ 5 O½ � þ 2ðMg2þ þO2�Þ ¼ 2MgO � P2O5ð Þ

K0H2MgO�P2O5¼ a2MgO�P2O5

a5Oa2MgOa

2P


=MP2O5

.P

ni

� �

a5ON2MgO½pct P�

2f2P�ð Þ

[19g]


2 P½ � þ 5 O½ � þ 3ðMg2þ þO2�Þ ¼ 3MgO � P2O5ð Þ

K0H3MgO�P2O5¼ a3MgO�P2O5

a5Oa3MgOa

2P


=MP2O5

.P

ni

� �

a5ON3MgO½pct P�

2f2P�ð Þ

[19h]

2 P½ � þ 5 O½ � þ 3ðMn2þ þO2�Þ ¼ 3MnO � P2O5ð Þ

K0H3MnO�P2O5¼ a3MnO�P2O5

a5Oa3MnOa

2P

¼ðpct P2O5Þ3MnO�P2O5

=MP2O5

.P

ni

� �

a5ON3MnO½pct P�

2f2P�ð Þ

[19i]

Therefore, the prediction model of phosphorous distri-bution ratio L

0P ¼ ðpct P2O5Þ

�½pct P]2 � LP can be pre-

sented using the oxygen activity aO of molten steel atthe slag–metal interface to describe the oxidation abil-ity of molten steel and NP2O5

¼ nP2O5=P

ni ¼ðpct P

2O5Þ= MP2O5

Pnið Þð Þ to express the mass action

concentration of NP2O5as[30]

L0P ¼ L0P;P2O5þ L0P; 3FeO�P2O5

þ L0P; 4FeO�P2O5þ L0P; 2CaO�P2O5

þ L0P; 3CaO�P2O5þ L0P; 4CaO�P2O5

þ L0P; 2MgO�P2O5

þ L0P; 3MgO�P2O5þ L0P; 3MnO�P2O5

¼ðpct P2O5ÞP2O5

½pct P�2þðpct P2O5Þ3FeO�P2O5

½pct P�2

þðpct P2O5Þ4FeO�P2O5


½pct P�2

þðpct P2O5Þ3CaO�P2O5


½pct P�2

þðpct P2O5Þ2MgO�P2O5

½pct P�2þðpct P2O5Þ3MgO�P2O5

½pct P�2

þðpct P2O5Þ3MnO�P2O5

½pct P�2

¼MP2O5a5O; ðFetOÞ�½O�f

2PðK0HP2O5

þ K0H3FeO�P2O5N3

FeO

þ K0H4FeO�P2O5N4

FeO þ K0H2CaO�P2O5N2

CaO

þ K0H3CaO�P2O5N3

CaO þ K0H4CaO�P2O5N4

CaO

þ K0H2MgO�P2O5N2

MgO þ K0H3MgO�P2O5N3

MgO

þ K0H3MnO�P2O5N3

MnOÞX

ni �ð Þ [17b]

B. Prediction Model of CPO3�4

or CPO3�4 ;index

from Phosphorous Distribution Ratio PredictionModel Based on IMCT

The prediction model of CIMCTPO3�

4

or CIMCTPO3�

4 ;indexbased on

IMCT[22–30] can be presented by inserting the twoprediction models of phosphorous distribution ratio[30]

LP and L0P shown in Eqs. [17a] and [17b] into Eq. [12] as

follows:

CNFetO;IMCT

PO3�4

¼1:3382 KH

O

� �5=2KH

P ½pct P�LP

fPf5=2O ½pctO�

5=2

¼189:94 KH

O

� �5=2KH

PN5FetO

fP½pct P�P

ni

f5=2O ½pctO�

5=2ðKH

P2O5

þKH3FeO�P2O5

N3FeO þ KH

4FeO�P2O5N4

FeO

þ KH2CaO�P2O5

N2CaO þ KH

3CaO�P2O5N3

CaO

þKH4CaO�P2O5

N4CaO þ KH

2MgO�P2O5N2

MgO

þ KH3MgO�P2O5

N3MgO þ KH

3MnO�P2O5N3

MnOÞ �ð Þ[20a]

CaO;IMCT

PO3�4

¼1:3382 KH

O

� �5=2KH

P ½pct P�L0

P

fPf5=2O ½pctO�

5=2

¼189:94 KH

O

� �5=2KH

P a5O;½Fe��ðFetOÞfP½pct P�

Pni

f5=2O ½pctO�

5=2

� ðK0HP2O5þ K

0H3FeO�P2O5

N3FeO þ K

0H4FeO�P2O5

N4FeO

þ K0H2CaO�P2O5

N2CaO þ K

0H3CaO�P2O5

N3CaO

þ K0H4CaO�P2O5

N4CaO þ K

0H2MgO�P2O5

N2MgO

þ K0H3MgO�P2O5

N3MgO þ K

0H3MnO�P2O5

N3MnOÞ ð�Þ

[20b]

CNFetO;IMCT

PO3�4 ;index

¼ 1:3382½pct P�LP

fPf5=2O ½pctO�

5=2

¼189:94N5

FetOfP½pct P�

Pni

f5=2O ½pctO�

5=2

� ðKHP2O5þ KH

3FeO�P2O5N3

FeO

þ KH4FeO�P2O5

N4FeO þ KH

2CaO�P2O5N2

CaO

þ KH3CaO�P2O5

N3CaO þ KH

4CaO�P2O5N4

CaO

þ KH2MgO�P2O5

N2MgO þ KH

3MgO�P2O5N3

MgO

þ KH3MnO�P2O5

N3MnOÞ �ð Þ [21a]

CaO;IMCT

PO3�4 ;index

¼ 1:3382½pct P�L0PfPf

5=2O ½pctO�

5=2

¼189:94a5O;½Fe��ðFetOÞfP½pct P�

Pni

f5=2O ½pctO�

5=2

� ðK0HP2O5þ K

0H3FeO�P2O5

N3FeO

þ K0H4FeO�P2O5

N4FeO þ K

0H2CaO�P2O5

N2CaO

þ K0H3CaO�P2O5

N3CaO þ K

0H4CaO�P2O5

N4CaO

þ K0H2MgO�P2O5

N2MgO þ K

0H3MgO�P2O5

N3MgO

þ K0H3MnO�P2O5

N3MnOÞ �ð Þ [21b]


It should be pointed out that the calculated

LP ¼ ðpct P2O5Þ�½pct P]2 by Eq. [17a] is equal to the

calculated L0P ¼ ðpct P2O5Þ

�½pct P]2 by Eq. [17b] no

matter how slag oxidation ability is presented usingthe mass action concentration NFetO of FetO in the slagsor how molten steel oxidation ability is presented usingthe oxygen activity ainterfaceO;ðFetOÞ�½O�

(abbreviated as aO) of

molten steel at the slag–metal interface. In the same

way, the calculated CNFetO;IMCT

PO3�4

by Eq. [20a] is equal to

the calculated CaO;IMCT

PO3�4

by Eq. [20b]; whereas the

calculated CNFetO;IMCT

PO3�4 ;index

by Eq. [21a] has the same value

with CaO;IMCT

PO3�4 ;index

by Eq. [21b].

The required parameters embodied in the developedIMCT CPO3�

4or CPO3�

4 ;index prediction model in Eqs. [20]

through [21] for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags are summarized as NFetO, NFeO, NCaO,

NMgO,NMnO,P

ni, ½pct O�interfaceðFetOÞ�½O� or [pct O], [pct P],KHO,

KHP , K

Hi in Eq. [16] or K

0Hi in Eq. [19]. The mass action

concentrations NFetO, NFeO, NCaO, NMgO, NMnO, andtotal equilibrium mole number

Pni in 100-g slags for 27

heats have been determined in previous paper[25]

and listed in Table III for convenient comparison.

Meanwhile, the specially defined NFetO from IMCT[22–

30] can be calculated by[25]

NFetO ¼ NFeO þ3� 2nFe2O3P

niþ 4� 2nFeO�Fe2O3P

ni

¼ NFeO þ 6NFe2O3þ 8NFeO�Fe2O3

�ð Þ ½22�

Themass percent of oxygen [pct O] in Eqs. [20] through

[21] is the abbreviation of ½pctO�interfaceðFetOÞ�½O� in Eq. [18c],

which is the oxygen content of molten steel at slag–metalinterface based on the (FetO)–[O] equilibrium reactionwith replacing aFetO by NFetO as shown in Eq. [18] rather

than the oxygen content ½pct O�bath½C��½O� of molten steel in

metal bath based on the constant product of [pct C] and[pct O] as 0.0027, i.e., [pct C] 9 [pct O] = 0.0027.[30] Themass percent of phosphorus [pct P] in Eqs. [20] through[21] is the phosphorus content in themetal bath, and it hasbeen given in Table I; meanwhile, the activity coefficientof phosphorus and oxygen in molten steel in Eqs. [20]through [21], i.e., fP and fO; can be determined by

lg fP ¼X

ejP½pct j�; lg fO ¼X

ejO½pct j� �ð Þ ½23�

The related values of interaction coefficients are taken[35]

as eCP=0.13, eSiP=0.12, eMnP = 0.0, ePP = 0.062, eSP =

�0.028, eOP = 0.13, and eCO = �0.45, eSiO = �0.131,

Table III. Calculated Total Equilibrium Mole NumbersP

ni of All Structural Units in 100-g CaO-SiO2-MgO-FeO-Fe2O3-MnO-

Al2O3-P2O5 Slags, Mass Action Concentrations of Structural Units, or Ion Couples as Components in the Slags and Defined NFetO

of the Slags at Top–Bottom Combined Blown Converter Steelmaking Temperatures Based on IMCT for 27 Heats

TestNo.

Pni (mol) NCaO (–) NSiO2

(–) NMgO (–) NFeO (–) NFe2O3(–) NMnO (–) NAl2O3

(–) N�P2O5(–) NFeO�Fe2O3

(–) NyFetO (–)

1 1.088 0.2688 0.0002 0.1801 0.2550 0.0199 0.0146 0.0011 0.0068 0.0239 0.56532 1.134 0.2519 0.0002 0.1767 0.2845 0.0242 0.0131 0.0011 0.0055 0.0324 0.68873 1.093 0.3100 0.0001 0.1846 0.2377 0.0157 0.0157 0.0008 0.0073 0.0175 0.47174 1.096 0.2685 0.0001 0.1877 0.2644 0.0238 0.0187 0.0013 0.0071 0.0282 0.63275 1.236 0.4177 0.0000 0.2413 0.1541 0.0066 0.0129 0.0006 0.0055 0.0048 0.23196 1.117 0.3121 0.0001 0.2264 0.2031 0.0129 0.0177 0.0011 0.0076 0.0125 0.38027 1.036 0.2986 0.0002 0.2190 0.1819 0.0116 0.0164 0.0009 0.0088 0.0099 0.33058 0.998 0.3011 0.0002 0.1920 0.2033 0.0126 0.0194 0.0010 0.0090 0.0121 0.37609 1.019 0.3232 0.0001 0.2185 0.1676 0.0097 0.0169 0.0006 0.0079 0.0075 0.286110 1.032 0.3473 0.0001 0.2236 0.1555 0.0090 0.0170 0.0007 0.0078 0.0065 0.261011 1.070 0.3466 0.0001 0.2165 0.1802 0.0097 0.0176 0.0007 0.0078 0.0082 0.304412 1.031 0.3103 0.0001 0.2129 0.1912 0.0123 0.0194 0.0008 0.0076 0.0109 0.352113 1.108 0.2666 0.0002 0.2067 0.2410 0.0138 0.0165 0.0009 0.0065 0.0151 0.444814 0.968 0.3007 0.0001 0.1957 0.1946 0.0131 0.0238 0.0014 0.0084 0.0124 0.372215 1.179 0.2932 0.0001 0.2109 0.2432 0.0179 0.0137 0.0010 0.0071 0.0198 0.508816 1.077 0.3116 0.0001 0.2049 0.2159 0.0149 0.0182 0.0008 0.0068 0.0150 0.425517 1.012 0.2431 0.0002 0.1914 0.2428 0.0202 0.0223 0.0010 0.0062 0.0223 0.542518 0.960 0.3415 0.0001 0.2601 0.1030 0.0058 0.0210 0.0007 0.0058 0.0028 0.160019 0.973 0.2924 0.0002 0.2214 0.1629 0.0103 0.0203 0.0013 0.0077 0.0080 0.288320 0.958 0.2739 0.0002 0.2128 0.1805 0.0126 0.0232 0.0014 0.0080 0.0106 0.341221 0.852 0.2561 0.0003 0.2150 0.1389 0.0157 0.0272 0.0017 0.0096 0.0104 0.316422 0.904 0.2462 0.0003 0.2026 0.1768 0.0177 0.0250 0.0017 0.0090 0.0143 0.397023 1.005 0.2373 0.0002 0.2319 0.1936 0.0178 0.0239 0.0023 0.0077 0.0165 0.432224 1.075 0.2558 0.0002 0.2306 0.2094 0.0142 0.0197 0.0018 0.0067 0.0139 0.405825 0.947 0.2681 0.0002 0.2508 0.1406 0.0134 0.0244 0.0015 0.0080 0.0088 0.291426 0.964 0.2955 0.0002 0.2346 0.1461 0.0114 0.0209 0.0012 0.0076 0.0078 0.277227 0.916 0.2707 0.0002 0.2243 0.1566 0.0129 0.0269 0.0016 0.0073 0.0096 0.3109

*NP2O5is calculated by NP2O5

¼ nP2O5=P

ni ¼ ðpct P2O5Þ= MP2O5

Pnið Þð Þ.

�NFetO is defined as NFetO ¼ NFeO þ 6NFe2O3þ 8NFeO�Fe2O3

.


eMnO = �0.21, ePO = �0.07, eSO = �0.133, and eOO =�0.2, respectively.

The relationship between KHi in Eqs. [16], [17a], [20a],

and [21a] and K0Hi in Eqs. [17b], [19], [20b], and [21b] can

be deduced by considering KHFetO

in Eq. [18b] as[30]

KHi ¼

K0Hi

KHFetO

� �5 �ð Þ ½24�

It is well known that the equilibrium constant KHi of

the formation reaction for molecule i can be determinedfrom its standard molar Gibbs formation energy changeDrG

Hm;i as

KHi ¼ expð�DrG

Hm;i=RTÞ ð�Þ ½25�

The standard molar Gibbs free energy changes of thepreviously mentioned nine dephosphorization reactionsin Eq. [16] have been determined by combining therelated values of standard molar Gibbs free energychanges for nine dephosphorization reactions as sum-marized in previous paper.[30] The values of both KH

O andKH

P in Eqs. [20] and [21] can be calculated from DrGHm;P in

Eq. [8a] and DrGHm;O in Eq. [9a] by Eq. [25].

Thereby, CPO3�4

or CPO3�4 ;index of the slags can be

predicted after knowing the required parameters in thedeveloped IMCT CPO3�

4or CPO3�

4 ;index model in Eqs. [20]

and [21]. The calculatedCIMCTPO3�

4 ;claculatedorCIMCT

PO3�4 ;index;claculated

of the slags for 27 heats in logarithmic form are alsosummarized in Table II.

V. COMPARISON OF CALCULATED CPO3�4

BY DIFFERENT CPO3�4

PREDICTION MODELS

A. Determination of Measured CPO3�4

and CPO3�4 ;index

for the Slags

It has been pointed out in Section III–B that CPO3�

4

and CPO3�4 ;index have a corresponding relationship with

LP ¼ ðpct P2O5Þ�½pct P]2 � L

0P or L00P ¼ ðpct PO3�

4 Þ�

½pct P] or L000P ¼ ðpct P2O5Þ=½pct P] shown in Eqs. [13],[14], and [15], respectively. The calculated LP ¼ðpct P2O5Þ

�½pct P]2 � L

0P, L00P ¼ ðpct PO3�

4 Þ�½pct P], and

L000P ¼ ðpct P2O5Þ=½pct P] are summarized in Table II.Therefore, the measured C

PO3�4 ;measured

and

CPO3�4 ;index;measured of the slags at the steelmaking end-

point of an 80-ton combined blown converter frommeasured LP;measured, L00P;measured, or L000P;measured through

Eqs. [13], [14], or [15] are also listed in Table II. Therelationship between lgLP;measured, lgL00P;measured, or

lgL000P;measured and lgCPO3�4 ;measured or lgCPO3�

4 ;index;measured

for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsequilibrated with molten steel at the steelmaking end-point during an 80-ton top–bottom combined blownconverter steelmaking process for 27 heats is illustratedin Figure 1, respectively. No obvious relationshipbetween lgLP;measured, lgL

00P;measured, or lgL000P;measured and

lgCPO3�4 ;measured or lgCPO3�

4 ;index;measured for the slags can

be observed from Figure 1.To compare CPO3�

4and CPO3�

4 ;index as well as

LP ¼ ðpct P2O5Þ�½pct P]2 � L

0P and L00P ¼ ðpct PO3�

4 Þ�

½pct P] or L000P ¼ ðpct P2O5Þ=½pct P], the relationshipbetween lgCPO3�

4 ;measured and lgCPO3�4 ;index;measured as well

as relationship between lgLP;measured and lgL00P;measured or

lgL000P;measured for CaO-SiO2-MgO-FeO-Fe2O3-MnO-

Al2O3-P2O5 slags equilibrated with molten steel at thesteelmaking endpoint during an 80-ton top–bottomcombined blown converter steelmaking process for 27heats are also illustrated in Figure 2. A good linearrelationship between the measured lgCPO3�

4 ;measured and

lgCPO3�4 ;index;measured as well as lgLP;measured and

lgL00P;measured or lgL000P;measured can be observed. This

implies that larger CPO3�4

corresponds to greater

CPO3�4 ;index for a slag; whereas larger LP lead to greater

L00P or L000P for a slag equilibrated with molten steel. Thevalue of CPO3�

4cannot be confused with that of

1617181920

(b)

lgCPO3−

4, measured

lgL' '

P , measured (−)

1 2 33

4

5

6

lgC

PO

3− 4, m

easu

red o

r lg

CP

O3− 4

, ind

ex, m

easu

red (

−)

lgCPO3−

4, index, measured

1617181920

(a)

lgCPO3−

4, measured

2 3 4 53

4

5

6 lgCPO3−

4, index, measured

lgC

PO

3− 4, m

easu

red o

r lg

CP

O3− 4

, ind

ex, m

easu

red (

−)

lgLP, measured

(−)

1617181920

(c)

lgCPO3−

4, measured

lgL' ' '

P , measured (−)

1 2 33

4

5

6

lgC

PO

3− 4, m

easu

red

or lg

CP

O3− 4

, ind

ex, m

easu

red

(−)

lgCPO3−

4, index, measured

Fig. 1—Relationship between lgCPO3�4 ;measured or lgCPO3�

4 ;index;measured and lgLP;measured as LP ¼ ðpct P2O5Þ�½pct P]2 (a), or lgL00P;measured as

L00P ¼ ðpct PO3�4 Þ�½pct P] (b) or lgL000P;measured as L000P ¼ ðpct P2O5Þ=½pct P] (c) for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated

with molten steel at the steelmaking endpoint during an 80-ton top–bottom combined blown converter steelmaking process for 27 heats.


CPO3�

4 ;indexfor the slags because the magnitude of

lgCPO3�4 ;measured in a range from 16 to 18 is much larger

than that of lgCPO3�4 ;index;measured in a range from 4 to 6.

Certainly, the magnitude of LP ¼ ðpct P2O5Þ�½pct P]2 �

L0P is much larger than that of L00P ¼ ðpct PO3�4 Þ�½pct P]

or L000P ¼ ðpct P2O5Þ=½pct P], especially for low [pct P]molten steel during deep dephosphorization operation.

B. Comparison between Measured and Predicted CPO3�4

or CPO3�4 ;index by IMCT model for the Slags

The predicted lgCIMCTPO3�

4 ;calculatedor lgCIMCT

PO3�4 ;index;calculated

from IMCT CPO3�4

model by Eqs. [20] or

[21], lgCIMCTPO3�

4 ;calculated=lgCPO3�

4 ;measured and lg

CIMCTPO3�

4 ;index;calculated=lgCPO3�

4 ;index;measured for the slags are

summarized in Table II. Inspecting the degree of agree-ment between the predicted CIMCT

PO3�4 ;calculated

by IMCT

CPO3�4

model and measured CPO3�4 ;measured is an effective

measure to verify the developed IMCT CPO3�4

model.

The comparison between the calculated lgCIMCTPO3�

4 ;calculated

or lgCIMCTPO3�

4 ;index;calculatedby the IMCT CPO3�

4model listed

in Table II and measured lgCPO3�4 ;measured or

lgCPO3�4 ;index;measured presented in Section IV–A for the

CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsequilibrated with molten steel at the steelmaking end-point during an 80-ton top–bottom combined blownconverter steelmaking process for 27 heats is illustratedin Figures 3(a) and (b), respectively. The relationship

3.5 4.0 4.5 5.0 5.515

16

17

18

19

20

lgCPO3−

4, meas.

=11.411+1.144 lgCPO3−

4, index, meas.

lgCPO3−

4, index, measured

(−)

lgC

PO

3 − 4, m

easu

red (−)

(a)

lgCPO3−

4, measured

2 3 4 51

2

3

4

1

2

3

4

lgL' '

'

P, m

easu

red (−)

lgL' '

P, meas. =0.184+0.510 lgL

P, meas.

lgL' ' '

P, meas. =0.0576+0.510 lgL

P, meas.

lgLP, measured

(−)

lgL' ' P

, mea

sure

d (−)

(b)

lgL' '

P, measuredlgL' ' '

P, measured

Fig. 2—Relationship between lgCPO3�4 ;measured and lgCPO3�

4 ;index;measured (a) and the relationship between lgLP;measured as LP ¼ ðpct P2O5Þ�½pct P]2

and lgL00P;measured as L00P ¼ ðpct PO3�4 Þ�½pct P] or lgL000P;measured as L000P ¼ ðpct P2O5Þ=½pct P] (b) for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

slags equilibrated with molten steel at the steelmaking endpoint during an 80-ton top–bottom combined blown converter steelmaking process for27 heats, respectively.

15 16 17 18 19 2015

16

17

18

19

20

(a)

lgCIMCT

PO3−

4, calculated

lgC

IMC

T

PO

3− 4, c

alcu

late

d (−

)

lgCPO3−

4, measured

(−)3 4 5 6 7

3

4

5

6

7

(b)

lgCIMCT

PO3−

4, index, calculated

lgC

IMC

T

PO

3− 4, i

ndex

, ca

lcul

ated

(−)

lgCPO3−

4, index, measured

(−)

4 5 616

17

18

19

lgCIMCT

PO3−

4, cal.

=11.228+1.197 lgCIMCT

PO3−

4, index, cal.

lgCIMCT

PO3−


(−)

lgC

IMC

T

PO

3− 4, c

alcu

late

d (−)

(c)

lgCIMCT

PO3−

4, calculated

Fig. 3—Comparison between measured lgCPO3�4 ;measured and calculated lgCIMCT

PO3�4 ;calculated

by IMCT model (a), measured lgCPO3�4 ;index;measured and

calculated lgCIMCTPO3�

4 ;index;calculatedby IMCT model (b), calculated lgCIMCT


and lgCIMCTPO3�

4 ;calculatedby IMCT model (c) for CaO-SiO2-MgO-

FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at the steelmaking endpoint during an 80-ton top–bottom combined blownconverter steelmaking process for 27 heats, respectively.


between the calculated lgCIMCTPO3�

4 ;calculatedand

lgCIMCTPO3�

4 ;index;calculatedby the IMCT model for the slags

is illustrated in Figure 3(c) for comparison of therelationship between the measured lgCPO3�

4 ;measured and

lgCPO3�4 ;index;measured is shown in Figure 2(a). The rela-

tionship between lgCIMCTPO3�


4 ;measured and

lgCPO3�

4 ;measuredas well as the relationship between

lgCIMCTPO3�


4 ;index;measured and

lgCPO3�4 ;index;measured for the slags are also depicted in

Figure 4, respectively.It can be obtained from Figures 3 and 4 that the

predicted lgCIMCTPO3�

4 ;calculatedby IMCT model has a good

corresponding relationship with the measuredlgCPO3�

4 ;measured with the average value of

lgCIMCTPO3�


4 ;measured as 1.020 for 27 heats in

Table II; while, the calculated lgCIMCTPO3�

4 ;index;calculatedhas a

reliable corresponding relationship with the measuredlgCPO3�

4 ;index;measured with the average value of

lgCIMCTPO3�


4 ;index;measured as 1.076 for 27

heats. The calculated lgCIMCTPO3�

4 ;calculatedor

lgCIMCTPO3�

4 ;index;calculatedby the developed IMCT model is

greater than the measured lgCPO3�4 ;measured or

lgCPO3�4 ;index;measured in a narrow range for most heats;

this result suggests that the calculated CIMCTPO3�

4 ;calculatedor

CIMCTPO3�

4 ;index;calculatedis more reasonable to present the

dephosphorization potential than the measuredCPO3�

4 ;measured and CPO3�4 ;index;measured because the slag–

metal dephosphorization reactions cannot reach, but be

near, the absolute chemical reaction equilibrium fromthe viewpoint of metallurgical thermodynamics accord-ing to the operation practice of a top–bottom combinedblown steelmaking converter.The quasi-equilibrium of the slag–metal dephosphor-

ization reactions can make the phosphorus content inmetal bath ½pct P]bath a little greater than the realequilibrium phosphorus content at slag–metal interface

½pct P]equilibriuminterface : The effect of difference between

½pct P]bath and ½pct P]equilibriuminterface ; i.e.,

½pct P]bath � ½pct P]equilibriuminterface ; on the measured

lgCPO3�4 ;measured is the same as that on the measured

lgCPO3�4 ;index;measured through affecting lgLP;measured or

lgL000P;measured. The magnitude of CPO3�

4

for a slag is much

greater than CPO3�4 ;index; such as

lgCPO3�4� lgCPO3�

4 ;index= 12.724 at 1873 K (1600 �C),with lgCPO3�

4 ;measured as 16–18 and lgCPO3�4 ;index;measured as

4–6. Hereby, the same value of

½pct P]bath � ½pct P]equilibriuminterface can make a larger influence

on lgCIMCTPO3�


4 ;index;measured than that on

lgCIMCTPO3�


4 ;measured. This is the reason that

lgCIMCTPO3�


4 ;index;measured for some heats

is near to 1.20, whereas lgCIMCTPO3�


4 ;measured

is near to 1.05 for the same heats; and the average valueof lgCIMCT


=lgCPO3�4 ;index;measured as 1.076 is

larger than that of lgCIMCTPO3�


4 ;measured as

1.020 for 27 heats.It can be concluded that the developed IMCT model

can be used to predict the phosphate capacity CPO3�4

and

phosphate capacity index CPO3�4 ;index of CaO-SiO2-MgO-

15 16 17 18

0.8

1.0

1.2

(a)

lgCIMCT

PO3−

4, calculated

/lgCPO3−

4, measured

lgC

IMC

T

PO

3 − 4, c

alcu

late

d/lgC

PO

3− 4, m

easu

red (

−)

lgCPO3−

4, measured

(−)

4.0 4.5 5.0 5.50.8

1.0

1.2

1.4

(b)

lgCIMCT

PO3−


/lgCPO3−

4, index, measured

lgC

IMC

T

PO

3 −4

, ind

ex, c

alcu

late

d/lgC

PO

3 −4

, ind

ex, m

easu

red (

−)

lgCPO3−

4, index, measured

(−)

Fig. 4—Relationship between lgCIMCTPO3�


4 ;measured and lgCPO3�4 ;measured (a) as well as lgCIMCT


=lgCPO3�4 ;index;measured and

lgCPO3�4 ;index;measured (b) for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at the steelmaking endpoint during

an 80-ton top–bottom combined blown converter steelmaking process for 27 heats, respectively.


FeO-Fe2O3-MnO-Al2O3-P2O5 slags with acceptablereliability.

C. Comparison between Measured and Predicted CPO3�4

or CPO3�4 ;index by Different CPO3�

4Prediction Models for

the Slags

Comparing the predicted results by the IMCT CPO3�4

model and other CPO3�4

models is also important toverify the feasibility of the developed IMCT CPO3�

4model besides a comparison of the measuredCPO3�

4 ;measured and the predicted CIMCTPO3�

4 ;calculatedby IMCT

CPO3�4

model.

1. Evaluation of other phosphate capacity predictionmodels

The widely recognized phosphate capacity CPO3�4

pre-

diction models for various oxidizing slags by differentresearchers[6,10–14] have been briefly summarized in Table -IV, in which Selin’smodel[10] includesB

0 ¼ xCaO=xSiO2and

temperature T; Mori’s model[11] and Suito’s model[6,12]

only cover optical basicity K; Young’s model[13] containsoptical basicity K, mass percent of FetO,MnO, and P2O5.However, most of these models are empirical modelsderived from the mathematical regression of experimentaldata. The mass percent of FetO is calculated by (pctFetO) = (pct FeO)+0.9(pct Fe2O3). The main conclu-

sions of these CPO3�4prediction models in Table IV can be

summarized as follows:

(a) Increasing the mass percent of basic components,such as CaO, as well as decreasing mass percent ofacidic components, such as SiO2 and Al2O3, canimprove dephosphorization potential, such as inSelin’s model.[10]

(b) Greater optical basicity K can result in a largerdephosphorization potential of a slag, such as inMori’s model,[11] Suito’s model,[6,12] and Young’smodel.[13]

(c) Iron oxides expressed as FetO and MnO has a neg-ative effect on CPO3�

4in Young’s model,[13] whereas it

is inconsistent with the results of LP predictionmodels proposed by Suito et al.,[36] Healy et al.,[37]

Sommerville et al.[38,39] and Balajiva et al.,[40] whichare summarized in previous publication.[30]

(d) P2O5 has a promotion effect on CPO3�4

in Young’smodel[13]; however, this result is contrary with that inmost LP prediction models proposed by Suitoet al.,[36] Healy et al.,[37] and Balajiva et al.,[40] whichare also summarized in previous publication.[30]

(e) High temperature can decrease the CPO3�4

of a slag

directly as shown in Selin’smodel,[10] Suito’smodel,[6,12]

and Young’s model.[13]

2. Comparison of calculated phosphate capacityby different modelsThe predicted Ci

PO3�4 ;calculated

by the other four CPO3�4

models can be calculated by the formulas listed inTable IV. It should be specially emphasized that thecalculated Ci

PO3�4 ;calculated

by Suito’s model[6, 12] and

Young’s model[13] has been transferred into

CPO3�4¼ pct PO3�

4

� �.pO2

�pH

� �5=4pP2

�pH

� �1=2� �rather

than the originally defined phosphide capacity index

CP3�;index ¼ ðpct PÞ.

aPa5=2O

� �in Suito’s model[6,12] as

well as in Young’s model[13] as listed in Table IV. Therelationship between the mass percent of P2O5 and masspercent of P in slags can be expressed as

ðpct PÞ ¼ ðpct P2O5ÞMP2O5

2MP ¼ 0:4364ðpct P2O5Þ �ð Þ ½26�

Therefore, Eq. [10] can be rewritten as

CPO3�4 ;index �

1:3382ðpct P2O5ÞaPa

5=2O

¼ 3:0664ðpct PÞaPa

5=2O

¼ 3:0664CP3�;index �ð Þ ½27�

Inserting Eq. [27] into Eq. [11b], the relationshipbetween C

PO3�4

and CP3�;index

can be obtained as

lgCPO3�4¼ lgCP3�;index þ

23531:25

Tþ 0:6472 �ð Þ ½11c�

Consequently, the calculated phosphide capacity

index CP3�;index ¼ ðpct PÞ.

aPa5=2O

� �by Suito’s model[6,12]

and Young’s model[13] as listed in Table IV must betransferred into CPO3�

4by Eq. [11c]. The predicted

CiPO3�

4 ;index;calculatedcan be calculated from the determined

Table IV. Formulas of Phosphate Capacity or Phosphide Capacity Index Prediction Models Reported in Related Literatures

Models Slags Formulas of Models Notes Ref.

Selin’smodel

CaO-SiO2-CaF2 slags lgCPO3�4¼ 2:016B

0 � 0:34B02 þ 52600T � 11:506

lgCPO3�4¼ 52600

T � 8:39

B0= 1.4–3.0, B

0 ¼ xCaO=xSiO2

B0> 3.0, B

0 ¼ xCaO=xSiO2

10

Mori’smodel

CaO-MgO-SiO2-FetOslags

lgCPO3�4¼ 17:55Kþ 5:75 T = 1873 K (1600 �C) 11

Suito’smodel*

CaO-MgO-FetO-SiO2

slagslgCP3� ;index ¼ 17:55Kþ 29990

T � 23:737 6,12

Young’smodel*

CaO-SiO2-MgO-MnOslags

lgCP3� ;index ¼ �18:184þ 35:84K� 22:35K2

þ 22930KT � 0:06157ðpct FeOÞ

�0:04256ðpctMnOÞ þ 0:359ðpct P2O5Þ0:3

13

*CP3� ;index is defined as CP3�;index ¼ ðpct PÞ�

aPa5=2O

� �in Suito’s model and Young’s model.


CiPO3�

4 ;calculatedthrough the relationship between CPO3�

4

and CPO3�4 ;index in Eq. [11b].

The comparison between the measuredlgCPO3�

4 ;measured and the calculated lgCIMCTPO3�

4 ;calculatedby

the IMCT model, lgCSelinPO3�

4 ;calculatedby Selin’s model,[10]

lgCMoriPO3�

4 ;calculatedby Mori’s model,[11] lgCSuito

PO3�4 ;calculated

by

Suito’s model,[6,12] or lgCYoung

PO3�4 ;calculated

by Young’s

model[13] is illustrated in Figure 5 with three-groupoptical basicities for FeO and Fe2O3 as (1) KFeO= 0.51and KFe2O3

= 0.48 from Pauling electronegativity[41], (2)KFeO= 0.93 and KFe2O3

= 0.69 from average electrondensity[42], (3) KFeO= 1.0 and KFe2O3

= 0.75 frommathematical regression,[43] for Mori’s,[11] Suito’s,[6,12]

and Young’s model[13] for calculating optical basicity ofthe slags, respectively. Because there is no term ofoptical basicity included in both IMCT model andSelin’s model,[10] the calculated lgCIMCT

PO3�4 ;calculated

by

IMCT model and lgCSelinPO3�

4 ;calculatedby Selin’s model[10]

are also given in Figures 5(a) through (c) for compar-ison. Similarly, the comparison between the measuredlgCPO3�

4 ;index;measured and calculated lgCIMCTPO3�

4 ;index;calculated

by IMCT model or lgCSelinPO3�

4 ;index;calculatedby Selin’s

model,[10] lgCMoriPO3�

4 ;index;calculatedby Mori’s model,[11]

lgCSuitoPO3�

4 ;index;calculatedby Suito’s model,[6,12] or

lgCYoung


by Young’s model[13] is also illus-

trated in Figure 6 with the previously mentioned three-group optical basicities for FeO and Fe2O3, respectively.Obviously, the predicted lgCSelin

PO3�4 ;calculated

or

lgCSelinPO3�

4 ;index;calculatedby Selin’s model[10] is much greater

than the measured lgCPO3�4 ;measured or

lgCPO3�4 ;index;measured, whereas the calculated

lgCMoriPO3�

4 ;calculatedor lgCMori


by Mori’s

model[11] with three-group optical basicities for FeOand Fe2O3 is much smaller than the measured

14 16 1810

12

14

16

18

20 ΛFeO

=1.0, ΛFe

2O

3

=0.75

IMCT model Selin's model Mori's model Suito's modelYoung's model

lgCPO3−

4, measured

(−)lg

Ci PO

3− 4, c

alcu

late

d (−

)14 16 18

10

12

14

16

18

20 ΛFeO

=0.51, ΛFe

2O

3

=0.48


lgCPO3−

4, measured

(−)

lgC

i PO

3− 4, c

alcu

late

d (− )

14 16 1810

12

14

16

18

20 ΛFeO

=0.93, ΛFe

2O

3

=0.69


lgCPO3−

4, measured

(−)

lgC

i PO

3 − 4, c

alcu

late

d (− )

(a) (b) (c)

Fig. 5—Comparison between calculated lgCiPO3�

4 ;calculatedby five phosphate capacity prediction models including IMCT model and measured

lgCPO3�4 ;measured of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at top–bottom combined blown converter

steelmaking temperatures with (1) KFeO= 0.51, KFe2O3= 0.48 (a); (2) KFeO= 0.93, KFe2O3

= 0.69 (b); and (3) KFeO= 1.0, KFe2O3= 0.75 (c) for

Mori’s model, Suito’s model, and Young’s model for 27 heats, respectively.

3.5 4.0 4.5 5.0 5.50

2

4

6

8

10 ΛFeO

=1.0, ΛFe

2O

3

=0.75


lgCPO3−

4, index, measured

(−)

lgC

i PO

3− 4, i

ndex

, cal

cula

ted (

−)

3.5 4.0 4.5 5.0 5.50

2

4

6

8

10 ΛFeO

=0.51, ΛFe

2O

3

=0.48


lgCPO3−

4, index, measured

(−)

lgC

i PO

3− 4, i

ndex

, cal

cula

ted (

−)

3.5 4.0 4.5 5.0 5.50

2

4

6

8

10 ΛFeO

=0.93, ΛFe

2O

3

=0.69


lgCPO3−

4, index, measured

(−)

lgC

i PO

3− 4, i

ndex

, cal

cula

ted (

−)

(a) (b) (c)

Fig. 6—Comparison between calculated lgCiPO3�

4 ;index;calculatedby five phosphate capacity index prediction models including IMCT model and

measured lgCPO3�4 ;index;measured of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at top–bottom combined

blown converter steelmaking temperatures with (1) KFeO= 0.51, KFe2O3= 0.48 (a); (2) KFeO= 0.93, KFe2O3

= 0.69 (b); and (3) KFeO= 1.0,KFe2O3

= 0.75 (c) for Mori’s model, Suito’s model, and Young’s model for 27 heats, respectively.


lgCPO3�4 ;measured or lgCPO3�

4 ;index;measured for the slags for

each heat. This result suggests that Selin’s model[10] andMori’s model[11] cannot be successfully used to predictCPO3�

4or CPO3�

4 ;index for CaO-SiO2-MgO-FeO-Fe2O3-

MnO-Al2O3-P2O5 slags equilibrated with molten steelat top–bottom combined blown converter steelmakingtemperatures.

The predicted lgCYoung

PO3�4 ;calculated

or lgCYoung


by Young’s model[13] is smaller than the measuredlgC

PO3�4 ;measured

or lgCPO3�4 ;index;measured when taking

KFeO= 0.51 and KFe2O3= 0.48[41], or it is greater than

the measured lgCPO3�4 ;measured or lgCPO3�

4 ;index;measured

when taking KFeO= 0.93 and KFe2O3= 0.69,[42] or

KFeO= 1.0 and KFe2O3= 0.75.[43] This result suggests

that the predicted lgCYoung

PO3�4 ;calculated

or

lgCYoung


by Young’s model[13] of the slags

can be largely influenced by the chosen KFeO and KFe2O3;

therefore, the Young’s model[13] is not recommended topredict CPO3�

4or CPO3�

4 ;index for the investigated com-

bined blown converter steelmaking slags.The Suito’s model[6,12] can be feasibly used to predict

CPO3�4

or CPO3�4 ;index for the slags with KFeO= 0.51 and

KFe2O3= 0.48[41]; however, the predicted lgCSuito

PO3�4 ;calculated

or lgCSuitoPO3�

4 ;index;calculatedby Suito’s model[6,12] is greater

than the measured lgCPO3�4 ;measured or

lgCPO3�4 ;index;measured for the slags with KFeO= 0.93 and

KFe2O3= 0.69,[42] or KFeO= 1.0 and KFe2O3

= 0.75.[43]

Among the previously mentioned five models, thedeveloped IMCT model and Suito’s model[6,12] withKFeO= 0.51 and KFe2O3

= 0.48,[41] but not KFeO= 0.93and KFe2O3

= 0.69,[42] or KFeO= 1.0 and KFe2O3=

0.75,[43] can be used successfully to predict CPO3�4

orCPO3�


VI. CONTRIBUTION OF BASIC OXIDES TOPHOSPHATE CAPACITY INDEX OF THE SLAGS

Considering the theoretical relationship betweenphosphate capacity CPO3�

4and phosphate capacity

index CPO3�4 ;index of a slag shown in Eq. [11b] and

the regressed relationship between phosphate capacityCPO3�

4and phosphate capacity index CPO3�

4 ;index of

CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsequilibrated with molten steel at top–bottom com-bined blown converter steelmaking temperaturesshown in Figure 3(c), the attention in the followingtext will be focused on phosphate capacity indexCPO3�

4 ;index rather than phosphate capacity CPO3�4

of the

slags. It is because that the phosphate capacity indexCPO3�

4 ;index introduced by Yang et al.[2,3] is more

practical than the more widely applied phosphatecapacity CPO3�

4proposed by Wagner.[1] Certainly, the

discussed relationship between the phosphate capacityindex C

PO3�4 ;index

of the slags and the related param-

eters in the following text can be easily converted intothe relationship between phosphate capacity C

PO3�4

and

the same parameters by the theoretical relationshipbetween CPO3�

4and CPO3�

4 ;index for any slags by Eq.

[11b] or the relationship between CPO3�

4

and CPO3�4 ;index

for the investigated slags shown in Figure 3(c) at theinvestigated temperature range.

A. Contribution of Basic Oxides to Calculated PhosphateCapacity Index of the Slags

It is known that four basic oxides of FetO, CaO,MgO, and MnO in the slags can react with phosphorousin molten steel to generate nine structural units asdephosphorization products, such as P2O5, 3FeOÆP2O5,

-14

-7

0

7

14P

2O

53FeO·P

2O

54FeO·P

2O

5

2CaO·P2O

53CaO·P

2O

54CaO·P

2O

5

2MgO·P2O

53MgO·P

2O

53MnO·P

2O

5

lgCIMCT

PO3−4 , index, calculated

(−)

lgC

IMC

T

PO

3−

4, i

ndex

,i, c

alcu

late

d (−)

4

(a) (b)

5 6 3.5 4.0 4.5 5.0 5.5-14

-7

0

7

14P

2O

53FeO·P

2O

54FeO·P

2O

5

2CaO·P2O

53CaO·P

2O

54CaO·P

2O

5

2MgO·P2O

53MgO·P

2O

53MnO·P

2O

5

lgCPO , index, measured

(−)

lgC

PO

, ind

ex,i

, mea

sure

d (−

)3−

4

3−4

Fig. 7—Contribution of nine dephosphorization reaction products containing P2O5 in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags on

calculated lgCIMCTPO3�

4 ;index;calculatedby IMCT model (a) or measured lgCPO3�

4 ;index;measured (b) of the slags at top–bottom combined blown converter

steelmaking temperatures for 27 heats, respectively.


4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5,2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5 as shownin Eqs. [16a] through [i] or in Eqs. [19a] through [i]. Thecalculated respective phosphate capacity indexCIMCT

PO3�4 ;index;i;calculated

of the previously mentioned nine

structural units containing P2O5 can be determined bythe developed IMCT model as the corresponding nineterms in right-hand side of Eq. [21].

The relationship between the calculatedlgCIMCT


of nine structural units containing

P2O5 and calculated lgCIMCTPO3�

4 ;index;calculatedof the slags by

the developed IMCT model at combined blown con-verter steelmaking temperatures is illustrated in Fig-ure 7(a), respectively. The formulas of the linearrelationship between the calculated CIMCT


of structural unit i containing P2O5 and calculatedCIMCT


of the slags are also summarized in

Table V. The slope of the linear relationship between thecalculated CIMCT


of structural unit i con-

taining P2O5 and calculated CIMCTPO3�

4 ;index;calculatedof the

slags can be treated as the contribution ratio ofstructural unit i containing P2O5 in the slags when theintercept of the linear relationship is much smaller thanthe calculated CIMCT


of the slags; otherwise,

the slop of the linear relationship between the calculatedCIMCT


of structural unit i containing P2O5

and calculated CIMCTPO3�

4 ;index;calculatedof the slags cannot be

treated as contribution ratio of structural unit i con-taining P2O5.

The average contribution ratio of each structural unitin nine structural unit i containing P2O5, i.e.,CIMCT


=CIMCTPO3�

4 ;index;calculated; for 27 heats is

also listed in Table V, respectively. Obviously, theaverage contribution ratio of P2O5, 3FeOÆP2O5, 4FeOÆ-P2O5, 2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5 asstructural units containing P2O5 to the calculatedCIMCT


of the slags by IMCT model is small

and can be ignored compared with contribution ratio of3CaOÆP2O5 as 96.01 pct, 4CaOÆP2O5 as 3.97 pct, and2CaOÆP2O5 as 0.016 pct, which is the same with thecontribution ratio of 3CaOÆP2O5, 4CaOÆP2O5, and2CaOÆP2O5 as structural units or complex moleculescontaining P2O5 to LIMCT

P;calculated by IMCT LP model

reported in previous publication.[30] Similar conclusionsby other researchers[44–50] have been obtained fromexperiments that most of phosphorus in slags can bebonded with 2CaOÆSiO2 particles as 3CaOÆP2O5 in slags.

B. Contribution of Basic Oxides to Measured PhosphateCapacity Index of the Slags

It is assumed that the contribution ratio of ninedephosphorization reactions to the total dephosphor-ization potential of the slags is unchangeable; the calcu-lated CIMCT

PO3�4 ;index;i;measured

of the previously mentioned

nine dephosphorization reaction products containingP2O5 based on the measured CPO3�

4 ;index;measured can be

also obtained. The relationship between the calculatedlgCIMCT


of structural unit i containing P2O5

by IMCT model and measured lgCPO3�4 ;index;measured for

the slags at combined blown steelmaking temperatures isshown in Figure 7(b). The regressed linear relationshipsbetween the calculated CIMCT


of nine struc-

tural units containing P2O5 as P2O5, 3FeOÆP2O5,4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5,2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5, and themeasured CPO3�

4 ;index;measured of the slags are also sum-

marized in Table V. The average contribution ratio ofeach structural unit in nine simple or complex mole-cules, i.e., CIMCT


=CPO3�4 ;index;measured, for 27

heats are also listed in Table V.Therefore, the comprehensive contribution of FetO,

CaO + FetO, MgO + FetO, and MnO + FetO to themeasured CPO3�

4 ;index;measured of CaO-SiO2-MgO-FeO-

Fe2O3-MnO-Al2O3-P2O5 converter steelmaking slags isapproximately 0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct,respectively. The contribution of FetO, CaO+FetO,MgO+FetO, and MnO+FetO to the calculatedCIMCT


by IMCT model or the measured

CPO3�4 ;index;measured is the same as that for the calculated

LIMCTP;calculated from IMCT LP model or measured LP;measured

of the slags equilibrated with molten steel reported in aprevious publication.[30]

VII. INFLUENCES OF COMPONENTS ONPHOSPHATE CAPACITY INDEX OF THE SLAGS

A. Relationship between Slag Basicity and PhosphateCapacity Index of the Slags

The relationship between the measuredlgCPO3�

4 ;index;measured or calculated lgCIMCTPO3�

4 ;index;calculated

of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsand the binary basicity (B = pct CaO)/(pct SiO2),complex basicity ðpct CaO) + 1:4ðpct MgO)ð Þ=ðpct SiO2Þ + (pct P2O5Þ + (pct Al2O3Þð Þ, or opticalbasicity with three-group optical basicities for FeOand Fe2O3 as (1) KFeO= 0.51 and KFe2O3

= 0.48 fromPauling electronegativity,[41] (2) KFeO= 0.93 andKFe2O3

= 0.69 from average electron density,[42] and (3)KFeO= 1.0 and KFe2O3

= 0.75 from mathematicalregression,[43] is illustrated in Figure 8, respectively. Itcan be observed from Figure 8(a) that there is ascattered parabolic relationship between the calculatedlgCIMCT


by IMCT model and binary

basicity with a top of (pct CaO)/(pct SiO2) as approx-imately 3.5–4.0. However, there is no obvious relation-ship between the measured lgCPO3�

4 ;index;measured and

binary basicity. The calculated CIMCTPO3�

4 ;index;calculatedby

IMCT model is more accurate to present CPO3�4 ;index than

the measured CPO3�4 ;index;measured of the slags. Thus, the


Table

V.

Regressed

ExpressionsofC

IMCT

PO

3�4;index;i;calculatedagainst

CIM

CT

PO

3�

4;index;calculatedandC

IMCT

PO

3�

4;index;i;m

easuredagainst

CPO

3�

4;index;m

easuredforNineDephosphorizationReaction

ProductsContainingP2O

5andAverageContributionRatioofNineDephosphorizationReactionProductsContainingP2O

5ToC

IMCT

PO

3�4;index;calculatedorC

PO

3�

4;index;m

easured

oftheSlagsatTop–Bottom

Combined

BlownConverter

SteelmakingTem

peraturesBasedonIM

CTFor27Heats

Item

Sim

ple

orComplex

Molecules

Form

ulasof

CIM

CT

PO

3�

4;index;i;calculatedagainst

CIM

CT

PO

3�

4;index;calculatedorC

IMCT

PO

3�4;index;i;m

easured

against

CPO

3�4;index;m

easured

ofNineSim

ple

orComplexMolecules

AverageContribution

RatioofNineSim

ple

orComplex

Moleculesto

CIM

CT

PO

3�

4;index;calculatedorC

PO

3�4;index;m

easured(pct)

Basedon

CIM

CT

PO

3�

4;index;calculated

P2O

5C

IMCT

PO

3�4;index;P

2O

5;calculated¼

4:446�10�13þ4:143�10�18C

IMCT

PO

3�4;index;calculated

1.02

910�15

3FeO

ÆP2O

5C

IMCT

PO

3�4;index;3FeO�P

2O

5;calculated¼

1:623�10�7þ2:107�10�12C

IMCT

PO

3�

4;index;calculated

3.79

910�10

4FeO

ÆP2O

5C

IMCT

PO


2O

5;calculated¼

1:205�10�6þ1:098�10�11C

IMCT

PO

3�

4;index;calculated

2.34

910�9

2CaO

ÆP2O

5C

IMCT

PO

3�4;index;2CaO�P

2O

5;calculated¼

2:604þ1:278�10�4C

IMCT

PO

3�

4;index;calculated

1.62

910�2

3CaO

ÆP2O

5C

IMCT

PO


2O

5;calculated¼�108:716þ0:961C

IMCT

PO


96.00

4CaO

ÆP2O

5C

IMCT

PO


2O

5;calculated¼

105:646þ0:038C

IMCT

PO


3.98

2MgO

ÆP2O

5C

IMCT

PO

3�4;index;2MgO�P

2O

5;calculated¼

0:409þ2:265�10�6C

IMCT

PO

3�

4;index;calculated

7.93

910�4

3MgO

ÆP2O

5C

IMCT

PO


2O

5;calculated¼

0:0573þ1:295�10�7C

IMCT

PO

3�

4;index;calculated

9.37

910�5

3MnO

ÆP2O

5C

IMCT

PO

3�4;index;3MnO�P

2O

5;calculated¼

1:841�10�7þ1:624�10�10C

IMCT

PO


1.91

910�8

Basedon

CPO

3�

4;index;m

easured

P2O

5C

IMCT

PO

3�4;index;P

2O

5;m

easured¼

5:034�10�13þ4:200�10�18C

PO

3�4;index;m

easured

1.02

910�15

3FeO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼

1:784�10�7þ2:192�10�12C

PO

3�

4;index;m

easured

3.79

910�10

4FeO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼

1:323�10�6þ1:162�10�11C

PO

3�

4;index;m

easured

2.34

910�9

2CaO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼

2:936þ1:282�10�4C

PO

3�

4;index;m

easured

1.62

910�2

3CaO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼�124:770þ0:961C

PO

3�

4;index;m

easured

96.00

4CaO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼

121:305þ0:0385C

PO

3�4;index;m

easured

3.98

2MgO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼

0:4632þ2:310�10�6C

PO

3�

4;index;m

easured

7.93

910�4

3MgO

ÆP2O

5C

IMCT

PO


2O

5;m

easured¼

0:0651þ1:345�10�7C

PO

3�

4;index;m

easured

9.37

910�5

3MnO

ÆP2O

5C

IMCT

PO

3�4;index;3MnO�P

2O

5;m

easured¼

5:665�10�7þ1:585�10�10C

PO

3�4;index;m

easured

1.91

910�8


parabolic relationship shown in Figure 8(a) can presentthe relationship between CPO3�

4 ;index and binary basicity

of the slags at top–bottom combined blown convertersteelmaking temperatures for 27 heats, respectively.

A parabolic relationship, rather than a linear rela-tionship, between the calculated lgCIMCT


by

IMCT model and complex basicity can be observed inFigure 8(b). Considering the fact that the measuredCPO3�

4 ;index;measured are calculated from the measured

LP;measured; which is obtained from the chemical compo-sitions of both slags and molten steel at the steelmakingendpoint rather than from slag–metal equilibriumexperiments, the linear relationship between the mea-sured lgCPO3�

4 ;index;measured and complex basicity is not

the intrinsic relationship compared with the parabolicrelationship between the calculated lgCIMCT


by IMCT model and complex basicity. Hereby, aparabolic relationship between CPO3�

4 ;index and complex

basicity can be deduced from the relationship betweenthe calculated lgCIMCT


by IMCT model and

complex basicity shown in Figure 8(b) with a top ofcomplex basicity as about 1.75.

A linear relationship between the calculatedlgCIMCT


by IMCT model and optical basi-city with KFeO as 0.51 and KFe2O3

as 0.48[41] can beobserved from Figure 8(c), in which increasing opticalbasicity K can lead to increasing of the calculatedlgCIMCT


by IMCT model, whereas no obvi-ous relationship between the calculatedlgCIMCT


by IMCT model and optical basi-city with KFeO as 0.93 and KFe2O3

as 0.69[42] or KFeO as1.0 and KFe2O3

as 0.75[43] can be observed. This impliesthat the reasonable linear relationship betweenCPO3�

4 ;index and optical basicity K can be established onlywith KFeO as 0.51 and KFe2O3

as 0.48[41] for the slags atthe steelmaking endpoint in an 80-ton top–bottomcombined blown steelmaking converter.

B. Relationship between Mass Percent of Componentsand Phosphate Capacity Index of the Slags

The effect of the mass percent of CaO, SiO2, MgO,FeO, Fe2O3, MnO, and Al2O3 as components in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3 slags on the mea-sured lgCPO3�

4 ;index;measured or calculated

lgCIMCTPO3�

4 ;index;calculatedof the slags at top–bottom com-

bined blown converter steelmaking temperatures isgiven in Figure 9, respectively. It has been pointed outin Section VII–A that the calculated CIMCT


by IMCT model is more accurate than the measuredCPO3�

4 ;index;measured to express CPO3�4 ;index of the slags.

Therefore, the corresponding curves are drawn only forthe relationship between (pct i) and the calculatedlgCIMCT


by IMCT model in Figure 9. A

parabolic relationship between the calculatedlgCIMCT


by IMCT model and (pct CaO),

(pct SiO2), (pct FeO), or (pct Fe2O3) can be regressedwith a top as 43 pct for (pct CaO), 13.5 pct for (pctSiO2), 12.5 pct for (pct FeO), and 20 pct for (pct Fe2O3).However, a linear relationship between the calculatedlgCIMCT


by IMCT model and (pct MgO),

(pct MnO), or (pct Al2O3) can be regressed, in whichincreasing (pct MgO) as well as (pct MnO) can result ina slowly decreasing of the calculated lgCIMCT


by IMCT model. Oppositely, increasing (pct Al2O3) willbe beneficial to improve the calculatedlgCIMCT


of the slags by IMCT model.

C. Relationship between Mass Action Concentrations ofComponents and Phosphate Capacity Index of the Slags

The effect of the calculated mass action concentra-tions of components, i.e., NCaO, NSiO2

; NMgO, NFeO,NFe2O3

; NAl2O3; NFeO�Fe2O3

; and NFetO ¼ NFeOþ

2 3 4 53

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

sure

d or

lgC

IMC

T

PO

3− 4, i

ndex

, cal

cula

ted (−)

Binary basicity (−)

1.0 1.5 2.0 2.53

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

sure

d or

lgC

IMC

T

PO

3− 4, i

ndex

, cal

cula

ted (−)

Complex basicity (−)

0.65 0.70 0.75 0.80 0.853

4

5

6

7

8 ΛFeO

, ΛFe

2O

3

0.51, 0.48 lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

0.93, 0.69 lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

1.0, 0.75 lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

sure

d or

lgC

IMC

T

PO

3− 4, i

ndex

, cal

cula

ted

(−)

(c)(b)(a)Optical basicity (−)

Fig. 8—Effect of binary basicity (pct CaO)/(pct SiO2) (a), complex basicity ðpct CaO) + 1:4ðpct MgO)ð Þ= ðpct SiO2Þ þ ðpct P2O5Þþð ðpct Al2O3ÞÞ(b), and optical basicity (c) of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags by choosing (1) KFeO= 0.51, KFe2O3

= 0.48, (2) KFeO= 0.93,

KFe2O3= 0.69, or (3) KFeO= 1.0, KFe2O3

= 0.75 on measured lgCPO3�4 ;index;measured or calculated lgCIMCT


by IMCT model at top–

bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


6NFe2O3þ 8NFe3O4

on the measured lgCPO3�4 ;index;measured

or calculated lgCIMCTPO3�

4 ;index;calculatedof the slags at top–

bottom combined blown converter steelmaking temper-atures is given in Figure 10, respectively. The curves ofthe relationship between mass action concentrations ofcomponents Ni and the calculated lgCIMCT


by IMCT model are illustrated in Figure 10 as the samereason described in Sections VII–A and VII–B.

There is a flat parabolic relationship between thecalculated lgCIMCT


by IMCT model and Ni

for NCaO, NSiO2; NMgO, NFe2O3

; NFeO�Fe2O3; and

NFetO ¼ NFeO þ 6NFe2O3þ 8NFeO�Fe2O3

; a linear relationfor NAl2O3

; an obvious parabolic relationship for NFeO

and NFetO: This result means the slag oxidizationability has a large influence on CPO3�

4or CPO3�

4 ;index of

the slags.

1 2 3 4 53

4

5

6

7 Al

2O

3

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

Mass percent of Al2O

3 (%)

30 35 40 45 50 55 603

4

5

6

7 CaO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

Mass percent of CaO (%)5 10 15 20 25

3

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

SiO2

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

Mass percent of SiO2 (%)

5 6 7 8 9 103

4

5

6

7 MgO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

Mass percent of MgO (%)

5 10 15 20 25 303

4

5

6

7 Fe

2O

3

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3−

4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

Mass percent of Fe2O

3 (%)

0.5 1.0 1.53

4

5

6

7 MnO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

Mass percent of MnO (%)0 5 10 15 20

3

4

5

6

7 FeO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

Mass percent of FeO (%)

(a) (b) (c)

(d)

(g)

(e) (f)

Fig. 9—Effect of mass percent of CaO, SiO2, MgO, FeO, Fe2O3, MnO and Al2O3 as components in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags on measured lgCPO3�

4 ;index;measured and calculated lgCIMCTPO3�

4 ;index;calculatedby IMCT model at top–bottom combined blown converter steel-

making temperatures for 27 heats, respectively.


D. Relationship between Ratio of Mass Percentfor Iron Oxides to Basic Oxides and Phosphate CapacityIndex of the Slags

It has been concluded in Section VI–A that the compre-hensive effect of slag oxidization ability and four basiccomponents affects the dephosphorization reactions. Thecomprehensive effect of slag oxidization ability and fourbasic components can be presented by the mass percent

ratio of iron oxides to basic oxides on CPO3�

4

or CPO3�4 ;index:

The relationship between the mass percent ratio of ironoxides, i.e., FeO, Fe2O3, and FetO, to basic oxides, i.e.,CaO, MgO, and MnO, and the measuredlgCPO3�



IMCT model of the slags at top–bottom combined blownconverter steelmaking temperatures is illustrated in

0.20 0.25 0.30 0.35 0.40 0.453

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

CaOlgC

PO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

NCaO

(−)0.0000 0.0002 0.0004

3

4

5

6

7 SiO

2

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NSiO

2

(−)0.15 0.20 0.25 0.303

4

5

6

7 MgO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

NMgO

(−)

0.0 0.1 0.2 0.3 0.43

4

5

6

7 FeO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

NFeO

(−)0.00 0.01 0.02 0.033

4

5

6

7 Fe

2O

3

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NFe

2O

3

(−)0.01 0.02 0.033

4

5

6

7 MnO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NMnO

(−)

0.0 0.2 0.4 0.6 0.83

4

5

6

7lg

CP

O3− 4

, ind

ex, m

eas. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

FetO

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

NFe

tO (−)

0.000 0.001 0.002 0.0033

4

5

6

7 Al

2O

3

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NAl

2O

3

(−)0.00 0.01 0.02 0.03 0.043

4

5

6

7 FeO·Fe

2O

3

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (− )

NFeO·Fe

2O

3

(−)

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 10—Effect of calculated mass action concentration of ion couples or simple or complex molecules of (Ca2++O2�), SiO2, (Mg2++O2�), (Fe2++O2�), Fe2O3, (Mn2++O2�), Al2O3, FeOÆFe2O3, and defined NFetO in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags on measured lgCPO3�

4 ;index;measuredor calculated lgCIMCT


by IMCTmodel at top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


0.0 0.2 0.4 0.63

4

5

6

7

(a)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (− )

(%FeO)/(%CaO) (−)0.0 0.3 0.6 0.93

4

5

6

7

(b)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (−)

(%Fe2O

3)/(%CaO) (−)

0.0 0.5 1.0 1.53

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

(c)

(d) (e) (f)

(g) (h)

(j) (k)

(i)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

(%FetO)/(%CaO) (−)

0 1 2 33

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (−)

(%FeO)/(%MgO) (−)0 1 2 3 4 5

3

4

5

6

7lg

CP

O3− 4

, ind

ex, m

eas. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

(%Fe2O

3)/(%MgO) (−)

0 2 4 6 83

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

(%FetO)/(%MgO) (−)

0 10 20 303

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

(%FeO)/(%MnO) (−)

0 10 20 30 40 503

4

5

6

7

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (− )

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

(%Fe2O

3)/(%MnO) (−)

0 10 20 30 40 50 60 703

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (−)

(%FetO)/(%MnO) (−)

0.30 0.35 0.40 0.45 0.503

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

(%FeO)/(%FetO) (−)

0.55 0.60 0.65 0.70 0.753

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3 − 4, i

ndex

, cal

. (−)

(%Fe2O

3)/(%Fe

tO) (−)

Fig. 11—Relationship between mass percent ratio of iron oxides, i.e., FeO, Fe2O3, and FetO, to basic oxides, i.e., CaO, MgO, MnO, and

lgCPO3�4 ;index;measured or lgCIMCT


(a)–(i) and plot of mass percent ratio of FeO or Fe2O3 to FetO against lgCPO3�4 ;index;measured or

lgCIMCTPO3�

4 ;index;calculated(j)–(k) at top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


0.0 0.5 1.0 1.5 2.03

4

5

6

7lgC

PO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NFeO

/NMgO

(−)0.00 0.04 0.08 0.12 0.163

4

5

6

7lgC

PO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NFe

2O

3

/NMgO

(−)0.00 0.05 0.10 0.15 0.203

4

5

6

7lgC

PO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NFeO·Fe

2O

3

/NMgO

(−)

0 5 10 15 20 253

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

NFeO

/NMnO

(−)0.0 0.5 1.0 1.5 2.03

4

5

6

7

NFe

2O

3

/NMnO

(−)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

0 1 2 33

4

5

6

7

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

NFeO·Fe

2O

3

/NMnO

(−)

0.00 0.04 0.08 0.123

4

5

6

7

(b)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

NFe

2O

3

/NCaO

(−)0.00 0.04 0.08 0.12 0.163

4

5

6

7

(c)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

NFeO·Fe

2O

3

/NCaO

(−)0.0 0.5 1.0 1.53

4

5

6

7

NFeO

/NCaO

(−)

(a)

(e) (f)(d)

(h) (i)(g)

(k) (l)(j)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

0.3 0.4 0.5 0.6 0.73

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3 − 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (− )

NFeO

/NFe

tO (−)

0.02 0.03 0.04 0.05 0.063

4

5

6

7

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

NFe

2O

3

/NFe

tO (−)

0.01 0.02 0.03 0.04 0.053

4

5

6

7

lgCPO3−

4, index, meas.

lgCIMCT

PO3−

4, index, cal.

lgC

PO

3− 4, i

ndex

, mea

s. o

r lg

CIM

CT

PO

3− 4, i

ndex

, cal

. (−)

NFeO·Fe

2O

3

/NFe

tO (−)

Fig. 12—Relationship between mass action concentration ratio of iron oxides, i.e., NFeO, NFe2O3; NFeO�Fe2O3

; to basic oxides, i.e., NCaO, NMgO,

NMnO, and lgCPO3�4 ;index;measured or lgCIMCT


(a)–(i) and plot of NFeO=NFetO; NFe2O3=NFetO; or NFeO�Fe2O3

=NFetO against

lgCPO3�4 ;index;measured or lgCIMCT


(j)–(k) at top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


Figures 11(a) through (i), whereas the relationshipbetween the mass percent ratio of FeO or Fe2O3 to FetOand the measured lgCPO3�

4 ;index;measured or calculated

lgCIMCTPO3�

4 ;index;calculatedby IMCT model of the slags at top–

bottom combined blown converter steelmaking tempera-tures is alsodepicted inFigures 11(j) and (k).The regressedcurves between the calculated lgCIMCT


by

IMCT model and the mass percent ratio are plotted inthe corresponding figures in Figure 11. The parabolicrelationships in Figure 11 suggest that the dephosphoriza-tion reactions are controlled by the comprehensive effectsof iron oxides coupled with basic oxides, rather than theindependent effects of iron oxides or basic oxides during atop–bottom combined blown converter steelmaking pro-cess. The optimal dephosphorization condition can befound at a reasonable mass percent ratio of FeO to Fe2O3

as 0.62 (=0.40/0.65) from Figures 11(j) and (k).

E. Relationship between Ratio of Mass ActionConcentrations for Iron Oxides to Basic Oxidesand Phosphate Capacity Index of the Slags

The relationship between mass action concentrationratio of iron oxides, i.e., FeO, Fe2O3, and FetO, to basicoxides, i.e., CaO, MgO, and MnO, and the measuredlgCPO3�



IMCT model of the slags at top–bottom combinedblown converter steelmaking temperatures is illustratedin Figures 12(a) through (i), respectively. The relation-ship between NFeO=NFetO, NFe2O3

=NFetO, orNFeO�Fe2O3

=NFetO and the measured lgCPO3�4 ;index;measured

or calculated lgCIMCTPO3�

4 ;index;calculatedof the slags by IMCT

model of the slags at top–bottom combined blownconverter steelmaking temperatures is also depicted inFigures 12(j) through (l). The regressed parabolic curvesbetween the calculated lgCIMCT


by IMCT

model and mass action concentration ratio of ironoxides to basic oxides can be observed in Figures 12(a)through (j) and Figure 12(l) except NFe2O3

=NFetO; therelationship between the calculated lgCIMCT


by IMCT model and NFe2O3=NFetO in Figure 12(k) is a

linearly decaying relationship with an increasing ofNFe2O3

=NFetO. The reasonable NFeO=NFetO as 0.5,NFeO�Fe2O3

=NFetO as 0.03, and small NFe2O3=NFetO can

promote the dephosphorization potential of the slagsfrom Figures 12(j) through (l).

VIII. CONCLUSIONS

A thermodynamic model for predicting the phosphatecapacity CPO3�

4and phosphate capacity index CPO3�

4 ;indexof CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsat the steelmaking endpoint during an 80-ton top–bottom combined blown converter process has beendeveloped based on IMCT, i.e., IMCT model. The mainsummary remarks can be obtained as follows:

1. The predicted phosphate capacity CIMCTPO3�

4 ;calculatedor

phosphate capacity index CIMCTPO3�

4 ;index;calculatedby the

developed IMCT model has a good agreement withthe measured phosphate capacity CPO3�

4 ;measured as

well as the measured phosphate capacity indexCPO3�

4 ;index;measured of CaO-SiO2-MgO-FeO-Fe2O3-

MnO-Al2O3-P2O5 slags at the steelmaking endpointduring an 80-ton top–bottom combined blown con-verter process. The developed IMCT model and Su-ito’s model with KFeO as 0.51 and KFe2O3

as 0.48 foroptical basicity can be used to predict C

PO3�4

and

CPO3�4 ;index of the slags reliably compared with other

phosphate capacity prediction models, such as Selin’smodel, Mori’s model, and Young’s model.

2. The phosphate capacity CPO3�4

or phosphate capacityindex CPO3�

4 ;index of the slags are controlled by the

comprehensive effect of slag oxidization ability ex-pressed as FetO and basic oxides rather than thesingle effect of slag oxidization ability or basic oxidecomponents. The contribution ratio of FetO, CaO +FetO, MgO + FetO, and MnO + FetO to the cal-culated phosphate capacity CIMCT

PO3�4 ;calculated

or phos-

phate capacity index CIMCTPO3�

4 ;index;calculatedof the slags by

IMCT model is approximately 0.0 pct, 99.996 pct,0.0 pct, and 0.0 pct, respectively. The generated2CaOÆP2O5, 3CaOÆP2O5, and 4CaOÆP2O5 as theproducts of dephosphorization reactions accounts for0.016 pct, 96.01 pct, and 3.97 pct of contribution tothe phosphate capacity CPO3�

4or phosphate capacity

index CPO3�4 ;index of the slags, respectively. Meanwhile,

the other dephosphorization reaction products, suchas P2O5, 3FeOÆP2O5, 4FeOÆP2O5, 2MgOÆP2O5,3MgOÆP2O5, and 3MnOÆP2O5 only have a negligiblecontribution to the phosphate capacity CPO3�

4or

phosphate capacity index CPO3�4 ;index of the slags.

3. The phosphate capacity CPO3�4

based on the slag–gasequilibrium is much greater than the phosphatecapacity index CPO3�

4 ;index based on slag–metal equi-

librium, whereas the value of lgCPO3�4

is 12.724 larger

than lgCPO3�4 ;index of a slag at 1873 K (1600 �C).

4. The predicted phosphate capacity CIMCTPO3�

4 ;calculatedor

phosphate capacity indexCIMCTPO3�

4 ;index;calculatedof the slags

by IMCT model is more accurate than the measuredphosphate capacityCPO3�

4 ;measured or phosphate capacity

index CPO3�4 ;index;measured to present dephosphorization

potential because the measured phosphate capacityCPO3�

4 ;measured or phosphate capacity index

CPO3�4 ;index;measured can be transferred from themeasured

phosphorus distribution ratio LP;measured of the slagsequilibrated or quasi-equilibrated with molten steel atthe steelmaking endpoint during an 80-ton top–bottomcombined blown converter process. The parabolicrelationship between the predicted phosphate capacityindex CIMCT


of the slags by IMCT model

and the binary basicity (pctCaO)/(pct SiO2) or complex


basicity ðpct CaO) + 1:4ðpct MgO)ð Þ= ðpct SiO2Þð+ (pct P2O5Þ + (pct Al2O3ÞÞ can be found with themaximum CIMCT


at binary basicity as 3.5–

4.0 or at complex basicity as 1.75. Meanwhile, the pre-dicted phosphate capacity index CIMCT


of

the slags by IMCTmodel has a linear relationship withoptical basicity only adopting KFeO as 0.51 and KFe2O3

as 0.48.5. There is a reasonable ratio ofmass percent (pct i) ormass

action concentration Ni of iron oxides FeO, Fe2O3, orFetO, to that of basic oxides CaO, MgO, or MnO, tomaintain the maximum phosphate capacity indexCPO3�

4 ;index of the slags. Meanwhile, the optimal ratio of

(pct FeO) to (pct Fe2O3) is 0.62 to maintain the maxi-mum phosphate capacity index CPO3�


NOMENCLATURE

ai activity of component i in slags ormolten steel (�)

ainterfaceO;ðFetOÞ�½O�

activity of dissolved oxygen inmolten steel at slag–metal interfacebased on (FetO)–[O] equilibrium(�)

B binary slag basicity of slags, i.e.,the ratio of (pct CaO) to (pct SiO2)(�)

B0

ratio of mole fraction betweenCaO and SiO2 in slags, i.e.,xCaO=xSiO2

ð�ÞCPO3�

4phosphate capacity of slags (�)

CPO3�4 ;index phosphate capacity index of slags

(�)CP3� phosphide capacity of slags (�)CP3�;index phosphide capacity index of slags

defined asðpct P)=½pct P] � ½pct O]5=2 inSuito’s and Young’s model (�)

CS2� sulfide capacity of slags (�)C

NFetO;IMCT

PO3�4

calculated phosphate capacity ofslags by IMCT model using NFetO

to present slag oxidation ability(�)

CaO;IMCT

PO3�4

calculated phosphate capacity ofslags by IMCT model using aO topresent molten steel oxidationability (�)

CNFetO;IMCT

PO3�4 ;index

calculated phosphate capacityindex of slags by IMCT modelusing NFetO to present slagoxidation ability (�)

CaO;IMCT

PO3�4 ;index

calculated phosphate capacityindex of slags by IMCT modelusing aO to present molten steeloxidation ability (�)

CPO3�4 ;measured measured phosphate capacity of

slags (�)

CPO3�4 ;index;measured measured phosphate capacity

index of slags (�)Ci

PO3�4 ;calculated

calculated phosphate capacity ofslags by model i (�)

CiPO3�

4 ;index;calculatedcalculated phosphate capacityindex of slags by model i (�)

CIMCTPO3�

4 ;i;calculatedcalculated respective phosphatecapacity of structural unit icontaining P2O5 in slags by IMCTmodel (�)

CIMCTPO3�

4 ;index;i;calculatedcalculated respective phosphatecapacity index of structural unit icontaining P2O5 in slags by IMCTmodel (�)

CIMCTPO3�

4 ;i;measuredcalculated respective phosphatecapacity of structural unit icontaining P2O5 in slags by IMCTmodel based on measuredphosphate capacity CPO3�

4 ;measuredof slags (�)

CIMCTPO3�

4 ;index;i;meaasuredcalculated respective phosphatecapacity index of structural unit icontaining P2O5 in slags by IMCTmodel based on measuredphosphate capacity indexCPO3�

4 ;index;measured of slags (�)e

ji activity interaction coefficient of

component j to component i inmolten steel (�)

fi activity coefficient of component iin molten steel (�)

DrGHm;i standard molar Gibbs free energy

change of forming component i (J/mol)

KHi equilibrium constant of chemical

reaction for forming component ior structural unit i (�)

LP calculated phosphorus distributionratio between slags and metalphase using NFetO to present theslag oxidation ability based onIMCT with the same meaning ofLIMCT

P;calculated or defined phosphorusdistribution ratio between slagsand metal phase asLP ¼ ðpct P2O5Þ=½pct P]2 (–)

L0P calculated phosphorus distribution

ratio between the slags and metalphase using aO to present themolten steel oxidation abilitybased on IMCT with the samemeaning of L0IMCT

P;calculated or definedphosphorus distribution ratiobetween the slags and metal phaseas L0P ¼ ðpct P2O5Þ=½pct P]2 � LP

(–)L00P phosphorus distribution ratio

between the slags and molten steeldefined asL00P ¼ ðpct PO3�

4 Þ=½pct P] (–)


L000P phosphorus distribution ratiobetween the slags and molten steeldefined asL000P ¼ ðpct P2O5Þ=½pct P] (–)

LP;measured measured phosphorus distributionratio between the slags and metalphase defined asLP;measured ¼ ðpct P2O5Þ=½pct P]2

(�)LS sulfur distribution ratio between

the slags and metal phase definedas LS ¼ ðpct SÞ=½pct S] (�)

LIMCTP;calculated calculated phosphorus distribution

ratio between the slags and metalphase by IMCT phosphorusdistribution ratio model (�)

Mi relative elemental mass of elementi or component i (�)

ni equilibrium mole number ofstructural unit i or ion couple i inslags (mol)

Rn0i total mole number of all

components in 100-g slags beforereaction equilibrium according toIMCT (mol)P

ni total equilibrium mole number ofall structural units in 100-g slagsaccording to IMCT (mol)

Ni mass action concentration ofstructural unit i or ion couple i inslags (�)

½pct O�interfaceðFetOÞ�½O� calculated mass percent ofdissolved oxygen in molten steel atthe slag–metal interface based on(FetO)–[O] equilibrium with NFetO

to express the slag oxidizationability or FetO activity (�)

½pct O�bath½C��½O� mass percent of dissolved oxygenin metal bath based on [C]–[O]equilibrium with product of [pct C]and [pct O] as a constant atconverter steelmakingtemperatures (�)

pi partial pressure of component i ingas phase (Pa)

pH standard pressure of gas at sealevel and 273 K (0 �C) as 101325Pa (Pa)

½pct P�equilibriuminterface mass percent of phosphorus inmolten steel at slag–metal interfacebased on dephosphorizationreaction equilibrium (�)

ðpct P2O5Þi mass percent of P2O5 in generatedstructural unit i or complexmolecule i containing P2O5, suchas complex molecule 3CaOÆSiO2

and so on, in slags (�)R gas constant, (8.314 J/(molÆK))T absolute temperature (K)xi mole fraction of components i in

slags (�)

(pct i) mass percent of component i inslag phase (�)

[pct i] mass percent of component i inmetal phase (�)

[pct i]interface mass percent of component i inmolten steel at slag–metal interface(�)

[pct i]bath mass percent of component i inmetal phase with the samemeaning as [pct i] (�)

GREEK SYMBOLS

K optical basicity of slags (�)Ki optical basicity of component i in slags (�)

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