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General mass balance for oxygen steelmaking

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General mass balance for oxygen steelmaking

N. Madhavan, G. A. Brooks, M. A. Rhamdhani, B. K. Rout, F. N. H. Schrama &

A. Overbosch

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IRONMAKING & STEELMAKING
https://doi.org/10.1080/03019233.2020.1731252

General mass balance for oxygen steelmaking

N. Madhavana, G. A. Brooksa, M. A. Rhamdhania, B. K. Routb, F. N. H. Schramab and A. Overboschb
a
Department of Mechanical and Product Design Engineering, Swinburne University of Technology, Hawthorn, Australia; bTata Steel, IJmuiden, The
Netherlands

ABSTRACT ARTICLE HISTORY

Mass balances provide a fundamental approach for analysing the oxygen steelmaking process. Received 13 November 2019
Steelmaking plants commonly have in-house mass balance models for controlling process Accepted 6 February 2020
parameters. However, there exist only a few details in the literature pertaining to the formulation of
KEYWORDS
such models. Recent research published by Urban et al. [1] surveyed more than 30 BOF around the Mass balance; static model;
world and found that the phosphorus partitioning ratio has a strong dependence on oxygen process control; optimization;
blowing technologies and tapping temperature. The current work develops a general mass balance basic oxygen steelmaking;
model using semi-empirical relations that can be used to compute the amount of flux based on model validation; slag
the tapping temperature and the desired phosphorus concentration in the steel, applicable for formation; de-
different steelmaking technologies. The static model predictions are presented using a nomogram phosphorization
that illustrates the variation of mass of slag as a function of tapping temperature, silicon content in
hot metal and final phosphorus content in the steel.

Introduction dependent on oxygen steelmaking blowing technologies

(such as blow stir, blow stir-splash, top blow-splash, bottom
Oxygen steelmaking is a batch process that accounts for hot
blow-splash) and tapping temperature that varies from plant
metal, flux, scrap and oxygen as inputs to produce steel
to plant operations. The differences in these technologies are
with the desired composition. Conducting a mass balance
represented in Table 1. The work also shows that the difference
analysis with real-time operating conditions can provide an
between the equilibrium and the industrial phosphorus parti-
insight into the optimum input resources required for produ-
tioning ratio is quite high and varies in the range of 150–500
cing steel with the desired composition. On the basis of a
depending on the blowing technologies. This provides
steady-state mass balance concept, static charge control
strong evidence that the dephosphorization reaction at indus-
models have been developed. These models do not capture
trial operations is far from equilibrium. In the present work, the
the in-process variation during the blowing. Hence, static
research of Urban et al. [1] is used as a basis for developing a
charge models are used for analysing an oxygen steelmaking
generalized approach for understanding the mass balance of
process based on the input and output specifications. Static
an oxygen steelmaking process applicable to different
models were developed quickly by operators with the
blowing technologies.
advent of oxygen steelmaking in the 1950s but the first pub-
lished model was in 1960 [2], and the formulation of all
dynamic models was proceeded by considering inputs from
Selection of empirical relations and components
static models. Philbrook [3] presented the idea of using the
for mass balance
mass balance and thermochemistry approach for approximat-
ing the calculations involved in the basic oxygen (LD) steel- The mass balance model is formulated via a set of equations
making process. Static mass balance models developed by that represents elemental charge balance as shown in Table 2.
Slatosky [4], Jain [5], Dauby et al. [6], Goel et al. [7] and The functional relations existing among the variables are used
Katsura et al. [8] were used to calculate the thermodynami- to derive the mathematical model. As one of the major com-
cally balanced charge for an LD converter. Using a mass ponents of the steelmaking process exists in polymeric melt
balance model, Katsura et al. [8] also showed that the form (i.e. slag), it is essential to understand the distribution
amount of refractory wear can be quantified for different of elements like Fe, Si, Mn, P in the hot metal and the slag
sets of heating conditions. before carrying out a mass balance.
To formulate a realistic mass balance model that represents An extensive study carried out by Turkdogan [9] high-
the oxygen steelmaking process, relations derived from kinetic lights that most of the reactions in the oxygen steelmaking
modelling and semi-empirical equations from plant data are process are non-equilibrium for higher carbon content at
required. However, only very few details are available in the turndown. Using the plant data collected from BOP
open literature and studies that discuss the formulation (basic oxygen process) and Q-BOP (quiescent basic oxygen
behind the charge balance. Information pertaining to process) shops of US Steel Corporation, Turkdogan
in-house mass balance models used by the industry is gener- formulated semi-empirical relations for a number of
ally not available. A recent study carried out by Urban et al. elements as given by Equations (2, 4 and 6). All the indus-
[1] from more than 30 basic oxygen furnace (BOF) plants trial data were collected at 1610 ± 20° from North American
around the world shows that phosphorus partition ratio is plants, reflecting their particular modes of operation. The

CONTACT N. Madhavan nmadhavanpillaisajee@swin.edu.au Department of Mechanical and Product Design Engineering, Swinburne University of Tech-
nology, Hawthorn, Victoria 3122, Australia
© 2020 Institute of Materials, Minerals and Mining
2 N. MADHAVAN ET AL.

Table 1. Various blowing technologies in Oxygen steelmaking as studied by

Urban et al. [1].
Blowing technology Description
Blow stir Top blowing + bottom stirring without Slag splashing
Blow stir-splash Top blowing + bottom stirring + Slag splashing
Top blow-splash Top blowing + slag splashing
Bottom blow-splash Bottom stirring + slag splashing

Table 2. Generic static mass balance equations for oxygen steelmaking.

Components Balance equation
Fe, Si, Mn, P Mass of element in the hot metal + scrap + coolant (Fe2O3) =
Mass of element in the slag + Mass of element in Steel
O Mass of Oxygen supplied via lance + Oxygen in Ore = Mass of
oxygen in the slag (SiO2, FeO, P2O5, MnO) + Mass of oxygen in
CO, CO2 + Mass of dissolved oxygen in steel
C Mass of Carbon in the hot metal + Carbon in Scrap = Mass of
carbon in steel + Mass of carbon in CO, CO2
Flux Mass of Flux added = Mass of compound in the Slag (CaO, MgO)

Figure 2. Variation of iron oxide in slag with turndown carbon content in steel
values associated with the equations have correction factors for BOP and Q-BOP [9].
that vary according to the operating conditions like tapping
temperature, type of reaction and slag composition [9].
Figures 1–3 show the plots from the semi-empirical relations [MnO] + [C] = [Mn] + CO(g) (5)
which are compared with the equilibrium conditions and
plant data for BOP and Q-BOP processes [9]. All the indus- [%Mn] 1
√



= 0.1 + 0.02, for BOF with C , 0.1%
trial data were collected for tapping temperatures ranging (%MnO) [C] (6)
from 1590°C to 1630°C. At low carbon concentration, it = 0.2 + 0.02, for Q-BOP with C , 0.1%
can be observed from Figures 1 and 3 that the product of
[ppm O] [%C] and ratio [%Mn]/(%MnO) exhibit a linear cor-
relation with the square root of the carbon content of the Understanding the mechanism of phosphorus refining
steel. Whereas, FeO has an inverse relation with final from hot metal is always a challenge in the field of steelmak-
carbon content as shown in Figure 2. The semi-empirical ing technology. Several studies pertaining to the factors
relations obtained by compiling the plant data are rep- affecting the phosphorus partitioning (Lp) have been carried
resented using the following equations [9] (Figure 4): out and mathematical models have been developed to quan-
tify Lp as a function of tapping temperature and slag chem-
[C] + [O] = CO(g) (1) istry [10–19]. An empirical relation suggested by Healy [14]
√





has been commonly used in various modelling studies of
[ppm O] [%C] =135 + 5, for BOF at C , 0.05%
(2) the oxygen steelmaking process. The coefficients of the
=80 + 5, for Q-BOP at C , 0.08% equation are estimated from experimental studies of metal/
[FeO] + [C] = [Fe] + CO(g) (3) slag reaction and thermodynamic calculations of free
energy of formation of P2O5. Healy’s equation, when used
(%FeO) =4.2 + 0.3, for BOF with C , 0.1% for industrial conditions, overestimates the phosphorus
(4) removal or underestimates the amount of lime required for
=2.6 + 0.3, for Q-BOP with C , 0.1%
achieving the required phosphorus level in steel [1]. Selected
phosphorus partitioning equations from previous studies are

Figure 1. Product of [ppm O] [%C] variation in steel for various turndown Figure 3. Distribution of manganese in slag and metal for various composition
carbon content in the steel [9]. of turndown carbon content in the steel [9].
 IRONMAKING & STEELMAKING 3

Figure 4. Solubility of MgO as a function of basicity and FeO concentration [9]. Figure 5. Effect of tapping temperature and oxygen steelmaking technology on
phosphorus partition ratio [1].

presented in Table 3. These equations consider the phos- amount of oxygen consumed by the FeO and in the post-
phorus relations at equilibrium-controlled conditions, but combustion gases.
the comprehensive overview of industrial data by Urban As oxygen steelmaking is a batch process, it is essential to
et al. [1] suggest that the real process is far from equilibrium. capture the nature and components present in the inflow and
This was indicated by the deviation of the equilibrium phos- outflow of the system as shown in Figure 6 to understand the
phorus partitioning ratio by a range of 150–500 when com- complexity of the process. Therefore, subsequent sections
pared to the plant values. Furthermore, their study revealed discuss the components accounted for in a mass balance
that the variation of phosphorus partition value depends on for the oxygen steelmaking process.
the tapping temperature and the type of blowing technol-
ogies as shown in Figure 5. This suggests that different
plants will require specific phosphorus refining models for Hot metal
their process. The composition of the hot metal depends on the output
The presence of flue gas is included in the mass balance via from the blast furnace [24]. The colder blast furnace generally
the elemental balance of carbon and oxygen. A non-dimen- produces hot metal with low silicon and high sulphur content.
sional number termed post-combustion ratio (PCR) is used The hot charge fed into the BOF typically composed of 4.3–5
to analyse the amount of carbon dioxide present in the mass% C, 0.3–1.5 mass% Si, 0.05–0.2 mass% P, 0.25–2.2 mass
total flue gas, i.e. %CO2/(%CO2 + %CO). Furthermore, post- % Mn and 0.03–0.08 mass% S. Chipman et al. [24,25] found
combustion can provide an insight into the evolution of out that saturated amount of carbon in the liquid iron
oxides of iron in slag. Owing to the heterogeneous nature depends on the temperature and presence of other elements
of post-combustion, it is difficult to predict the proportions as produced by Equation (7).
of CO and CO2 in the flue gas. Huin et al. [21,22] developed
an integrated jet model for a 6-tonnes converter to predict % Csat (hot metal) = 0.64 + 0.00254 T(K) + 0.034(%Mn)
the PCR as a function of oxygen flow from the lance. Hirai − 0.34(%Si + %P + %S) (7)
et al. [23] carried out blowing tests and collected results
from a 250-tonnes converter to formulate a model for post- Generally, the desulphurization is performed before allowing
combustion using empirical equations. The composition of the hot charge into the BOF. The hot metal has a low O-activity
oxygen consumed by FeO and post-combustion gases CO/ and high S-activity coefficient; that makes de-S prior to BOF
CO2 in oxygen steelmaking is not generally available in the more efficient; that in turn makes the process low cost [26,27].
open literature. Hence, by considering suitable assumptions,
the mass balance model can be used to estimate the
Scrap
Scrap metal charged into the converter serves dual purpose pri-
Table 3. Selected phosphorus distribution equation from previous studies. marily as a source of iron and second as a coolant required for
Investigators Empirical equation Log (%P)/[%P] the oxygen steelmaking process. Typically 15–25% of the met-
Balajiva et al. [20] −0.36 + 0.5T+2.5log(%FeOn) + 5.9log(%CaO) + 0.5log(% allic charge is fed in the form of scrap into the BOF. The quantity
P2O5)
Turkdogan [21] 21740/T+0.071(%CaO+0.3%MgO) + 2.5log(%FeO)−9.87
of scrap added is a function of silicon in the hot charge, tapping
Healy [14] 22350/T+0.08(%CaO) + 2.5log(%Fet)−16.00 temperature and coolant supplied. A hot charge with more
Suito et al. [11] 10,730/T+4.11log(%CaO+0.3%MgO+%{CaF2}−0.05%FetO) silicon results in surplus heat that can be utilized by adding
+ 2.5log(%FeO) + 0.5log (%{P2O5})−13.8
Ide and Fruehan 10,730/T+4.11 log (%CaO+0.15%MgO + CaF2-0.05%FetO)
more scrap [24]. The different type of scraps that goes into a
[15] + 2.5log(%FeO) + 0.5log (%P2O5)−13.87 furnace includes trimmer scrap, sheet scrap, ingot butts and
Ogawa et al. [16] 2.5 log(%Fet) + 0.0715 (%CaO+0.25%MgO) + 7710.2/T+ slab ends. Lighter scraps melt faster and are generally preferred
(105.1/T + 0.0723) [%C]−8.55
compared to heavier scraps and are also likely to lower refractory
4 N. MADHAVAN ET AL.

Figure 6. Schematic representation of input and output in a BOF.

damages. A balance between light and heavy scrap is required composition of the slag is 45–52 wt-% CaO, 13–16 wt-% SiO2,
to achieve good process control. Therefore, scrap selection is 4–7 wt-% MnO, 10–30 wt-% FeO, 5–20 wt-% MgO, 1.2–
based on cost, quality, grade, size and various refractory con- 1.6 wt-% P2O5 and 1–8 wt-% Fe2O3 [26,32]. The study [33] per-
straints at the particular plant. taining to foams and emulsion in steelmaking describes that
during the initial phase of the blow, the oxygen reacts with
Flux the metal bath and initiates the slag formation. The oxidation
of silicon generates enough heat to dissolve fluxes into the slag
The quality and quantity of the flux decide the refining potential and lowering of lance promotes decarburization via FeO
of the BOF process. Inadequate strength of the flux material leads reduction. The refining action in steelmaking process is deter-
to erroneous basicity, dust formation that mixes flux with the flue mined by factors such as the slag composition, metal droplet
gas and an increase in pH level of water in the gas-cleaning plant generation, behaviour of droplet in the slag, liquidus tempera-
[28]. Generally, flux is added in the form of lime, dolomitic or lime- ture of the slag and mixing intensity [34–36]. In addition to
stone. Calcining of limestone in rotary hearth type kilns results in that, the layer formed by slag prevents exposure of the
burnt lime with 96 mass% CaO, 1 mass% MgO and 1 mass% SiO2 metal bath to air and regulates the bath temperature.
[23,28]. The factors determining the quality of the flux material
include its ability to maintain basicity, tendency to avoid slag
attack on refractory, dissolution property of flux and fluidic Flue gas
nature of the slag [25]. The flux requirement for the steelmaking
Analysis of flue gas from industrial results reveals that it consists
process can be calculated as a function of the amount of hot
of CO, CO2 and dust in the form of iron oxides and fumes. Inves-
metal, silicon content in hot metal and final composition of the
tigations [36–39] involving off-gas collection from the mouth of
steel. Burnt lime added typically ranges from 19 to 45 kg per
the converter reports that CO constitutes around 80% and CO2
tonne of steel produced. In the case of dolomitic lime, the com-
ranges from 10 to 20%. The variation in CO2 is mainly attributed
position is 55–59 wt-% CaO, 36–42 wt-% MgO and the amount
by the heat content, air entrainment and tapping temperature.
added ranges from 13 to 36 kg t−1 of steel produced [24]. The
Furthermore, the Fe2O3 in the dust collector accounts for 0.7
MgO requirement is decided based on the slag temperature
mass% of total iron charged [32,40]. The flue gas composition
and composition. In addition to that, excess MgO (i.e. above sat-
is derived from the mass balance of carbon, oxygen and level of
uration) is added in some operations to protect the vessel early in
post-combustion. The current model assumes the PCR and by
the blow, where a SiO2 rich slag is formed with a higher satur-
coupling carbon and oxygen mass balance with the PCR, the
ation level of MgO [29].
flue gas composition is calculated.

Oxygen
Coolants
Oxygen supplied via lance into the converter must be 99.5%
pure to ensure the production of the desired composition Coolants are added during the steelmaking process along
of carbon steel [28]. The rest is 0.005–0.015% nitrogen and with fluxes. Different types of coolants are iron ore in the
argon [30]. BOFs having 230–300 tonnes capacity operate form of pellets or lump and carbonates of calcium and mag-
with lance tips containing 4–6 nozzles supplying oxygen nesium. The main reason to use coolants is to control the
around 2.7–3 Nm3 min−1 per tonne of steel [24,31]. In the temperature at the endpoint and close temperature
case of bottom blown converters, using 14–22 tuyeres, balance. In addition to that, it serves the purpose of flux dis-
around 4–4.5 Nm3 min−1 of oxygen is supplied for producing solution, reduces the viscous nature of the slag and slopping
1 t of steel [24,29]. at mid blow [24]. The present mass balance calculations
assume 100% Fe2O3 as coolant added during the process.
The other coolants are added in minor amounts and it is
Slag
reasonable to neglect those variables in the general approach
Slag is a polymeric melt formed by oxides of impurities other of this mass balance model.
than carbon present in the hot metal. Other components He et al. [40] carried out a material balance analysis to
present in the slag include flux and refractory materials in dis- observe the mass flow, energy flow and carbon emission
solved or solid form. The density of a slag is lower than the hot from the BF-BOF plant. The amount of mass consumed and
steel in the liquid state [32] and the lower dense slag floats byproducts formed are plotted as shown in Figure 7. It was
above the steel. Slag is often referred to as a reservoir of observed that to produce 1 t of steel, around 2.69 tonnes of
oxide impurities and specified by the composition of oxides total mass input (BF and BOF) comprising of ore, coal, flux,
such as CaO, MgO, MnO, SiO2, P2O5, FeO and Fe2O3. Generally, scrap and oxygen was required.
 IRONMAKING & STEELMAKING 5

Figure 8. Comparison of phosphorus partition ratio predicted by Healy’s corre-

Figure 7. Major materials and byproducts by the mass quantity of producing lation with industrial data for various blowing technologies [1,46].
one metric ton of crude steel [40].

With these basic understandings about mass conservation that was used in various modelling studies of the oxygen steel-
and components involved in the mass balance equation, the making process. It should be noted, Urban et al. [1] have inves-
process control models can be developed to calculate the tigated and compared numerous P distribution equations and
influx charge before starting the oxygen injection. Therefore, recommended that Healy’s equation, in general, is the sim-
the subsequent section discusses the formulation and plest one to express the P distribution with the minimum
equations involved in developing static mass balance number of variables. However, the results from the Healy’s
control models. equation overestimate the industrial phosphorus removal
(Lp ranging from 200 to 700) or underestimates the amount
of lime required for achieving the required phosphorus in
Mass balance formulation and control equations steel. This variation is due to the fact that industrial Lp
Development of the static model starts with forming a series values are far from the equilibrium condition [1] and kinetics
of equations based on elemental mass balance and enumer- must be included in the kinetic model as per the studies high-
ating the specific types of variables involved in the equations. lighted by Basu et al. [44] and Rout et al. [45]. In addition to
These variables are divided into three categories: major vari- that, factors like slag temperature, operation parameters like
able, constant variables and neglected variables. The major blowing modes, lance height, stirring intensity and timing of
variables include the weight and composition of hot metal, iron ore and flux additions can decide the P distribution.
flux, liquid steel, slag, coolant (100% Fe2O3) and quantity of Hence, equations to correct the values from Healy’s equation
oxygen supplied. The final composition of carbon and phos- to the observed industrial phosphorus partition (Lpindustrial) for
phorus in steel, PCR and tapping temperature for each set different blowing technology were developed in the present
of calculations are considered to be constant variables. study and used. These are represented by Equations (13–15)
Lastly, the parameters such as degree of scrap oxidation, and were derived from Figure 8 that compares the range of
fume/dust losses, liquidus temperature of slag and other Lp values for different blowing technologies with the Lp
oxides in the slag like TiO2, V2O5 and Cr2O3 were taken as neg- value calculated via Healy’s equation.
lected variables for the formulation. To attain realistic results The saturation limit of MgO dissolution at 1600°C is calcu-
from the static control models, the equations are coupled lated from Equation (16) that is derived from an empirical fit to
using semi-empirical relations acquired from various graphs an equilibrium phase data represented in Figure 4 [9] for FeO
and industrial data. Previous studies [37,41] reveal that the percentage ranging from 20 to 30%. For tapping temperature
assumptions like steady-state process, deterministic model, above 1600°C, the amount of MgO dissolved in the quatern-
complete oxidation of silicon, complete utilization of oxygen ary slag containing CaO–FeO–SiO2 is calculated by Equation
and no oxygen presence in hot steel do not impair the accu- (17) developed by Carvalho [43] that depends on the
racy of the solution. Considering the different types of vari- tapping temperature. Further calculations inside the iteration
ables and assumptions, the elemental mass balance loop are carried out by solving the simultaneous Fe, Mn and P
equation can be written in the form: mass balance equations along with the semi-empirical
relations. A convergence criterion is set based on the error
Mass of element in the hot metal in phosphorus mass balance and the final iteration will
= Mass of element in the slag provide composition and weight of slag generated.
+ Mass of element in the steel √






(% FeO) [%C] = 4.2 + 0.3, for BOF with C , 0.1%
+ Mass of element in flue gas (8)
at Tap Temp.1610 + 20o C (9)
The simultaneous control equations formulated using the
mass of hot charge, hot steel and slag are coupled via empiri- [%Mn] 1
√



= 0.1+0.02, for BOF with C , 0.1%
cal relations represented as Equations (9–17) [1,8,13,23,42,43]. (%MnO) [C]
The mass balance model considers the final mass percentage at Tap Temp.1610 + 20o C (10)
of carbon and phosphorus in steel, hot charge mass and scrap
mass as the input. (%P)
Lp = where Lp:phosphorus partition (11)
The solution procedure for the model starts with the calcu- [%P]
lation of FeO in slag using Equation (9). The algorithm further
22, 350
proceeds by guessing the mass of slag. The %CaO in the slag logLp = + 2.5log(%Fet ) + 0.08(%CaO) − 16 + 0.4
T(K)
corresponding to the required composition of phosphorus in
(12)
steel is calculated using Healy’s equation (Equation (12)) [14]
6 N. MADHAVAN ET AL.

Lpindustrial = 0.099Lp + 30 (Top Blown) (13) are calculated. The flux amount is calculated as the sum of
predicted CaO and MgO in the slag. The calculation steps
Lpindustrial = 0.160Lp + 48 (Combined Blown) (14) involved in the static mass balance model are schematically
represented in Figure 9.
Lpindustrial = 0.2 Lp + 60 (Bottom Blown) (15)

(%MgOs,1600 ) = 0.23B 4 − 3.16B3 + 16.4B2 − 40B

+ 45.2 where B:basicity (16) Results and discussion

%MgOsat, T(K) = (%MgOs,1600 ).e(5.5478−(10391/T(K))) To validate the static balance model, the data pertaining to
(17) hot metal, scrap and end blow steel and slag composition
where PCR:Post Combustion ratio were taken from 35 heat sets of industrial heats provided by
%CO2 Tata Steel Netherlands. The Tata Steel BOF shop operates a
PCR = where PCR:Post Combustion ratio 330-tonne capacity converter integrated with combined
%CO + %CO2
blowing technology. The oxygen is delivered through a 6-
(18)
hole lance at supersonic speed and bottom stirring is
The calculations pertaining to carbon and oxygen balance achieved via injecting Ar/N2. Along with the hot metal,
are coupled using a dimensionless parameter known as PCR fluxes in the form of lime, raw dolomite, burnt dolomite and
(Equation (18)). Finally, from the overall mass balance coolants, such as recycled slag and iron ore, are also added
equation, the amount of flux and volume of oxygen supplied during the blowing period.

Figure 9. Calculation steps in static mass balance model.

 IRONMAKING & STEELMAKING 7

Figure 10. Validation of phosphorus partition values obtained from mass

Figure 11. Validation of amount of slag supplied obtained from mass balance
balance model with results from Tata Steels and Urban et al. [1].
model with results from Tata Steel.

Figure 10 shows the effect of tapping temperature on

phosphorus partition calculated via the mass balance
model. The typical range of the phosphorus partition ratio
of Tata Steel’s operation with top blow bottom stir technology
varies from 30 to 110. Industrial values acquired from Urban’s
study ranges from 50 to100 for the same technology as
inferred from Figure 8. The results reveal that the Lp predicted
by the model is consistent with the values obtained from Tata
Steel.
Figures 11 and 12 shows validation of the model with
oxygen supplied and the amount of slag generated for
various sets of heat data. In the present study, the amount
of oxygen supplied is calculated for different values of
assumed PCR. But, it was observed that when PCR is
assumed to be 0.16, the majority of the values predicted by
the model are in reasonable agreement with the plant data.
PCR value can be further optimized to achieve more accuracy.
The possible inaccuracies of the predicted values can be due
to following reasons: Figure 12. Validation of mass of oxygen values obtained from mass balance
model with results from Tata Steel.

(a) Assumptions considered and neglected variables such as

degree of scrap oxidation and fume/dust losses. technology with temperature ranging from 1700 to 1770°C
(b) The FeO, MnO and P2O5 in the slag are calculated using and final wt-% of phosphorus from 0.012 to 0.020% to calcu-
Equations (9, 10 and 12) that have a specific range of con- late the slag quantity at the HKM plant in Duisburg, Germany
stants based on tapping temperature. [1]. The present study calculates the slag generated to
(c) Hot metal C is determined by the saturation C formula achieve the final wt-% of phosphorus in steel (0.008–
(Equation (7)), which may not represent the accurate C 0.016%) from hot metal containing 0.4–0.85% silicon and
concentration. A small error in C concentration can tapping temperature ranging from 1600 to 1690°C with
make some difference in the oxygen requirement. which most of the oxygen steelmaking furnaces operate.
The specification of parameters used for the modified nomo-
gram construction is given in Table 4.
Conducting a static mass balance aids in calculating the The industrial significance of the modified nomogram
quantity of slag generated, flux required and oxygen sup- shown in Figure 13 is that it allows the amount of slag
plied for achieving the desired end composition of the required to be easily calculated based on a desired phos-
steel. The nomogram shown in Figure 13 calculates the phorus composition in steel and the silicon content of the
mass of slag generated based on silicon present in hot hot metal for a given tapping temperature. Figure 13(b) is
metal, the initial composition of phosphorus in hot metal drawn to estimate the mass of phosphorus in slag based on
and final composition of phosphorus in steel for a top the mass of P in hot metal and the final level of P in steel
blow bottom stir technology. The idea of developing a (0.008 and 0.016%). Figures 13(a) calculates the mass of slag
modified nomogram for the present model was derived for various final levels of P in steel (0.008 and 0.016%) at
from the study of Urban et al. [1]. The nomogram con- different levels of tap temperature and silicon in the hot
structed by Urban et al. [1] was for top blown bottom stir metal of 0.4%.
8 N. MADHAVAN ET AL.

the steelmaking process. Higher dephosphorization requires

more oxides in the slag, so the supply of oxygen needs to
be increased. Another phenomenon that depends on the
supply of oxygen is the decarburization effect. Higher decar-
burization requires more oxygen that results in high CO gas
formation and thus less oxygen is available for reaction with
CO to form CO2. The PCR generally ranges between 0.1 and
0.16 [47]. It is also observed that the amount of oxygen com-
puted by the mass balance model is underpredicted by 2–5%
compared to the industrial results of Tata when the PCR is set
to 0.16. In addition to oxygen supplied, the amount of flux
decides the possibility of achieving the desired composition
of steel from the oxygen steelmaking process. According to
the fundamentals of oxygen steelmaking, a higher tempera-
ture favours phosphorus reversion instead of dephosphoriza-
tion. Therefore, an additional amount of flux is required to
obtain the final percentage composition in steel. Results
plotted from the mass balance model, shown in Figure 15,
depicts the same behaviour. As the tap temperature is
increased from 1600 to 1690°C, the amount of flux added,
indicated via basicity, has also increased from 2.65 to 3.10
to achieve a phosphorus partition ratio of 60. Therefore,
a higher tap temperature requires more flux for
dephosphorization.
Figure 16 illustrates a linear relationship for the require-
ment of oxygen based on Si in hot metal at various compo-
sitions of phosphorus in steel and a tap temperature of
1650°C. The model is developed with the assumption that
silicon in the hot metal is completely oxidized. Hence, the pre-
diction shows that to achieve complete desiliconization and
higher dephosphorization to about 0.008% phosphorus in
steel, the oxygen requirement ranges from 37 to 40 Nm3 t−1
as the silicon content in hot metal increased from 0.4 to
0.7%. Results of the flux requirement predicted by the
model at various silicon concentrations in hot metal and a
Figure 13. Modified Nomogram from static mass balance model for top blow tap temperature of 1650°C are depicted in Figure 17. As the
bottom stir technology with Si in the hot metal of 0.4% using the approach silicon content in the hot metal is increased from 0.4 to 0.7
by Urban et al. [1] and to achieve 0.008% final phosphorus in steel, the flux
required found was increased by 20% for a specified tap
temperature of 1650°C and hot metal composition. The
Table 4. Specifications of parameters used for establishing nomograms.
higher composition of Si in hot metal results in increased
Parameters Values
SiO2 in the slag, which is acid in nature. Therefore, more
Hot metal to scrap 3.4–3.5
Wt. of hot metal 276.5 tonnes flux, in the form of lime and dolomite, is added to maintain
Wt. of liquid steel 336.3 tonnes
C, Si, Mn, P in hot metal 4.5%, 0.4–0.85%, 0.2–0.3%, 0.05–0.065%
End blow C 0.045%
PCR 0.16
Blowing technology Top blowing oxygen, bottom blowing Ar/N2
Flux Lime, burnt dolomite, raw dolomite
Tap temperature 1600–1690°C

The modified nomogram compositions in the summarized

form as per the approach of Urban et al. [1]. With the phos-
phorus in hot metal and calculated phosphorus in slag,
′
′′
points (aPslag and a′′Pslag ) are spotted in Figure 13 (b). This
point is then projected on to Figure 13(a) to find out the
amount of slag required to achieve phosphorus in slag for
silicon in the hot metal of 0.4% as denoted by points
′
a′′P Si 0.4 and a′′P Si 0.4 . Similar nomograms are developed for
silicon content 0.55, 0.7 and 0.85% in the hot metal and for
different blowing technologies(combined and bottom blow);
they are provided in Appendices I, II, and Appendices III.
The trend of variation in oxygen supplied shown in Figure 14. Effect of oxygen supplied on final wt-% of phosphorus for different
Figure 14 is in accordance with the physical chemistry of PCR.
 IRONMAKING & STEELMAKING 9

Figure 15. Variation of basicity with phosphorus partition at different tap Figure 17. Amount of flux required to achieve final phosphorus content in steel
temperatures. at different levels of Si in hot metal at 1650°C.

Conclusion
It can be inferred from the present calculations and analysis that:

. The static model developed with the mass balance concept

and semi-empirical relation obtained from the industrial
studies shows a good agreement with the plant data
from Tata Steel.
. The validation of the model with the industrial results re-
assures that, in the practical scenario, phosphorus parti-
tioning is not reaching the equilibrium condition. There-
fore, the Lp value calculated via Healy’s equation must be
scaled down to an industrial Lp value using the approach
of Urban et al. [1] as represented by Equations (13–15) dis-
cussed in the paper.
. A nomogram diagram useful for BOF process was estab-
lished from the mass balance model for a tapping tempera-
ture ranging from 1600 to 1690°C and Si in hot metal from
Figure 16. Dependence of oxygen supplied to Si in hot metal for various final
phosphorus content in steel at 1650°C. 0.4 to 0.85 wt-%. This diagram can be used for calculating
the mass of slag generated at the end of the process or the
amount of flux required to achieve the desired liquid steel
high basicity. On the other hand, even at higher Si in hot composition.
metal, to achieve lower [%P], a higher amount of flux is . As the silicon level in the hot metal is raised from 0.4 to
required. This behaviour is correctly predicted by the model 0.7 wt-%, the flux mass requirement was found to increase
developed with the concept of static mass balance. from 18 to 25% to achieve the desired composition of
However, it needs to be acknowledged that as the model phosphorus in steel varying from 0.004 wt-% to 0.012 wt-
has not been validated against Si in hot metal <0.37% % at a tapping temperature of 1650°C.
(lower limit from plant data), a further study is required to . The current model can be extended to analyse the static
understand the applicability of this model at low silicon in heat balance for BOF steelmaking to understand the
hot metal. effect of PCR, scrap added and Si hot metal on optimizing
In general, the model developed from the concept of mass the heat loss in a real-time converter process.
balance and semi-empirical relation was found to be consist-
ent with the practical scenario. However, the limitation of this
model can be improved by (a) identifying more accurate Acknowledgement
equations for predicting tapping levels of FeO, MnO and
This research was supported by Tata Steel Europe in the Netherlands, by
P2O5, (b) considering the neglected variables such as level providing financial, technical assistance and industrial data for validating
of scrap oxidation, fume/dust losses, air entertained, liquidus with the static mass balance model.
temperature of slag, dissolution of lining material and slag
splashing in the calculations to approximate with the real-
time operating condition. Further validation with the plant
data is required to confirm the generalized approach taken Disclosure statement
in this paper. No potential conflict of interest was reported by the author(s).
10 N. MADHAVAN ET AL.

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[35] Dogan N, Brooks GA, Rhamdhani MA. Chemeca 2011-39th Australas. Figure A1. Modified Nomogram from static mass balance model for top blow
Chem. Eng. Conf.; 2011. pp. 1–14. bottom stir technology with Si in the hot metal of 0.55%.
 IRONMAKING & STEELMAKING 11

Figure A2. Modified Nomogram from static mass balance model for top blow Figure A3. Modified Nomogram from static mass balance model for top blow
bottom stir technology with Si in the hot metal of 0.7%. bottom stir technology with Si in the hot metal of 0.85%.
12 N. MADHAVAN ET AL.

Appendix 2. Combined blow technology

Figure A4. Modified Nomogram from static mass balance model for combined Figure A5. Modified Nomogram from static mass balance model for combined
blow technology with Si in the hot metal of 0.4%. blow technology with Si in the hot metal of 0.55%.
 IRONMAKING & STEELMAKING 13

Figure A6. Modified Nomogram from static mass balance model for combined Figure A7. Modified Nomogram from static mass balance model for combined
blow technology with Si in the hot metal of 0.7%. blow technology with Si in the hot metal of 0.85%.
14 N. MADHAVAN ET AL.

Appendix 3. Bottom blow technology

Figure A8. Modified Nomogram from static mass balance model for bottom
Figure A9. Modified Nomogram from static mass balance model for bottom
blow technology with Si in the hot metal of 0.4%.
blow technology with Si in the hot metal of 0.55%.
 IRONMAKING & STEELMAKING 15

Figure A10. Modified Nomogram from static mass balance model for bottom Figure A11. Modified Nomogram from static mass balance model for bottom
blow technology with Si in the hot metal of 0.7%. blow technology with Si in the hot metal of 0.85%.

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