METHOD FOR CONVERTER BLOW CONTROL

METHODE DE COMMANDE-REGULATION DE SOUFFLAGE POUR CONVERTISSEUR

English Abstract

FP-3886-KS
ABSTRACT OF THE DISCLOSURE
A method for converter blow end-point control which
comprises carrying out waste gas analyses on a continuous or
intermittent basis in a final stage of the blow and, based
on decarburization rate data (waste gas information) obtained
from said waste gas analysis, determining the end-point of
the blow where the carbon content of the bath equals a target
carbon content. The method is characterized by the use of
the decarburization rate equation:
<IMG> which is a differential equation
taking account of the delay time (T) of said waste gas in-
formation which is a period of time from the time-point of
occurrence of a decarburization reaction in the converter till
the time when it is detected as said decarburization rate
data, and an equation:
b'=g(b)
which is a functional equation for increasing the predictability
of carbon content of the bath at the end-point of the blow.

Claims

The embodiments of the invention in which an exclusive
property or privilege is claimed are defined as follows:-
1. A method for controlling the endpoint of the converter
blow in an oxygen converter for the manufacture of low-carbon
steel comprising carrying out waste gas analyses in a final
stage of the blow to determine the rate at which carbon is being
removed from the steel and thereby the decarburization rate of
the blow, measuring the carbon content of the metal in said
converter; solving a model differential decarburization rate
equation, which takes into account the time delay between the
occurrence of a decarburization reaction in the converter and its
detection in the waste gas analyses, for the endpoint of the
converter blow, wherein said model differential decarburization
rate equation (1) is
<IMG> ( 1 )
wherein
? is the time delay (minutes),
<IMG> is the decarburization rate (% min.),
b is the decarburization rate index (1/%) as determined
for each heat of molten metal,
c is the carbon content (%) of the molten metal,
F is a function obtained by the integration of a
fundamental decarburization model formula,
<IMG>
f-1 is an expression derived from said fundamental
decarburization model formula,
<IMG>
where c is a dependent variable, and t is time
and
b' = g(b) (2)

Claim 1 continued...
wherein
b' is the decarburization rate index (1/%) near
the endpoint of the blow, and
g(b) is a function for improving the predictability of
the carbon content of the molten metal at the endpoint
of the blow;
and stopping said blow when the calculated endpoint is
reached.
2. The method for controlling the endpoint of the con-
verter blow, according to claim 1, wherein said waste gas analyses
are made continuously.
3. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein said waste gas analyses are
made intermittently.
4. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein said model differential
decarburization rate equation (1) is selected from the group con-
sisting of the following equations:
<IMG> (3)
- ab? = 1n (bx) - 1n(?) (4)
and
<IMG> (5)
wherein in equations (3), (4) and (5)
x is c-co where co is the minimum carbon content (%) for
steel making reactions;
a is a constant given by 12 F02/112W where F02 is
the oxygen flow rate (Nm3/min) and W is the weight of molten steel
(tons) in the final stage of the blow; and
31

Claim 4 continued...
? is the oxygen efficiency for decarburization
<IMG>
5. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein said equation (2) is:
b' = .alpha. b + .beta. (6)
wherein
is a coefficient of b, and
.beta. is a constant.
6. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein in determining the de-
carburization rate index, b, in said model differential de-
carburization rate equation (1), which takes into account the
time delay, ?, said decarburation rate index, b, is directly
determined for each heat by means of said equation (1) from
the decarburization rate obtained by the waste gas analyses in
the final stage of the blow and the measured carbon content of
the metal in the converter as found by a sublance measurement
of the carbon content.
7. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein in determining the decar-
burization rate index, b, in said model differential decarburi-
zation rate equation (1), which takes into account the time
delay, ?, said decarburization rate index, b, is determined for
each heat by means of a time-change equation (7):
<IMG>
wherein
to is the time point at which the decarburization rate
is detected in the final stage of the blow;
32

Claim 7 continued...
t is an arbitrary time point between to and the end
of the blow; and
<IMG> are the decarburization rates
obtained at the time points t = to and t = t, respectively.
8. The method for controlling the endpoint of the converter
blow, according to claim 16, wherein said time change equation (7)
is selected from the group consisting of the following
equations:
<IMG> (8)
- ab (t-to) = P-Po wherein P = ln? (9)
<IMG> (10)
wherein in equations (8), (9) and (10), P and Po are the values
of P at t=t and t=to, respectively.
9. The method for controlling the endpoint of the converter
blow, according to claim 6, wherein said equation (2) is:
b' = .alpha.i b + a2 CSL + .alpha.3 TSL + .beta.1 (11)
wherein
CSL is the carbon content of the molten metal at the
time of the sublance measurement;
TSL is the temperature of the molten metal at the time
of the sublance measurement;
.alpha.i (i = 1, 2, 3) are coefficients for b, CSL and
TSL, respectively, and
.beta.1 is a constant.
10. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein in determining the de-
carburization rate index, b', near the endpoint of the blow by
substituting the decarburization rate index, b, into equation (2),
33

laim 10 continued. . . .
control of the carbon content of the molten metal is
achieved by substituting b' for b in equation (1), substituting
the decarburization rate obtained by the waste gas analyses into
equation (1) and the time point at which the so calculated carbon
content coincides with a preselected target carbon content is
the endpoint of the blow.
11. The method for controlling the endpoint of the converter
blow, according to claim 1, wherein in determining the decarbu-
rization rate index, b', near the endpoint of the blow by
substituting the decarburization rate index, b, into equation (2),
control of the carbon content of the molten metal is achieved
by substituting b' for b in equation (1), substituting a pre-
selected target carbon content into equation (1) and the time
point at which the so calculated decarburization rate coincides
with the decarburization rate obtained by waste gas analyses
is the endpoint of the blow.
12. A method for controlling the endpoint of a converter
blow, in an oxygen converter for the manufacture of low-carbon
steel which comprises:
(A) introducing oxygen continuously through a lance into
said converter to refine a molten steel in said converter;
(B) analyzing the waste gases issuing from said
converter for carbon content and flow rate thereby determining
the decarburization rate of said converter;
(C) measuring the carbon content of the molten steel
in said converter;
(D) determining the oxygen efficiency for decarburization,
wherein the oxygen efficiency for decarburization is
<IMG>
wherein
<IMG> is the decarburization rate; and
a is the constant = 12 F02/(11.2 x l0W)
34

Claim 12 continued...
wherein
F02 is the oxygen flow rate (Nm3/min.); and
W is the weight of molten steel (tons) in the final
stage of the blow;
(E) determining the oxygen efficiency for decarburization
associated with a given carbon content of the molten steel,
taking into account the time delay between the occurrence of
a decarburization reaction in said waste gas analysis;
(F) terminating the converter blow when the measured
oxygen efficiency corresponds to the oxygen efficiency associated
with a preselected carbon content of the molten steel.
13. The method for controlling the endpoint of a converter
blow, according to claim 12, wherein the waste gases are analyzed
continuously.
14. The method for controlling the endpoint of a converter
blow, according to claim 12, wherein the waste gases are
analyzed intermittently.

Description

21:2
1 BACKGROUND OF THE INVENTION
Field of_the Art
This invention relates to a method for dynamic
control of the end-point of the converter blow.
Descri tion of the Prior Art
P, . _
In converter processes, control for increasing the pre-
dictability of carbon content and bath temperature in the final
stage of blow to thereby obtain slags with improved chemical
compositions plays an important role and has so far been the
subject of much study. For example, it has been proposed to
estimate the carbon content of the bath solely based on the rate
of carburization near the end-point of the blow and, thereby,
control the end-point carbon content. This procedure, however,
is not only liable to significant errors due, for example, to
changes in amount of the slag formed on the bath surface, and the
consequent large variation of accuracy, but also has the dis-
advantage that it cannot be used for temperature control or to
detect the iron oxide content of the slag. Recently the sub-
lance method has been widely and successfully utilized whereinthe carbon content and temperature of the bath are directly
measured by means of sublances for end-point control purposes.
However, this method is not only disadvantageous in that measur-
ing errors due to the uneven distribution of chemical components
and temperature in the bath must be solved with some ingenuity
but has the drawback that the iron oxide content of the slag
cannot be determined. There has also been reported a control
system wherein waste gas information is constantly read and
updated and the parameters of a decarburization rate model
expression are determined using the up to-date information.

111~32~2
1 Notwithstanding the complicated computations required, it
is said that the method is inadequate in predictability. More-
over, the following specific procedures have recently been
proposed for blow control based on a combination of carbon content
measured by sublance (CsL) with waste gas information. ~ first
of these procedures is one using CsL as an integral constant
("Tetsu-to-Hagane" _, 4, p.114).
CE CsL k ~ tE ( dc )dt
tSL
where CE: The carbon content of the bath at end point of
the blow
CsL: The carbon content of the bath at the time-point of
sublance measurement
tE: Time of blow end point
tSL: The time of sublance measurement
k : A coefficient for conversion of the amount (kg) of
carbon to the concentration (%) of carbon.
However, as will be readily understood from the above equation,
this control method using an integral value of decarburization
>
rate is not practically useful, because a(CE) = ~CsL) and,
hence, the error in the sublance measurement is controlling
over the accuracy of carbon content at the end point of the
blow lthe uneven distribution of chemical constituents in the
bath and the error inherent in the rapid carbon analysis (carbon
content detector), taken together, result in a fairly large
error in measured CsL value].
A second control method, which is reported in Tetsu-to-
Hagane 63, 9, p. 21, is such that control is carried out by
means of an arbitrary parameter in the equation for obtaining
dc/dt from CsL and YsL (oxygen efficiency for decarburization at

212
1 the time of sublance measurement). (In the reported case, as
to the equation dc/dt= a+~ exp(-yc), ~ is determined from
CsL and YSL) However, because this method disregards T,
carbon content in the bath is estimated only inaccurately~
Moreover, when use is made of a parameter such as that used in
the reported case, the indefinite physical meaning of the
parameter fails to provide a clear picture of its relationship
with other factors in converter blow [T control (control of
the bath temperature at the end point of the blow) and detection
of the iron oxide content of the slag] which is possible in the
case of this invention. Thus, attempts to correlate the sub-
lance information with the waste gas information have so far
failed to meet with success.
SU~MARY OF THE INVENTION
In regard to the quality control of converter steel-
making, an increasingly higher accuracy has been demanded and
the development is awaited of a control method which would
provide an improved predictability of carbon content and bath
temperature at the end point of the blow. Furthermore, where
converters are not provided with sublance means as well as in
situations where the costs of the measuring probes are important
considerations, it is necessary to develop a method for
obtaining and utilizing information from waste gas analyses
alone.
This invention fulfils this need and, at the same
time, provides a neat solution to the above-mentioned technical
problems involved in the end-point blow control of converters.
It is, thus, an object of this invention to provide a
method for converter blow control by which the carbon content
of the bath at the end point of the blow can be controlled far
-- 3 --

2~2
1 more accurately than by any of the prior art methods, that is
to say a new method which provides an accurate assessment of
the condition of each heat and an accurate prediction of blow
end-point based on the result of such assessment.
It is another object of this invention to provide a con-
trol method which, in addition to the above-mentioned advantage,
provides an improved accuracy of bath temperature control and
further permits a quantitation of the iron oxide content of
the slag.
To accomplish the above-mentioned ob]ects, this
invention relates, in one aspect, to a method for converter blow
end-point control comprising carrying out waste gas analyses
either continuously or at timed intervals in a final stage of
the blow and determining the end-point of the blow when the
carbon content of the bath coincides with a target carbon content,
characterized in that said control is effected using a de-
carburization rate equation:
-T=F(c,b)-F[f l(-dt, b), b] ____-- (1)
which is a differential equation taking account of the delay
time of waste gas information from the time of occurrence of
the decarburization reaction in the converter till the time of
said information being detected as decarburization rate data
and a functional expression:
b' = g(b) ______- (2)
which is a functional equation for improving the predictability
of the carbon content of the bath at the end point of the blow.
In the above equations (1) and (2),~ is the delay time
(in minutes) of waste gas information; -ddt is the decarburization
rate (% per minute); b is the decarburization rate index (1/%)
determined for each heat; b' is the decarburization rate index

1 (1/~) near the end point of the blow; c is the carbon
- content (~) of the bath; F is the function obtained by the
integration of a fundamental decarburization rate formula
-ddt = f(c,b); f 1 is a transformation of the fundamental de-
carburization model formula -ddt = f(c,b), in which c is a
dependent variable; and g(b) is a function for improving the
predictability of the carbon content of the bath at the end point
of the blow.
In a second aspect of this invention, the above-mentioned
equation (1) is at least one member selected from the class
consisting of the following equations:
-abT =Qn ~exp(bx)-l} -QnlYy ---------- (3)
-abT =Qnbx - Qny -~ -- (4)
bx ( ~ ~ ~ )~~~~~~~ (5)
In the above equations (3) to (5), x is C-Co, where Co means the
minimum carbon content (%) for steel-making reactions; a is
a constant which is defined by 12 F02/(11.2 x 10 w), where F02
is oxygen flow rate (Nm3/min.) and W is the weight (tons) of the
molten steel in the final stage of the blow, and ~ i8 the oxygen
efficiency for decarburization as defined by ~a ddt
In a third aspect of this invention, the equation (2)
mentioned in connection with the first aspect thereof is:
b' = ~b + ~ -------- (6)
where ~ is a coefficient of b, and ~ is a constant.
A fourth aspect of this invention is such that, in
determining the decarburization rate index b in the decarburization
rate equation (1) which takes account the said delay time T
of waste gas information, said decarburization rate index b is
directly determined for each heat from the decarburization rate

32~2
1 data from waste gas analysis in a final stage of the blow and
the carbon content of the bath as measured by means of sublance
at that time.
A fifth aspect of this invention is such that, in
determining the decarburization rate index b in said decar-
burization rate equation (1) which takes account of the delay
time T of waste gas information, said decarburization rate
index b is determined for each heat by means of the
-(t-to) = F[f ((-dt)t,b),b]-F[f ((-dt to,b),b] -----(7)
which is an equation which accounts for the change with time of
the decarburization rate from the waste gas analysis made in
the final stage of the blow. In the above equation (7), to is
the time-point of detecting the decarburization rate value in
the final stage of the blow; t is an arbitrary time-point
between to and the end point of the blow; and (-dt )~ and
(-dt)t are the decarburization rates at t=to and t, respectively.
A sixth aspect of this invention is such that, in the
above fifth aspect, the equation (?) is at least one equation
selected from the group consisting of the equations:
-ab(t-to) = P-PO where P - QnlY -~ 8)
-ab(t-to) = P-PO where P = Qny ----- (9)
ab(t-to) = P-PO where P = ~ _ ~ _____ (10)
l-y Y
Referring to the equations (8) through (10), PO i.s the value of
P at t=to
A seventh aspect of this invention is such that, in
the fourth aspect described above, the equation (2) is:
b~ = alb + a2CsL + a3TSL + ~1 ~----------- (11)
where CsL is the carbon content of the bath at the time of
-- 6 --

212
1 sublance measurement; TSL is the bath temperature at the time
of sublance measurement; ai(i=1,2,3) are the coefficients of b,
CsL and TSL, respectively; ~1 is a constant.
An eighth aspect of this invention is such that, in
the first aspect described hereinbefore, wherein said de-
carburization rate index b is substituted in said equation (2)
to determine the decarburization rate index b' near the end
point of the blow, said decarburization rate equation (1) in which
b is substituted with said b' is used as such, the decarburi-
zation rate data from said waste gas analysis are read in andthe carbon content of the bath is determined from each de-
carburization rate data thus read in and the time-point at which
the carbon content data thus obtained equals a target carbon
content is used as the end point of the blow. A ninth aspect
of this invention is such that, in said first aspect thereof,
the decarburization rate index b determined as aforesaid is
substituted in said equation (2) to determine the decarburization
rate index b' near the end point of the blow, said equation ~1)
in which b has been substituted with this b' is employed as such,
a target carbon content is previously substituted in said
decarburization rate equation ~1) to calculate a target
decarburization rate value, the decarburization rate data
from said waste gas analysis is read in and the time-point at
which the decarburization rate data thus read in equals said
target decarburization rate value is used as the end point of
the blow.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a diagram showing the relation of the carbon
content of the bath with oxygen efficiency for decarburization,
the solid line representing the relation of y with C actually
-- 7 --

lll~Z12
1 observed in the converter which is due to the delay time T 0
waste gas information;
Fig. 2-1 is a graphic representation showing the
reaction of b, the decarburization rate index at the time-point
of sublance measurement, with b, the decarburization rate index
at the end point of the blow, according to exponential model;
Fig. 2-2 is a graphic representation showing the
relation of b, the decarburization rate index at the end point
of the blow, with _, the calculated decarburization rate index
at the end point of the blow, according to exponential model;
Fig. 3 is a graph showing the relation of bath carbon
content C with oxygen efficiency y for decarburization;
Fig. 4 is a graph showing the relation of the predicted
carbon content at the end point of the blow with the observed
carbon content at the same time point;
Fig. 5 is a graph showing the relation of oxygen
efficiency for decarburization y with decarburization rate index
b;
Fig.6 is a graph showing the relation of decarburization
rate index b with the rate of temperature increase;
Fig. 7 is a graph showing the relation of end-point
carbon content CE with the total Fe content of the slag;
Fig. 8 is a graph showing the relation of time with
oxygen efficiency for decarburization y; and
Fig. 9 is a graph showing the relation of time with
-P=Qn~
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
. _ .... . . .. .
This invention relates to a method for controlling the
end point of the blow in converter operation which comprises
carrying out waste gas analyses either continuously or inter-
-- 8 --

32~2
1 mittently in a final stage of the blow and, based on ~he de-
carburization rate data obtained from results of said waste gas
analyses, accurately determinin~ the end point of the blow where
the carbon content of the bath reaches the target carbon content.
More particularly, this invention relates to a method for con-
trolling the converter blow which comprises employing a funda-
mental decarburization rate equation (1):
~ dt = f(c,b) ---------- (1)
where ~ dt : decarburization rate ~%/min.)
f(c,b): the function of the fundamental decarburization
model,
c : carbon content of the bath (%),
b : a decarburization rate index determined for
each heat (1/~)
rearranging the same equation mathematically to a differential
decarburization rate equation (2), which takes account of the
delay time T of waste gas information which is a period of time
from the time-point of occurrence of a decarburization reaction
in the converter till the time when it is detected as said de-
carburization rate data,
- ~=F(c,b)-F[f l(-ddt ,b),b] ---------- (2)
where ~ : the delay time of waste gas information (min.)
F : the function obtained by the integration of funda-
mental decarburization model equation (1)
f 1 : the expression obtained by transforming C in
fundamental decarburization model formula (1)
into a dependent variable, and

111~2~2
1 a function (3) which is designed to improve the predictability
of said carbon content of the bath for achieving an accurate
control of the carbon content of the bath at the end point of
the blow.
b' = g(b) -------- (3)
where b' : the decarburization rate index near the end point
of the blow (1/%)
g(b): the function for improving the predictability of
the carbon content of the bath at the end point of
the blow.
It should be understood that the term "converter" as
used herein means any of the LD converter, bottom-blown con-
verter (Q-BOP), argon oxygen decarburization (AOD) vessel and
vacuum oxygen decarburization (VOD) vessel.
It should also be understood that the aforementioned
fundamental decarburization rate equation (1) means at least
~; one formula selected from the group consisting of the following
equations :
Exponential model : Y = ~a dt = l-exp (-bx) ~ (4)
Linear model : y = _1 ddt = bx -------------- (5)
IRSID model : Y a- dt = (bx) / {l+(bx)2~ ----- (6)
where y : the oxygen efficiency for decarburization as given
by ~a dt;
a : the constant given by 12 F02/(11.2x10W), where FO2
is oxygen flow rate (Nm3/min.) and W is weight of
molten steel (tons) in final stage of the blow;
x : C-Co, where Co is the minimum carbon content (%) for
steel making reactions.
Now, a general transformation of the above fundamental
-- 10 --

1 dccarbllrizcltic)ll model form~ 1) CJiVeS the aforementioned
decarburi~ation rate equatioll (2) as follows.
Integrating formula (1) yie]ds:
- 5clt=J dc/f(c,b) ---~ (7)
Therefore, from equation (7~,
-t = F(c,b) ~ -- (8)
where F(c,b) = Jdc/t(c-,b); I is an integral constant.
Assuming tha-t C = Cl and C at the time-points of t
and t, respectively, I is eliminated to ob-tain:
1 0
~ (t-tl) = F(c,b) - F(Cl,b) ---------- (9)
Now, to posi-tively take account of said delay time
of waste gas information, it is postulated:
t = tl ~~ I ~~~~~~~~~~~~ ~10)
Then,- ddt as found at t = t is the decarburization rate
obtaining in the conver-ter at the time-point of tl and, therefore,
dt f(cl,b) _________ (11)
Equation (11) is rearranged to :
Cl = f l(_ .dt, b) ---------- (12)
Substituting equations (10) and (12) into ecruation (9)
gives the aforementioned decarburiation rate equation (2):
-T=F(c,b)-F[f l(_ dt, b), b~ ---- (2)
This represents the actual relation of C with _ dt
which obtains in a con~ercial converter where T cannot be
neglected.
Therefore, in accordance with this invention, b in
said equation (2) is determined at a suitable time-point in a
final stage of the bl.ow and the equation (2) is used in eom-
bination with the aforementioned equation (3) to control the

32~2
1 carbon content of the bath at the end point of the blow with
improved accuracy.
Since the fundamental decarburization model formula (1)
means any of the three different decarburization models given
by said equations (4) to (6), it actually represents at least
one member selected from the group consisting of the following
equations :
~ -- (13)
-abT =Qn ~exp(bx)-l~ -Qn-Y-
-ab~ =Qnbx-Qny ------------------------ (14)
-ab~ = bx-lx - (~-~~ ~ ) ----------- (15)
To control the carbon content of the bath at the end
point of the blow, the decarburization rate index b appearing
in said equations (2) must be determined. This index may be
determined by the following two alternative procedures.
[I] From the decarburization rate data obtained from the waste
gas analysis performed in a final stage of the blow and the
carbon content of the bath as found by sublance measurement,
the decarburization rate index b is directly calculated for
each heat by means of the aforementioned equation (2).
[II] Alternatively, the decarburization rate index b is de-
termined for each heat by means of a time-change equation (16)
which is applicable to the decarburization rate found by the
waste gas analysis performed in a final stage of the blow:
(( dt)t,b)~b]-F[f l((_ dc) b) b]
where to : the time-point at which the decarburization rate is
determined in a final stage of the blow;
t : an arbitrary time-point between to and the end point
of the blow;
0 (-ddt)t ' (-dt)t: the decarburization rates at the time-points
of t=to and t, respectively.
- 12 -

111~3Z~2
1 The equation (16~ can be derived in the same manner
as equation (2). Thus, assuming, again, that C=Cl when t=tl and
C=C when t=t, the fundamental decarburization model formula (1)
will be:
( dt)t=t+T =f(c,b) ~17)
( dt)t=tl+l f(cl,b) (18)
The equations (17) and (18) are respectively re-
arranged to:
C=f [(-dt)t=t+T,b] (19)
Cl=f [(-dt)t=tl+T' ] ~20)
Substituting (19) and (20) into equation (8) respectively
gives: .
-(t+~)=F[f _ ~(-dt)t+T~b}~b] ~21)
(tl+T) F[f ~(-dt)t +T~b~b] ~22)
The integral constant I can be eliminated by sub-
tracting (22) from (21). Since the time-points on the left-hand
side and the right-hand side are relevant to t + T and tl + T
for both equations (21) and (22), rewriting them as t and to
gives the aforementioned time-change equation (16) for de-
carburization rate (-dt).
{( dt)t+l~b}~b] - Flf-l {(_dc) b } (16)
Therefore, by finding the change of -dt with time
through use of this equation (16), the decarburization rate index
b in said equation (2) can be determined for the particular
heat.
- 13 -

2~;2
1 Further, rewriting the above time-change equation (16)
~r decarburization rate for each of the three different funda-
mental decarburization models given by equations (4) to (6)
hereinbefore yields:
-ab(t-tO)=P-P0 , where p=QnlYy (23)
-ab(t-tO)=P-pO , where P=Qny (24)
-ab(t-tO)=P-P0 , where P= ~ _ ~ (25)
l-y Y
In the above equations t23) to (25), P0 represents
the value of P at the time-point of t=to. Thus, equation (16)
represents at least one member selected from the group con-
sisting of equations (23), (24) and ~25).
~ he derivations of the various decarburization models
given above are summarized in Table l, where for brevity's
sake, the fundamental decarburization model formula
-ddt = f (c,b) is written as y=f (x,b) herein Y=~a dt ~ x=C-Coj,
~: that is to say as a relation of x with y.
- 14 -

2~;~
.. . . .. .. . ,.. , ,..... .....
,~
~1
u~ 0 ~ 1 V ~o ~ P~ 1l a~ ~1
~ ~ ~ 11 11 11
0-~1 ~ ~ ~ ~ ~
v ~: 3 v ~ ~, v v _ ~1;
~ ._ . ._ _ ___
r ~ q' R ~ :~
o v ~ ~ ~,,P~r,~ r X ~1
O ~.3 R t~ ~ Il, I
O ~ X 11 X 0 R R
. ._ ~X' ' ... . _
X ~
~,1 X X ~ X
E~ H ~1 ~4 ~1 IR~ IR0~ IR0
~ R --- _ _ .
r ~d ~1 R ~ R ~IR l~ --IIR
x ~ x ~ x ~ 1l
~ _ ~ _
r o C ~ ~ _ ~ r~,,
. _
-- 15--

321~
1 ~s will be apparent from the foregoing description,
the blow control method according to this invention is
characterized by the employment of said differential decarbu-
rization rate equation (2) which includes and takes account of
the delay time T of waste gas information and said functional
equation (3) which is adapted to improve the predictability of
the carbon content of the bath at the end point of the blow.
More particularly, the method according to this invention is
characterized in that:
(A): the decarburization rate index b is determined from the
carbon content of the bath at the time of sublance measurement
(CsL) and the oxygen efficiency for decarburization at that
time (YSL) or
(B): the decarburization rate index _ is determined from the
change with time of oxygen efficiency for decarburization y.
Now, this invention will be further described in
detail. The above aspect (A) will first be described in
detail. In accordance with this aspect of the invention, the
carbon content of the bath is first measured by means of a sub-
lance at a suitable time-point in a final stage of the blow and~
the decarburization rate is determined from a waste gas analysis
which is also performed at the same time-point. The aforementioned
equation (2) is applied to the data thus obtained to determine
the decarburization curve (decarburization rate index b) for
the particular heat and this curve is used to determine the
end point of the blow. There is no particular limitation on
the method for measuring the carbon content of the bath and the
method for determining the decarburization rate. That is to say,
the invention is characterized in that, in correlating the
measured carbon content of the bath with the decarburization rate
- 16 -

21~
1 obtaining at the very time-point, the delay time involved in
the waste gas informa~ion is properly taken into account and the
equation (2) thus derived to include this delay time is used
in the form of a differential expression to thereby construct
a decarburization curve with ease and accuracy and,hence, permit
a very precise control of the end-point carbon content of the
bath which has never been feasible by the prior art methods
where waste gas information and sublance information are
independently utilized, where these data are correlated without
consideration of the delay time or where the two data are
correlated by an integral formula.
Now, the procedure for determining the decarburization
curve will be explained with reference to the curve based on the
exponential model, i.e. equation (4), it being to be under-
stood that the same argument applies as well in cases where
other model equations (5) and (6), both given hereinbefore, are
. . ,
respectively employed.
It is generally acknowledged that in a final stage
of the blow, the following relation holds as aforesaid between
the decarburization rate [-dt (%/min.)J and the carbon content
[C(%)] of the bath (exponential model~.
dt a[l-exp~-b(C-Co)}] (4)
Using the oxygen efficiency for decarburization
which is given by y=-- dt ~ the above relation may also be
written as y = 1 - exp ~-b(C-Co)} ~4)
Co in the above formulas is a constant representing
the minimum carbon content for steel-making reactions and, for
general purposes, may be set at about 0.02%. The symbol b
denotes the decarburization rate index for the particular heat,
and is a determinant of the decarburization curve. The curves
- 17 -

21~
1 indicated in bro~en lines in Fig. 1 show the relation of C
with _ in eql~ation (4) ~or various values of b. The decarbu-
rization reaction would proceed along this curve if the waste
gas information involves no delay time. In an actual converter
operation, however, the waste gas information involves a delay
time (T ', 0.3 to 0.5 min.) which varies from one plant to
another depending on equipmen~ and operating conditions and,
in the practice of this invention, the magnitude of such delay
time should be individually determined and properly reflected
in the construction of the decarburization curve. Thus
equation (4)' does not hold true as a relation between y and C
as measured. This is why the present inventor has derived -the
aforementioned equation (2) [which corresponds to the equation
(13) given hereinbefore for the exponential model] which takes
account of the delay time.
Referring, again, to Fig. 1, the curves shown in solid
line represent the case in which such a delay time is taken into
account, that is to say the decarburization rate curve
according to equation (13). [The expression Y~l eexp(bbx) e~p( abT)
in Fig. 1 is a transformation of equation (13)].
It will be seen that the curves given in broken and
solid lines are markedly different.
Substituting C=CsI, CE and Y YSL~ YE q
(13) [where CsL, YSL~ CE and YE are the carbon content of the
bath and the oxygen efficiency for decarburization, at the
time of sublance measurement and at the end point of the blow,
respectively] mathematically yields the values of b (designated
as bSL and bE) based on the values of C and y at the time of
sublance measurement and at the end point of the blow, res-
pectively. The application of the data obtained by actual
- 18 -

Z12
1 operations has shown that, as will be apparent from Fig. 2-1,
the values are distributed between 2 and 8 while satisfying
the relation of bSL-bE. This is indicative of the fact that,
in an actual converter, the decarburization curve is approximated
by equation (13) and this invention has been conceived and
developed on the basis of a discovery of the above relationship.
However, as is evident from Fig. 2-1, actual converter operations
do not strictly follow the relation of bE=bSL. That is to say,
the use of bSL as such does not provide a sufficiently accurate
control of end-point carbon content. This problem can,
however, as is apparent from Fig. 2-2, be overcome by means of
an apparent relation between bSL and bE, such as:
b'=g(b) (3)
=g(bsL)=absL + ~ is a coefficient for bSL, ~ is a
constant (26)
or
- b'=g(bsL, CsL' TSL) 127)
=albsL + a2CsL + a3TSL ~1 (28)
(TSL is the bath temperature obtained at the time
of sublance measurement).
Therefore, the carbon content of the bath at the end
point of the blow can be controlled with exceedingly high
accuracy by means of equations (2) and (3) or equations (2)
and (27).
Once the value of b' has thus been obtained, the
carbon content of the bath at the end point of the blow can be
accurately controlled by any of various procedures, such as:
Procedure I:
3 The values of y from waste gas analyses are read (Yi)
and Ci is determined from each Yi by means of equation (13).
-- 19 --

111~2~
1 The time-point when the Ci thus determined coincides with the
target carbon content is regarded as the end point of the blow
(Fig. 3).
Procedure II:
YA (Fig. 3 ) is determined by substituting b' and
target carbon content into equation (13) and the time-point
at which the y value from waste gas analysis equals YA is
regarded as the end point of the blow.
Which of these alternative procedures to take is at
the option of the person who may wish to work this invention.
Table 2 shows the comparison of CE as estimated from
YE at the end-point of the blow by means of equation (13)
with CE as found in actual converter operations. It is apparent
that the method of this invention provides a markedly higher
predictability than does any of the prior art method depending
solely on sublance information.
TABLE 2
The accuracy of end-point carbon content predictions
Carbon content of Accuracy of
bath at the end carbon content a ~%)
point of blow ~ ~ dL~$~n _ __ _ _
This invention Prior art* This invention Prior art*
. _ -- . _
CE50.06 within + 0.01 within + 0.02 0.007 0.017
.
0.06CCE~-0.1 within + 0.02 85 to 90% 0.012 0.018
_. . , .. _ . ._
O.l~CE-0.2 not less than within + 0.02 0.016 0.030
+ 0.02 _
- .__ _
*Prior art method depending solely on sublance information
without using waste gas information.
- 20 -

Z~2
ll Ta~le 2, (J denotes -the standarcl ~evia-tion in the
differenc:es between t~e pre~licted en~-poirlt carbon con-ten-t and
the field operatinn da-ta. The advantage of the method of this
invention is at once apparent and the predictability oE this
invention is particular:Ly high in the region of low carbon
conten-t.
Fiy. ~ shows the predicted carbon conten-t at the end
point of the b]ow versus the actual carbon con~ent. It is
apparent that there is a good agreement between the two sets of
values.
It is thought that the high carbon predictability of
this invention can be attrihuted to the following.
(i) Because the carbon content found by sublance measurement
is correlated with the decarburization rate obtaining at the
time of such measurement, the variation in decarburization rate
from one heat to another is eliminated.
(ii) Because the influence of the delay time involved in waste
gas data is properly evaluated in the correlation mentioned above
in (i), an end-point control reflecting the characteristics of
~ each heat is made feasible. This also provides a basis for the
possibility of improving temperature control and detection of
the iron oxide content of the slag which are to be described
hereinafter.
(iii) As will be explained below, the influence of an error in
the measurement of CsL on the carbon content at the end point
of the blow decreases exponentially with a drop in carbon content.
Moreover, since the influences of errors in CO and C02 analyses
at the time of sublance measurement and at the end point of the
blow work in the same direction, these errors are not signi-
ficant factors-
- 21 -

111~2i;~:
1 Fig~ S is a graphic representation showing the
relation of oxygen efficiency ~or decarburization with de-
carburization rate index b as given by equation (2) at varying
C of the bath. According to the graph, if the true CsL=0.34%
but the measured CsL-0.4% (or vice versa) when y=0.9, ~CsL is
0.4-0.34=0.06% and the carbon content error (%) at a later stage
when y has decreased with the progress of the blow to y=0.28 is
0.06-0.054=0.006. Thus, the error in sublance measurement at
y=0.9 (0.06%) is reduced to 0.006 (%) at this later time-point
or only about 10% of the previous value. It is, therefore,
clear that the influence of errors in the measurement of CsL
can be effectively eliminated by the method of this invention.
As is apparent from the above, the control method
according to this invention provides a considerably high % carbon
predictability.
- It has also been found that the method of this
invention provides an improved predictability as to the bath
temperature at the end point of the blow. Thus, while Fig. 6
is a graphic representation showing the relationship of b as
calculated by equation (13) at the time-point of sublance
measurement with the measured rate of temperature increase ~e).
It will be apparent from Fig. 6 that the rate of temperature
increase decreases as the magnitude of b increases. This is
presumably because the higher the value of b, the higher the
oxygen efficiency for decarburization and, hence, the com-
bustion reaction ratio of carbon becomes greater than the
combustion reaction ratio of Fe. In any event, because the
accuracy of estimation of the rate of temperature increase is
significantly improved by using the index bSL, the accuracy of
3~ estimation of the bath temperature which has heretofore been
- 22 -

212
1 estimated by the computation Eormula:
T = TSL + ~G2
(~G02 : the amount of oxygen blown after sublance measurement)
can be further improved.
By way of illustration, the field data obtained by the
present applicant have shown that the accuracy of prediction
of the rate of temperature increase drops from 10.1 to 8.0 C/
1000 Nm302 in the standard deviation thereof.
The feasibility of delineating the iron oxide content
of the slag, which is another advantage of this invention, will
now be described. In converter blow, the iron oxide content
of the slag must not be less than a certain level in order to
accelerate the removal of P and S but if the iron oxide content
is too high, the iron yield is decreased and the life of the
converter refractory is shortened. It is, therefore, another
consideration in steel-making to control the iron oxide content
within an appropriate range. However, there has been available
no effective procedure for detecting the T-Fe level (the pro-
portion of iron present in the form of iron oxide in the slag)20
in the course of the blow.
Fig. 7 is a graphic representation showing the plots of
T-Fe % against CE in the case of this invention, where the
carbon content CE(%) at the end point of the blow and the
T-Fe values (%) of the slag as grouped by bE are represented
on the horizontal and vertical axes, respectively.
It will be seen from this graph that the higher the
value of _, the smaller the value of T-Fe and this phenomenon
seems to arise from the fact that as b is increased, the oxygen
efficiency for decarburization becomes greater and, hence,the
combustion reaction ratio of Fe is decreased. As a result, the
- 23 -

111~3212
1 order of T-Fe (~) for a given heat can be ascertained by
knowing the value of _ and, accordingly, numerous advantages
such as an improvement in predictability for that charge, a
stabilization of dephosphorization and desulfurization processes
and a stabilization o~ iron yield can be obtained.
While the foregoing description has been directed to
the exponential model, substantially the same control accuracy
can be, and has been,obtained in the case of the other models as
well. Typical such results are shown in Table 3. In the
table, the values in brackets represent the CE predictabilities
of the various models when T=O and the relation of b'=absL+~
is not employed, for comparison purposes. The comparison
clearly demonstrates the advantage of this invention which
takes account of the delay time T of waste gas information and
employs the functional equation b'=g(bsL) for improving the
predictability of the carbon content of the bath at the end
- point of the blow.
- 24 -

2~2
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-25

32~2
1 The control method involvin~ the use of sublance in-
formation in combination with waste gas information has been
described. The Procedure ~B~ mentioned hereinbefore will now be
described in detail.
The control method of this invention, which is pertinent
to Procedure (B), is characterized in that, in grasping the con-
dition of the particular heat during the blow solely from the waste
gas information obtained by continuous or intermittent measure-
ments, the condition of the bath during the blow is grasped on the
basis of said equation (16).
Where sublance is available for controlling the carbon
content of the bath, Procedure (A) described hereinbefore provides
control with exceedingly high accuracy but in the case of converters
not equipped with sublance (e.g. small-sized converters) as well
as where the measuring probes are important economic considerations,
it is necessary to obtain and utilize sufficiently effective
information from waste gas data alone. This invention has been
accomplished in view of the above fact, too.
Attainment of effective information from waste gas data
alone is possible, for example by deriving an expression relevant
to the change with time of the oxygen efficiency for decarburization
Y
It is for this purpose that the time-change equations for
the various decarburization models in Table 1 [corresponding to
the aforementioned equations (23) to (25)] have been derived.
As in the case of Procedure (A), the above operation will
be explained with reference to the exponential model.
A further transformation of said equation (23) gives:
y= ____------ (29)
l+y Yo exp ~ab(t-tO)J
This equation is used as a correlation formula corres-
ponding to the chart pattern of a decarburization rate detector.
- 26 -

21~
1 E~ig. 8 is a graphic representation of equation (29)
when oxygen flow rate FO2 is 650 Nm3/min. and the weight of
molten steel W in the final stage of the blow is 250 tons, where
the curves correspond to b=2,~,6,and 8, respectively. This
graph bears a close resemblance with the observed pattern.
Fig. 9 is an example of the plots of Qn~ against
t as obtained by reading the decarburization rate charts. There
is a relationship of good lineality which suggests the validity
of the relation given by equation (23'~.
The procedure for calculating b by means of equation
(23) will now be explained. Let it now be assumed that
Y = Yl and Y = Y2 when t=tl and t=t2, respectively. Then, from
equation (23),
-ab(tl~t2~=Pl P2
Since tl-t2 represents the time over which y drops from Yl to
Y2, it is now rewritten as ~t. Thus, b=al ~t ------~31)
It is, thus, possible to calculate the decarburization rate
index b for the particular heat without using the sublance
information (carbon content of the bath as measured with the
sublance).
The desired control of end-point carbon content by
means of the value of b thus obtained can be performed with
accuracy by using the following equation (26)' in the same manner
as described hereinbefore with reference to equation (26).
b' = g(b) -------(3)
= ab+~ -------(26)'
In controlling the end-point carbon content using the
b' obtained as above, a couple of procedures similar to the
Procedures I and II described hereinbefore may be mentioned by
way of example.
- 27 -

3212
1 Field converter control trials with the use of
equation (23) have ~iven the results set forth in Table 4. The
results are set forth in the table together with comparative
data by other control methods.
TABLE 4
Comparison of the accuracy of end-point
carbon prediction
Control method~(%)X100 ~(~)X100 a(%)X100
E( ) t CE( ) at CE(~)=
0.06 or less 0.06-0.1 0.1-0.2
1 0
sublance 1.7 1.8 3.0 -
sublance plus 0.7 1.2 1.6
waste gas analysi
Waste gas analysis 0.8 1.5 1.9
It will be apparent from the above description that
this invention provides an improved carbon content predictability
solely on the basis of waste gas information. It has also been
found that this invention has an additional advantage that it
enables the iron oxide content of the slag to be grasped as
well. Thus, because the higher the oxygen efficiency for
decarburization, that is to say the greater the value of b, the
lower the iron oxide content of the slag, and the value of b
can now be obtained by means of equation (31), the iron oxide
content of the slag can now be accurately determined. Of
course, the same reasoning is applicable to the other models
as well.
As has already been mentioned hereinbefore, this
invention provides an estimation of the decarburization curve
without being significantly influenced by errors in the inter-
mediate carbon measurement, because the carbon content at the
time of sublance measurement is correlated with the decarburization
.
- 28 -

~atc~ ~It thclt ~ e-~)Oint: whi1e thc~ delay time of was-te gas
informLItion :i.s ta~erl into accoun-t. ~s a result, -the invention
permits an easy and accurate control of the end-point carbon
content and bath tempera-ture, for instance, thus making for
a still improved stability of converter operations. This
invention further makes it possible to obtain a high-precision
prediction of the carbon content, iron oxide conten-t of the
slag and other variables at the end point of the converter blow,
thus contributing again to an improved stability oE converter
operations.
- 29 -