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Mathematical Model of RH Blow Argon Mode Affecting: Decarburization Rate in Ultra-Low Carbon Steel Refining
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=iO ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 20129 19(5) : 23-28
Mathematical Model of RH Blow Argon Mode Affecting : Decarburization Rate in Ultra-Low Carbon Steel Refining LI Chong-wei'
,
CHENG Guo-guang'
,
WANG Xin-hua'
,
ZHU Guo-sen3,
CUI Ai-min3
(1. Beijing Beiye Functional Materials Corporation, Beijing 100192, China; 2. School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China; 3. Shougang Qian'an Iron and Steel Co Ltd, Qian'an 064400, Hebei, China)
Abstract: A mathematical model in present study has been established to investigate the effect of Rheinstahl Heraeus ( R H ) blow argon mode on the decarburization rate in ultra-low carbon steel refining based on the R H equipment of Shougang Qian'an Iron and Steel Co Ltd (SQISCO). The calculated results show that the increase of argon flowrate promotes the carbon elimination from argon gas bubble surface, molten steel free surface in vacuum as well as splash droplet surface, while reduces that from the interior of liquid steel. It has been found the critical turning point of flowrate ascension is at the 5'h minute and the optimum blow argon flowrate in later stage is 2 100 L/min in accordance with the 2 stages argon blow mode, which have been confirmed in the commercial production in SQISCO. Key words: RH ; vacuum; mathematical model; argon flowrate: decarburization
Efficient refining of I F steel requires the carbon concentration less than 0. 003% and refining time less than 15 min. The decarburization reaction in RH generally occurs in following four locations: free surface of liquid steel in vacuum chamber, argon gas bubble surface, interior of liquid steel in vacuum"] and splash droplet surfaceCz1.Argon injected from a up-snorkel in RH as the power source of liquid steel circulation, its flowrate directly affects the circulation behaviour of molten steel and the decarburization reaction. Because of the difference of the decarburization mechanism along with the proceeding of RH refining process, the practical production cannot adopt only a constant blow argon flowrate during whole decarburization period. But there is little detailed statements reported on how to determine the best mode of blow argon flowrate so far. The purpose of the present study is to establish a mathematical model of blow argon mode to investigate the mechanism affecting the decarburization rate of ultra-low carbon steel refining and optimize the argon blow regime, based on the commercial production data of Shougang Qian'an Iron and Steel GILtd (SQISCO). The optimum blow
argon mode put forward by this paper has been confirmed reasonable to acquire extra-low carbon concentration in relatively shorter time.
1 Establishment of Mathematical Model for RH Decarburization Thermodynamics of decarburization reaction The decarburization reaction in the reaction site can be represented by the following equation. CCl+COl =CO(g) (1) In this reaction, the equilibrium constant K is expressed as followingc3]. K- Pco* 'Co* = 10'1 160/T+Z.003) (2) 1.1
acao
-
WCCl
q01
1 . 2 Establishment of RH natural decarburization mathematical mode The RH natural decarburization mathematical model was established on the basis of the 4 decarburization sites: interior of liquid steel, argon gas bubble surface, free surface and splash droplet surfaceC4].The diagrammatic sketch of RH decarburazition sites is shown in Fig. 1.
Foundation Item: Item Sponsored by National Key Technology Research and Development Program in 11"' FiveYear Plan of China (2006BAE03A13)
Biogr8phy:LI Chong-wei(l982-),
Male, Doctor;
E-mail: lichongwei-l23@yahoo. com. cn;
Received Date: March 28, 2011
VOl. 19
Journal of Iron and Steel Research, International
24
where, Ab is surface area; pm is the density of melt; is liquid phase mass transfer coefficient of carbon! and ZU[~I,is equilibrium carbon content on gas-liquid surface which is estimated using the following equation.
kb
bubblesurface
I 1innersites I
n
I
I
Fig. 1 Diagrammatic sketch of RH decarburazition sites
The following assumptions are made. 1 ) For each calculation circulation of the model, the carbon and oxygen content in the ladle and vacuum are constant respectively ; 2) The decarburization reaction proceeds in the vacuum vessel only; 3) The carbon and oxygen concentration at the gas-metal interface is in equilibrium with the partial pressure of CO in the gas phase; 4) The rate of decarburization is controlled by the mass transfer of carbon. The mass balance of carbon and oxygen in the vessel under these conditions is represented by Eqn. ( 3 ) to Eqn. (7). (3) W(dw[clL/dt) =Q(w[cl, -wcclL 1 (4) W(dwcolL/dt) =Q(w[olV -w[o], ) W(dw[clV/dt)=Q(w[clL-W[C], )-(CAcI,+
CAcI =CACIA~
P C 0 . b is the partial pressure of CO gas in the bubble and is calculated using the following equation.
CAcIin +CAcIface CACIspt ) (5) CAcIin 4- CAcl~me C A c l s p ~ (6) M O
W(dw[olv /dt> =Q(ut[ol, - ~ [ o ] ), --(dAr+ MC
+ +
(7) din dface dspl ) where, Mc , Mo are the molecular mass of carbon and oxygen, kg/mol; [ACIA, , [ACIin, [ACIf.,, , [Ac].,l are the carbon removing quantity on argon gas bubble surface, in internal liquid steel, on free surface and splash droplet surface respectively, t/min; and Subscript L, V is ladle and vacuum chamber.
1.3 Decarburization mathematical model of argon gas bubble surface In Ref. [5] : reaction sites are in thermodynamics balance; the rate determining step of the C-0 reaction is controlled by the mass transfer of carbon. Thus, the decarburization rate of reaction on argon gas bubble surface can be expressed as follows:
(10)
where, ni, is the number of moles of Ar; nko is the moles of CO gas in the bubble; n&, is calculated by summing the reaction quantity with the rising bubble; and Pbubble is the pressure of the bubble and is represented by its relationship with bubble size using the following equation. Pbubble
=p n o x
[ 2.J
-3
(11)
where, Pnois hydrostatic pressure at the nozzle position; dbis the bubble diameter; and d b . 0 is the initial diameter of argon gas bubble and assumed to be 0.006 m. In the Higbie’s model, the mass transfer coefficient for a rising bubble in a liquid can be expressed as the following.
(12) where, Dc is the diffusion coefficient of dissolved carbon m2/s) ; and t. is the contact time in the melt (3.0 X which is estimated using the following equation. d t =b (13) Uslip
where uslipis the relative velocity of bubble. From the above mentioned, the decarburization quantity of Ar bubble surface in unit time can be expressed as follows:
(14) On the basis of above established mathematical model, the changes of overall decarburization rate with blow argon modes could be calculated and discussed. A lot of commercial carbon samples were taken once every minute in SQISCO with different blow argon modes designed while the other conditions such as initial steel compositions of carbon and oxygen and pressure drop curve were controlled similar. The process of I F steel production in SQISCO is: “KR-+BOF+RH+CC”. Its main parameters of RH are shown in Table 1.
Issue 5
Mathematical Model of RH Blow Argon Mode Affecting: Decarburization Rate
25
Table 1 Main parametem of RH equipment in Qian’an Iron and Steel
2
Parameters
Total melt in ladle/t
Diameter of vacuum vessel/mm
Diameter of snorkel/mm
Length of snorkel/mm
Flowrate of blowing argon gas/(L min-’)
Numerical value
210
2 138
650
1075
800- 2 000
the following formula Eqn. (21)c63and Eqn. (22)c’1 :
Parameters Determination in Model
In the RH process, Ar gas injected at the upsnorkel wall causes strong fluid flow. The melt circulates from the ladle to the vacuum vessel through the snorkels. Due to the existence of viscosity between the bubble and steel liquid, there exists a relative velocity to the steel liquid for Ar bubbles. Assuming the bubbles shape is always spherical, the relative velocity of bubble uslipcan be expressed as the following formulaC6’:
(15) where, u is surface tension of molten steel, 1. 8 N/m; viscosity of steel, 0. 005 7 kg/rns; pAris density of Ar gas, kg/m3 9 and b is the constant (-30). In the previous studyc7], the continuity equation of Ar bubble radius variation in the floatation process is: um,ltis
(16) The circulation of liquid steel is expressed as the following formulaC8’:
Q=11. 404/3G1/3
(17)
The velocity of liquid steel:
Q
u=
60Xplx? The up-floating time of bubble: H t=u
+
uslip
(18)
(19)
where, Pv is pressure of the vacuum vessel9 and H is height of the melt. By the ideal gas equation of state, the number of Ar bubble in liquid steel could be written as the following formula :
So, the surface area A band volume value Gmof Ar bubble in liquid steel at any time can be calculated using the mathematical methods. The driving energy of rising gas is expressed as
E=
nRT/VdV=QRT/6OX22.4
ln(Po/Pv)
V1
(21) E=g$,,,--pA,) X l o 3 V, a (1-(I) (22) where, (I is the gas volume relative ratio in total gasliquid two phase region; and Vi is the total volume of gas-liquid two phase region. In Eqn. (21) and Eqn. ( 2 2 ) , the volume of gasliquid two phase region could be expressed as the following:
(23) It could be observed that Vi , the volume of gasliquid two phase area as indicated in Fig. 2 , has direct relation with the pressure in vacuum and the blow argon flowrate, which influences the internal decarburization behavior of liquid steel. When the pressure in vacuum keeps constant, the gas volume of gas-liquid two phase tends to be larger with the increase of blow argon flowrate. A coefficient 7 is introduced to describe the influence of blowing argon flowrate on internal decarburization of liquid steel. 7 is defined as: Vi (24) 1=1-- VI where VI is volume of liquid steel in vacuum. It could be deduced from above Eqn. (24) that the upgrading of blow argon flowrate, which makes the volume of gas-liquid two phaseincreasing, results in the reduction of the internal decarburization
I
h
Fig. 2 Diagram of infloence of g~wliqoidtwo phase volume on internal decarblvization
reaction coefficient ( v ) , that is unfavorable to internal decarburization.
3
VOl. 1 9
Journal of Iron and Steel Research, International
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Calculated Results
The blowing argon of R H refining process not only has some extent of decarburization ability itself but also can lead to the change of carbon removing quantity at other decarburization reaction sites. The calculated results about the effect of different blow argon modes on the overall carbon concentration based on the above model are to be discussed in details in the following to make clear the decarburization mechanism.
3 . 1 Critical ascension turning point of argon blow flowrate Generally a argon blow mode in R H is composed of 2 stages in whole decarburizing process with respect for the difference of reaction mechanism along with the refining proceeding, which is taken a lower argon blow flowrate firstly from the start of vacuum refining, then is turned into a stronger one until the end of decarburing. So it is very important for decarburization with high efficiency to decide the turning point of argon blow flowrate from the first lower to the latter strong. This critical turning point is defined as Tc in this paper and the optimum Tc is got from the model calculated results and has to be proven reasonable in commercial practice. The argon blow flowrate, which takes Heat No. 08102179 in SQISCO as example, is 1200 L/min in the former stage and 2100 L/min in the latter respectively, the Tc is settled as first, 3'h, 5'h, 7'h, gth minute from the start of vacuum treatment to investigates the carbon concentration changes comparatively. It is shown in Fig. 3 that the decarburization rate is the fastest and the endpoint of carbon content
0
1
Fig. 3
3
6
7
9
Timdmin
11
1316
Influence of blow argon modes on carbon concentration
is the lowest as Tc is designed 5'h minute. On the other hand, Tc, that is settled earlier than 5'h or later than this moment makes the decarburization rate slower and result in the increase of endpoint carbon content unfavorably in the same way. In conclusion that the optimum Tc was the fifth minute through the model calculation for R H in SQISCO.
3.2 Effect of argon blow flowrate on carbon elimination quantitiy at decarburization reaction sites Fig. 4 describes the internal decarburizing quantity changes as a function of time in the 5 different modes. It is clear from this Fig. 4 that the internal carbon removing quantity is increased with the extension of T c , which is higher 35 X l o p 6 when 7°C as gth minute than that as first minute. This result suggests that the Tc settled should not be too early.
I
5
.I
Fig. 4
I /
Internal decarborization quantity of 5 different modes changes with time
Fig. 5 and Fig. 6 describes the carbon removing quantity at argon gas bubble, vacuum free surface and splash droplet changes with time in the above same 5 modes. The quantity of carbon taken off at those sites is increased with the ascension of blow argon
0
1
Fig. 5
3
6
7
9
Time/min
1 1 1 3 1 6
Argon gas bubble carbon removing quantity changes with time
Issue 5
Mathematical Model of R H Blow Argon Mode Affecting: Decarburization Rate
-
"I I
-Intemaldecarbrizationrate I I \ -.- Other sites decarburhationrate I
$cJ Fig. 6
3
5
7
Timdmin
11
8
1
4
2
0 9
-.-.-.
I
0
1
27
,
I
6
8
10
12
14
16
1 3 1 5
Surface and splash droplet carbon removing quantity changes with time
flowrate, earlier. For instance, the carbon removing quantities from argon gas bubble surfaces in Fig. 5 and from free surfaces and splash droplets in Fig. 6 reach the maximum. It is demonstrated that earlier asention of blow argon flowrate is favorable to the decarburization.
3.3 Determination of critical turning point ( T c ) of argon blow flowrate Through the above analysis it is clear that the influence of blow argon flow on overall decarburization eiists plus and minus 2 circumstances. Under the same initial conditions, the earlier ascension of argon flowrate promotes the decarburization on the argon gas bubble surface, free surface and splash droplet surface while it reduces that in interior of liquid steel. Because the influence is contradictory to each other, there exists a critical ascension turning point of blow argon flowrate to make sure the decarbonization efficiency highest during overall decarburing process. In order to find out the critical turning point accurately, Fig. 7 shows the changes of decarburization rate in the steel interior and at other sites with time according to the initial conditions of Heat No. 08102179. Tc could be determined from the intersecting point of both lines of internal decarburization and other sites decarburization in Fig. 7. Hence, it is reasonable that the flowrate of argon blow should be kept lower prior to Tc in Fig. 7 and then raised rapidly until the end of decarburization. In other words the ascension of blow argon flowrate before the Tc suggested in Fig. 7 is unnecessary, but the immediate increase of blow flowrate after that time can improve the whole decarburization rate effectively.
Fig. 7 Changes of internal decarburization rate and other sites decarburization rate with time
Flowrate of argon blow at later stage The argon blow flowrate at later stage (after Tc) is another important key factor for R H decarburization after the determination of critical turning point Tc , although the flowrate in the former period (before T c ) is not changed so much in general from the consideration of steel circulating well at early stage. T h e five later flowrate blow argon modes were settled as 1500, 1800, 2 100, 2 400, 2 700 L/min respectively and their initial conditions were similar with the Heat No. 08102179 which its initial flowrate was 1200 L/min before T c as 5 th minute. The carbon concentration changes calculated from the model with time is shown in Fig. 8. It is demonstrated from this Fig. 8 that the decarburization rate in blow flowrate modes as 1500, 1800 L/ min is obviously lower than that in other modes and the final carbon concentration are also higher than that in other modes. When blow flowrate is increased to 2 100, 2 400 and 2700 L/min, the change of carbon content curves are little. Hence the optimal later blow argon flowrate could be concluded as 2100 L/min.
3.4
0
1
3
5
7 0 Timelmin
11
1316
Fig. 8 Influence of flowrate on carbon concentration in 5 different modes
Journal of Iron and Steel Research. International
28 *
Validation of commercial date to model Both of the representative heats (No. 082012179 and No. 08303643) were selected to check the consistency between the model calculated results and commercial ones. The initial carbon concentration of , 260 X and the those two heats were 230 X other initial conditions including vacuum pumping curves were very similar, only different parameters were the blowing argon flowrate modes. The changes of carbon concentration and blow argon flowrates in refining process are drawn in Fig. 9.
3.5
Timebin
Fig. 9 Changes of carbon concentration and blow argon flow of chosen heats with time
VOl. 19
the interior of liquid steel, especially in early refining stage, while promotes the carbon elimination from argon gas bubble surface, molten steel free surface in vacuum as well as splash droplet surface. 2) The critical ascension turning point (Tc)of argon blow flowrate is the key parameter for obtaining a higher decarburizing efficiency, which could be determined from the intersecting point of lines of internal decarburization rate and other three sites decarburization rate in accordance with the decarburization mathematical model. 3) It is shown from the present calculating model that the argon blow flowrate at later stage (after T c ) has much influence on the decaburization rate. Generally, the higher the flowrate of argon blow is, the faster the decarburization rate becomes. However over bigger flowrate is unnecessary due to a further raising of decarburizing rate being very limited. 4) It has been found the critical ascension turning point of argon blow flowrate is at the 5th minute and the optimum blow argon flowrate in later stage is 2100 L/min in SQISCO , which have been confirmed in the commercial production. References:
The carbon concentration changing curves of the both heats are nearly same until 5& minute. After then, the blow argon flowrates of No. 08303643 and No. 08102179 were to ascend at 5* and gth respectively. Obviously the decarburization rate of No. 08303643 was significantly faster than that of No. 08102179 correspondingly. So according to the actual condition of Shougang Qian'an Iron and Steel Co Ltd, the critical turning point of blow argon blow rate Tc should be the 5th minute and after that the blow argon flowrate should be ascended to 2100 from 1200 L/min as soon as possible to ensure high efficient decarburization.
4
Conclusions
1) There is an obvious relationship between decarburization rates and argon blow modes. The increase of argon flowrate reduces decarburizing rate in
Masamitsu T, Hiroshi M, Tadashi S. Mechanism of Decarburization in R H Degasser [J]. ISU International. 1995, 35 (12): 1452 (in Japanese). YU Neng-wen. Mathematical and Physical Modeling of Multifunction R H Refining Process [D]. Shanghai: Shanghai University, 2001 (in Chinese). The Japan Society for the Promotion of Science. Steelmaking Data Sourcebook [MI. New York: GBSP Publishers, 1984. LI Chong-wei, CHENG Gucquang, W m G Xin-hua, et al. The Establishment of RH Natural Decarburization Mathematical Model and the Study of Mechanism of Decarburization [J]. Journal of the Chinese Rare Earth Society, 2010(3): 112 (in Chinese). Levich V G. Physicochemical Hydrodynamics [MI. Engle wood Cliffs: PrenticeHall Inc. 1962. Harashima K , Mizoguchi S, Kajioka H. Kinetics of Decaburization of Low Carbon Liquid Iron under Reduced Pressures [J]. Tetsu-tcrHagane, 1988, 74: 449. Park Y G , Do0 W C, Yi K W , et al. Numerical Calculation of Circulation Flow Rate in the Degassing Rheinstahl-Heraeus Process [J]. ISIJ International, 2000, 40: 749. Wallis G B, Mcgraw-Hill. OneDirnensional Twcrphase Flow [MI. New York: [s. n. 3, 1969.
=iO ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 20129 19(5) : 23-28
Mathematical Model of RH Blow Argon Mode Affecting : Decarburization Rate in Ultra-Low Carbon Steel Refining LI Chong-wei'
,
CHENG Guo-guang'
,
WANG Xin-hua'
,
ZHU Guo-sen3,
CUI Ai-min3
(1. Beijing Beiye Functional Materials Corporation, Beijing 100192, China; 2. School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China; 3. Shougang Qian'an Iron and Steel Co Ltd, Qian'an 064400, Hebei, China)
Abstract: A mathematical model in present study has been established to investigate the effect of Rheinstahl Heraeus ( R H ) blow argon mode on the decarburization rate in ultra-low carbon steel refining based on the R H equipment of Shougang Qian'an Iron and Steel Co Ltd (SQISCO). The calculated results show that the increase of argon flowrate promotes the carbon elimination from argon gas bubble surface, molten steel free surface in vacuum as well as splash droplet surface, while reduces that from the interior of liquid steel. It has been found the critical turning point of flowrate ascension is at the 5'h minute and the optimum blow argon flowrate in later stage is 2 100 L/min in accordance with the 2 stages argon blow mode, which have been confirmed in the commercial production in SQISCO. Key words: RH ; vacuum; mathematical model; argon flowrate: decarburization
Efficient refining of I F steel requires the carbon concentration less than 0. 003% and refining time less than 15 min. The decarburization reaction in RH generally occurs in following four locations: free surface of liquid steel in vacuum chamber, argon gas bubble surface, interior of liquid steel in vacuum"] and splash droplet surfaceCz1.Argon injected from a up-snorkel in RH as the power source of liquid steel circulation, its flowrate directly affects the circulation behaviour of molten steel and the decarburization reaction. Because of the difference of the decarburization mechanism along with the proceeding of RH refining process, the practical production cannot adopt only a constant blow argon flowrate during whole decarburization period. But there is little detailed statements reported on how to determine the best mode of blow argon flowrate so far. The purpose of the present study is to establish a mathematical model of blow argon mode to investigate the mechanism affecting the decarburization rate of ultra-low carbon steel refining and optimize the argon blow regime, based on the commercial production data of Shougang Qian'an Iron and Steel GILtd (SQISCO). The optimum blow
argon mode put forward by this paper has been confirmed reasonable to acquire extra-low carbon concentration in relatively shorter time.
1 Establishment of Mathematical Model for RH Decarburization Thermodynamics of decarburization reaction The decarburization reaction in the reaction site can be represented by the following equation. CCl+COl =CO(g) (1) In this reaction, the equilibrium constant K is expressed as followingc3]. K- Pco* 'Co* = 10'1 160/T+Z.003) (2) 1.1
acao
-
WCCl
q01
1 . 2 Establishment of RH natural decarburization mathematical mode The RH natural decarburization mathematical model was established on the basis of the 4 decarburization sites: interior of liquid steel, argon gas bubble surface, free surface and splash droplet surfaceC4].The diagrammatic sketch of RH decarburazition sites is shown in Fig. 1.
Foundation Item: Item Sponsored by National Key Technology Research and Development Program in 11"' FiveYear Plan of China (2006BAE03A13)
Biogr8phy:LI Chong-wei(l982-),
Male, Doctor;
E-mail: lichongwei-l23@yahoo. com. cn;
Received Date: March 28, 2011
VOl. 19
Journal of Iron and Steel Research, International
24
where, Ab is surface area; pm is the density of melt; is liquid phase mass transfer coefficient of carbon! and ZU[~I,is equilibrium carbon content on gas-liquid surface which is estimated using the following equation.
kb
bubblesurface
I 1innersites I
n
I
I
Fig. 1 Diagrammatic sketch of RH decarburazition sites
The following assumptions are made. 1 ) For each calculation circulation of the model, the carbon and oxygen content in the ladle and vacuum are constant respectively ; 2) The decarburization reaction proceeds in the vacuum vessel only; 3) The carbon and oxygen concentration at the gas-metal interface is in equilibrium with the partial pressure of CO in the gas phase; 4) The rate of decarburization is controlled by the mass transfer of carbon. The mass balance of carbon and oxygen in the vessel under these conditions is represented by Eqn. ( 3 ) to Eqn. (7). (3) W(dw[clL/dt) =Q(w[cl, -wcclL 1 (4) W(dwcolL/dt) =Q(w[olV -w[o], ) W(dw[clV/dt)=Q(w[clL-W[C], )-(CAcI,+
CAcI =CACIA~
P C 0 . b is the partial pressure of CO gas in the bubble and is calculated using the following equation.
CAcIin +CAcIface CACIspt ) (5) CAcIin 4- CAcl~me C A c l s p ~ (6) M O
W(dw[olv /dt> =Q(ut[ol, - ~ [ o ] ), --(dAr+ MC
+ +
(7) din dface dspl ) where, Mc , Mo are the molecular mass of carbon and oxygen, kg/mol; [ACIA, , [ACIin, [ACIf.,, , [Ac].,l are the carbon removing quantity on argon gas bubble surface, in internal liquid steel, on free surface and splash droplet surface respectively, t/min; and Subscript L, V is ladle and vacuum chamber.
1.3 Decarburization mathematical model of argon gas bubble surface In Ref. [5] : reaction sites are in thermodynamics balance; the rate determining step of the C-0 reaction is controlled by the mass transfer of carbon. Thus, the decarburization rate of reaction on argon gas bubble surface can be expressed as follows:
(10)
where, ni, is the number of moles of Ar; nko is the moles of CO gas in the bubble; n&, is calculated by summing the reaction quantity with the rising bubble; and Pbubble is the pressure of the bubble and is represented by its relationship with bubble size using the following equation. Pbubble
=p n o x
[ 2.J
-3
(11)
where, Pnois hydrostatic pressure at the nozzle position; dbis the bubble diameter; and d b . 0 is the initial diameter of argon gas bubble and assumed to be 0.006 m. In the Higbie’s model, the mass transfer coefficient for a rising bubble in a liquid can be expressed as the following.
(12) where, Dc is the diffusion coefficient of dissolved carbon m2/s) ; and t. is the contact time in the melt (3.0 X which is estimated using the following equation. d t =b (13) Uslip
where uslipis the relative velocity of bubble. From the above mentioned, the decarburization quantity of Ar bubble surface in unit time can be expressed as follows:
(14) On the basis of above established mathematical model, the changes of overall decarburization rate with blow argon modes could be calculated and discussed. A lot of commercial carbon samples were taken once every minute in SQISCO with different blow argon modes designed while the other conditions such as initial steel compositions of carbon and oxygen and pressure drop curve were controlled similar. The process of I F steel production in SQISCO is: “KR-+BOF+RH+CC”. Its main parameters of RH are shown in Table 1.
Issue 5
Mathematical Model of RH Blow Argon Mode Affecting: Decarburization Rate
25
Table 1 Main parametem of RH equipment in Qian’an Iron and Steel
2
Parameters
Total melt in ladle/t
Diameter of vacuum vessel/mm
Diameter of snorkel/mm
Length of snorkel/mm
Flowrate of blowing argon gas/(L min-’)
Numerical value
210
2 138
650
1075
800- 2 000
the following formula Eqn. (21)c63and Eqn. (22)c’1 :
Parameters Determination in Model
In the RH process, Ar gas injected at the upsnorkel wall causes strong fluid flow. The melt circulates from the ladle to the vacuum vessel through the snorkels. Due to the existence of viscosity between the bubble and steel liquid, there exists a relative velocity to the steel liquid for Ar bubbles. Assuming the bubbles shape is always spherical, the relative velocity of bubble uslipcan be expressed as the following formulaC6’:
(15) where, u is surface tension of molten steel, 1. 8 N/m; viscosity of steel, 0. 005 7 kg/rns; pAris density of Ar gas, kg/m3 9 and b is the constant (-30). In the previous studyc7], the continuity equation of Ar bubble radius variation in the floatation process is: um,ltis
(16) The circulation of liquid steel is expressed as the following formulaC8’:
Q=11. 404/3G1/3
(17)
The velocity of liquid steel:
Q
u=
60Xplx? The up-floating time of bubble: H t=u
+
uslip
(18)
(19)
where, Pv is pressure of the vacuum vessel9 and H is height of the melt. By the ideal gas equation of state, the number of Ar bubble in liquid steel could be written as the following formula :
So, the surface area A band volume value Gmof Ar bubble in liquid steel at any time can be calculated using the mathematical methods. The driving energy of rising gas is expressed as
E=
nRT/VdV=QRT/6OX22.4
ln(Po/Pv)
V1
(21) E=g$,,,--pA,) X l o 3 V, a (1-(I) (22) where, (I is the gas volume relative ratio in total gasliquid two phase region; and Vi is the total volume of gas-liquid two phase region. In Eqn. (21) and Eqn. ( 2 2 ) , the volume of gasliquid two phase region could be expressed as the following:
(23) It could be observed that Vi , the volume of gasliquid two phase area as indicated in Fig. 2 , has direct relation with the pressure in vacuum and the blow argon flowrate, which influences the internal decarburization behavior of liquid steel. When the pressure in vacuum keeps constant, the gas volume of gas-liquid two phase tends to be larger with the increase of blow argon flowrate. A coefficient 7 is introduced to describe the influence of blowing argon flowrate on internal decarburization of liquid steel. 7 is defined as: Vi (24) 1=1-- VI where VI is volume of liquid steel in vacuum. It could be deduced from above Eqn. (24) that the upgrading of blow argon flowrate, which makes the volume of gas-liquid two phase
I
h
Fig. 2 Diagram of infloence of g~wliqoidtwo phase volume on internal decarblvization
reaction coefficient ( v ) , that is unfavorable to internal decarburization.
3
VOl. 1 9
Journal of Iron and Steel Research, International
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Calculated Results
The blowing argon of R H refining process not only has some extent of decarburization ability itself but also can lead to the change of carbon removing quantity at other decarburization reaction sites. The calculated results about the effect of different blow argon modes on the overall carbon concentration based on the above model are to be discussed in details in the following to make clear the decarburization mechanism.
3 . 1 Critical ascension turning point of argon blow flowrate Generally a argon blow mode in R H is composed of 2 stages in whole decarburizing process with respect for the difference of reaction mechanism along with the refining proceeding, which is taken a lower argon blow flowrate firstly from the start of vacuum refining, then is turned into a stronger one until the end of decarburing. So it is very important for decarburization with high efficiency to decide the turning point of argon blow flowrate from the first lower to the latter strong. This critical turning point is defined as Tc in this paper and the optimum Tc is got from the model calculated results and has to be proven reasonable in commercial practice. The argon blow flowrate, which takes Heat No. 08102179 in SQISCO as example, is 1200 L/min in the former stage and 2100 L/min in the latter respectively, the Tc is settled as first, 3'h, 5'h, 7'h, gth minute from the start of vacuum treatment to investigates the carbon concentration changes comparatively. It is shown in Fig. 3 that the decarburization rate is the fastest and the endpoint of carbon content
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Influence of blow argon modes on carbon concentration
is the lowest as Tc is designed 5'h minute. On the other hand, Tc, that is settled earlier than 5'h or later than this moment makes the decarburization rate slower and result in the increase of endpoint carbon content unfavorably in the same way. In conclusion that the optimum Tc was the fifth minute through the model calculation for R H in SQISCO.
3.2 Effect of argon blow flowrate on carbon elimination quantitiy at decarburization reaction sites Fig. 4 describes the internal decarburizing quantity changes as a function of time in the 5 different modes. It is clear from this Fig. 4 that the internal carbon removing quantity is increased with the extension of T c , which is higher 35 X l o p 6 when 7°C as gth minute than that as first minute. This result suggests that the Tc settled should not be too early.
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Fig. 4
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Internal decarborization quantity of 5 different modes changes with time
Fig. 5 and Fig. 6 describes the carbon removing quantity at argon gas bubble, vacuum free surface and splash droplet changes with time in the above same 5 modes. The quantity of carbon taken off at those sites is increased with the ascension of blow argon
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Argon gas bubble carbon removing quantity changes with time
Issue 5
Mathematical Model of R H Blow Argon Mode Affecting: Decarburization Rate
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-Intemaldecarbrizationrate I I \ -.- Other sites decarburhationrate I
$cJ Fig. 6
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Surface and splash droplet carbon removing quantity changes with time
flowrate, earlier. For instance, the carbon removing quantities from argon gas bubble surfaces in Fig. 5 and from free surfaces and splash droplets in Fig. 6 reach the maximum. It is demonstrated that earlier asention of blow argon flowrate is favorable to the decarburization.
3.3 Determination of critical turning point ( T c ) of argon blow flowrate Through the above analysis it is clear that the influence of blow argon flow on overall decarburization eiists plus and minus 2 circumstances. Under the same initial conditions, the earlier ascension of argon flowrate promotes the decarburization on the argon gas bubble surface, free surface and splash droplet surface while it reduces that in interior of liquid steel. Because the influence is contradictory to each other, there exists a critical ascension turning point of blow argon flowrate to make sure the decarbonization efficiency highest during overall decarburing process. In order to find out the critical turning point accurately, Fig. 7 shows the changes of decarburization rate in the steel interior and at other sites with time according to the initial conditions of Heat No. 08102179. Tc could be determined from the intersecting point of both lines of internal decarburization and other sites decarburization in Fig. 7. Hence, it is reasonable that the flowrate of argon blow should be kept lower prior to Tc in Fig. 7 and then raised rapidly until the end of decarburization. In other words the ascension of blow argon flowrate before the Tc suggested in Fig. 7 is unnecessary, but the immediate increase of blow flowrate after that time can improve the whole decarburization rate effectively.
Fig. 7 Changes of internal decarburization rate and other sites decarburization rate with time
Flowrate of argon blow at later stage The argon blow flowrate at later stage (after Tc) is another important key factor for R H decarburization after the determination of critical turning point Tc , although the flowrate in the former period (before T c ) is not changed so much in general from the consideration of steel circulating well at early stage. T h e five later flowrate blow argon modes were settled as 1500, 1800, 2 100, 2 400, 2 700 L/min respectively and their initial conditions were similar with the Heat No. 08102179 which its initial flowrate was 1200 L/min before T c as 5 th minute. The carbon concentration changes calculated from the model with time is shown in Fig. 8. It is demonstrated from this Fig. 8 that the decarburization rate in blow flowrate modes as 1500, 1800 L/ min is obviously lower than that in other modes and the final carbon concentration are also higher than that in other modes. When blow flowrate is increased to 2 100, 2 400 and 2700 L/min, the change of carbon content curves are little. Hence the optimal later blow argon flowrate could be concluded as 2100 L/min.
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Fig. 8 Influence of flowrate on carbon concentration in 5 different modes
Journal of Iron and Steel Research. International
28 *
Validation of commercial date to model Both of the representative heats (No. 082012179 and No. 08303643) were selected to check the consistency between the model calculated results and commercial ones. The initial carbon concentration of , 260 X and the those two heats were 230 X other initial conditions including vacuum pumping curves were very similar, only different parameters were the blowing argon flowrate modes. The changes of carbon concentration and blow argon flowrates in refining process are drawn in Fig. 9.
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Fig. 9 Changes of carbon concentration and blow argon flow of chosen heats with time
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the interior of liquid steel, especially in early refining stage, while promotes the carbon elimination from argon gas bubble surface, molten steel free surface in vacuum as well as splash droplet surface. 2) The critical ascension turning point (Tc)of argon blow flowrate is the key parameter for obtaining a higher decarburizing efficiency, which could be determined from the intersecting point of lines of internal decarburization rate and other three sites decarburization rate in accordance with the decarburization mathematical model. 3) It is shown from the present calculating model that the argon blow flowrate at later stage (after T c ) has much influence on the decaburization rate. Generally, the higher the flowrate of argon blow is, the faster the decarburization rate becomes. However over bigger flowrate is unnecessary due to a further raising of decarburizing rate being very limited. 4) It has been found the critical ascension turning point of argon blow flowrate is at the 5th minute and the optimum blow argon flowrate in later stage is 2100 L/min in SQISCO , which have been confirmed in the commercial production. References:
The carbon concentration changing curves of the both heats are nearly same until 5& minute. After then, the blow argon flowrates of No. 08303643 and No. 08102179 were to ascend at 5* and gth respectively. Obviously the decarburization rate of No. 08303643 was significantly faster than that of No. 08102179 correspondingly. So according to the actual condition of Shougang Qian'an Iron and Steel Co Ltd, the critical turning point of blow argon blow rate Tc should be the 5th minute and after that the blow argon flowrate should be ascended to 2100 from 1200 L/min as soon as possible to ensure high efficient decarburization.
4
Conclusions
1) There is an obvious relationship between decarburization rates and argon blow modes. The increase of argon flowrate reduces decarburizing rate in
Masamitsu T, Hiroshi M, Tadashi S. Mechanism of Decarburization in R H Degasser [J]. ISU International. 1995, 35 (12): 1452 (in Japanese). YU Neng-wen. Mathematical and Physical Modeling of Multifunction R H Refining Process [D]. Shanghai: Shanghai University, 2001 (in Chinese). The Japan Society for the Promotion of Science. Steelmaking Data Sourcebook [MI. New York: GBSP Publishers, 1984. LI Chong-wei, CHENG Gucquang, W m G Xin-hua, et al. The Establishment of RH Natural Decarburization Mathematical Model and the Study of Mechanism of Decarburization [J]. Journal of the Chinese Rare Earth Society, 2010(3): 112 (in Chinese). Levich V G. Physicochemical Hydrodynamics [MI. Engle wood Cliffs: PrenticeHall Inc. 1962. Harashima K , Mizoguchi S, Kajioka H. Kinetics of Decaburization of Low Carbon Liquid Iron under Reduced Pressures [J]. Tetsu-tcrHagane, 1988, 74: 449. Park Y G , Do0 W C, Yi K W , et al. Numerical Calculation of Circulation Flow Rate in the Degassing Rheinstahl-Heraeus Process [J]. ISIJ International, 2000, 40: 749. Wallis G B, Mcgraw-Hill. OneDirnensional Twcrphase Flow [MI. New York: [s. n. 3, 1969.