MATHEMATICAL MODELING OF NITROGEN BEHAVIOR
AT PLASMA- ARC AND VACUUM-ARC REFINING
M. Shalimov
Ural State Technical University, Ekaterinburg, Russia
ABSTRACT. Attention of many authors is attracted to the behavior of nitrogen at plasma-arc refining (PAR) and at vacuum-arc refining (VAR) [1-5]. As established, at PAR alloying of metal by nitrogen is possible from above equilibrium values of concentration, while at VAR, basically, degassing of metal is proceeded. However there are no data now to make definite conclusions concerning
limiting stages of processes of absorption and outgassing of nitrogen at PAR and VAR. The absence
of the mathematical description of these processes in view of technological parameters complicates
optimization of technological process, compelling to use the expensive empirical approach.
In the given work the mathematical models are offered which allow to describe behavior of
nitrogen at PAR and VAR and to predict its contents in finished metal.
Plasma-arc refining model
Following scheme of "nitrogen-containing plasma - liquid metal" interaction is in a basis of
model [1-3]:
- nitrogen in plasma jet is dissociated and is ionized up to balance according to reactions:
1/2 {N2} = {N},
(1)
+
{N} = {N } + ē.
(2)
Thus the gas contains: Ar, N2, N, N+, ē;
- in a diffusion surface layer of metal deionization of nitrogen in atoms occurs, The latter
*
ones are united into the exited molecules N 2 . An estimation of a degree of development of such
processes in diffusion layer was done by Damkeler criterion [1]. It shows, that the formation of molecules of nitrogen occurs quickly enough;
*
- the formed molecules N 2 are diffused to metal and also are dissolved in it by reaction:
*
1/2 { N 2 } = [N].
The constant of balance of this reaction is expressed by equation:
lg K *N  2264 T  1,16
(3)
(4)
It's value is much above, than for reaction of dissolution of the non-exited nitrogen molecules:
1/2 {N2} = [N]
(5)
lg K N   293 T  1,16
(6)
So nitrogen content in surface layer of metal exceeds equilibrium one by reaction (6);
- diffusion and circulation of metal transfer this "superequilibrium" nitrogen into volume of
a metal bath, and after crystallization it remains in an ingot;
- on a part of a bath surface, which is free from contact to plasma, the nitrogen can desorbs
into gas;
- volumetric "boiling" of bath begins at achievement of a critical oversaturation degree of
metal by nitrogen. Here speed of nitrogen removal from metal is so high, that further oversaturation
the metal over critical value does not occur.
As commonly accepted, slowed-down nitrogen diffusion into metal
is limiting stage of
total process [1-3]. However we showed, that it is necessary to take into account diffusion both in
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metal and in gas at two consecutive stages: electrode and bath. The conclusion about the main braking stage in specific conditions can be made on the basis of the solution of combined equations,
where the above listed factors are taken into account.
The structure of plasma is determined by conditions of balance of reactions (1) and (2) at
given initial structure of gas, pressure and temperature. At constant total pressure (P) in diffusion
layer the contents of the exited molecules can be found from the following equation:
(7)
P *  PN  P  2 1  PN  3P  2P  ,
N2

N
 
N


Correcting denominator in brackets takes into account reduction of volume owing to deionization
and molization of nitrogen atoms. The calculation shows, what at T 6000 K the partial pressure of
active particles, which determines transition of nitrogen into metal, is close to partial pressure of nitrogen in plasma-forming gas and can be approximated by the equation:
(8)
P *  0,7PN 2
N2
The balance of nitrogen (kg/s) in metal drops on electrode can be described as follows:
m[ N ]0 100  VЭSЭ M N  m[ N ]K 100 ,
(9)
here [N]0 and [N]K - contents of nitrogen in preparation and in drops, mas. %; m – melting speed, kg
/s; MN - molecular mass of nitrogen; VЭ - rate of reaction (3) at electrode stage, (moles of N)
/(м2 s); SЭ - the surface square of electrode, on which reaction (3) proceeds, m2.
The balance of nitrogen on the bath is the following:
m
[ N ]C
[ N ]K
m d[ N ]B
 VBS B M N   m
 VDS D M N (1  )  B
,
100
100
100d
(10)
here left part items represent rates of receipt of nitrogen into bath with drops and from plasma ( contacting with plasma share of bath surface SB,); right part items represent nitrogen leaving
rates, namely, going away rate into crystallizing metal, desorption into gas on bath surface part,
which is free from plasma, and accumulation in bath. In quasi-stationary mode the latter one
item can be neglected.
The concentration of nitrogen in a bath and ingot are in the ratio:
[N]C = æN [N]B,
(11)
here æN - segregation factor of nitrogen.
At model development were taken into account the following: process of nitrogen absorption
on electrode proceeds in diffusion mode; rate of nitrogen diffusion in gas and metal, with reference
to reaction (3), are identical at stationary mode. Experimental data allowing describing occurrence of
volumetric boiling of a metal bath and dependence of temperature of metal bath surface from gas
composition and value of an operating current.
Rise of volumetric boiling in metal bath and dependence of temperature of metal bath surface
from gas composition and value of an operating current were described according to experimental
data from sources [1 – 3]. Table 1 shows that model gives close results of steel alloying degree by
nitrogen. Steel 06Х21Г11АН4М in plant У-365 was treated at following mode of operation: refining rate - 4-5 mm/min; concentration of nitrogen in initial steel 0,1 mas. %; nitrogen content 24 37 %; operating current of plasmatron 400 A; pressure in the furnace 1.5 atm.
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Table 1. Results of calculations and experiments for repeated PAR
№ of specimen
Nitrogen partial presNitrogen content in ingot, mas. %
sure in the
Experiment
Calculation
furnace, atm
433, 1st fusion
0,386
0,25 – 0,44
0,42 – 0,47
d
436, 2 fusion
0,430
0,61 – 0,90
0,65 – 0,74
439, 3d fusion
0,470
0,96 – 1.0
0,78 – 0,80
st
435, 1 fusion
0,473
0,28 – 0,37
0,32 – 0,49
d
437, 2 fusion
0,430
0,38 – 0,43
0,46 – 0,70
440, 3d fusion
0,487
0,62 – 0,76
0,58 – 0,77
A number of the conclusions about kinetics of nitrogen absorption from plasma were done
according to calculation analysis. High concentration of nitrogen is to be noticed. In the area of the
constant's values, accepted on the literary data [1, 2], it comes to 1-2 мас. %, in drops. Diffusion
braking in metal at electrode stage is insignificant, on the contrary, diffusion braking in gas is essential. The contribution of bath stage to nitrogen absorption is comparable with electrode stage. Diffusion in gas is determining factor.
Thus, PAR model of nitrogen - metal interaction kinetics can be used for predictions.
Vacuum-arc refining model
The following theoretical preconditions and simplifying assumptions were accepted for denitration in VAR model:
- convective mass-transfer of atoms of the dissolved nitrogen from melting metal volume to
the metal – gas interface is denitration limiting stage;
- during gases removal two stages come first: liquid film on electrode and bath. And at stage
of bath degassing occurs uniformly on all surface of melted metal, which is free from slag;
- at each stage denitration can be characterized by average sizes of interaction area, convection constant and denitration rate;
- influence of alloying elements and impurities on removal process of nitrogen is shown
through change of it's equilibrium solubility in metal.
At such approach the rate of nitrogen removal at stage of electrode is determined from the
following equation:




VNЭ  [ N ]Э  [ N ]P  100 M N  M eD 0N,5 M e  100SЭ M N m Э ,
(12)
here [N]Э and [N]Р - current and equilibrium content of nitrogen in a liquid film at end face of electrode, mas.%; Me- convection constant for metal bath, s-0,5; DN – diffusion coefficient of nitrogen in metal, m2/s; mЭ – electrode melting rate, kg/s.
For bath stage the non-stationary process is considered. Thus for each moment of time  the
rate of nitrogen removal is expressed by the equation:
 
VB   M eD 0N,5 M e ([ N ]B  [ N ]P ) 100 M N  ,
(13)

here N B - current concentration of nitrogen in bath, mas.%.
Accordingly, the contents of nitrogen in drops of electrode metal, which is getting into bath,
is the following:
[ N ]K  [ N ]Э  100 VNЭSЭ M N m Э
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(14)
and the content of nitrogen in liquid metal of a bath at the moment of time  we find from the equation:
[ N ]B  {([ N ] K  {N ]B1 æN) mЭ  100V B S B M N } / m B  [ N ]B1 ,
(15)
here  - calculation time period, s; mВ – current bath mass, kg.
Model verification was tested by comparison of calculation results and experimental data
concerning nitrogen behavior at VAR. Concentrations of nitrogen in liquid film at electrode end face
N Э  and in ingot N СЛ  were compared. The following parameters of mass-transfer were assumed: for electrode stage Me = 1.0 s-0,5; for bath stage Me = 0,4 s-0,5; for gas phase  = 8.0 s-0,5.
Steel 12Х18Н10Т and low-carbon steel 14ХН3МА were treated at following operation mode: electrode diameter - 0,57 м; crystallizer diameter - 0,65 м; pressure in the furnace chamber - 110-4 atm;
pressure of nitrogen - 1,1110-5 atm. As seen from tables 2, 3 the calculation gives close results to
experimental data concerning nitrogen removal.
Table 2. Results of calculations and experiments for VAR of steel 12Х18Н10Т [4]
Linear rate of refining, sm/s
[N]Э/[N]СЛ
Experiment
Calculation
1,29
1,3 – 1,4
1,41
0,89
1,4 – 1,6
1,60
0,70
1,7 – 1,9
1,87
0,50
2,0 – 2,6
2,10
Table 3. Results of calculations and experiments for VAR of steel 14ХН3МА [5]
Linear rate of refining, kg/s
[N]Э, mas.%,
[N]СЛ, mas.%,
[N]СЛ, mas.%,
experiment
experiment
calculation
0,123
0,0099
0,0061
0,0058
0,208
0,0099
0,0076
0,0069
The developed model and program of computer-aided calculation allow predicting change of
metal structure of ingot. It can be used for designing VAR technology for constructional nitrogencontaining steels.
REFERENCES
1. Lakomski V. I. Plasma - arc refining. Kiev. Technica, 1974.
2. Erohin A. A. Rules of plasma - arc alloying and refining of metals. Moscow. Nauka,
1984.
3. Grigorenko G. M., Pomarin Yu. M. Hydrogen and nitrogen in steels at plasma – refining. Kiev. Naykova dymka, 1989.
4. Shalimov A. G., Gotin V. N., Tulin A. Y. Intensification of special electrometallurgy
processes. Moscow. Metallurgy, 1988.
5. Sergeev A. B., Shved F. I., Tulin A. Y. Vacuum-arc refining of constructional steels.
Moscow. Metallurgy, 1974.
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