# 6.2. A dynamic sample piece of distribution of sulphur between phases

For definition of seeming (effective) constants of speed of transition of sulphur from metal in slag and from slag in gas, have developed the complex dynamic sample piece, allowing to predict sulphur distribution in oven ROMELT in the course of a real fusion.
The sample piece has formally kinetic character and does not consider the process mechanism.
At construction of a sample piece started with following substantive provisions. At movement of sweat balls of iron in slag sulphur passes from metal in slag:
[S] = (S) (6.12)
Disposal of sulphur from slag in a gas phase is carried out at its blowing through kislorodsoderzhashchim by gas:
(S) - {S> (6.13)
The sulphur allocated from coal with flying, and sulphur deleted from slag at a blowing through, are distributed between a gas phase and a dust. And this distribution varies at movement pylegazovogo a stream on gazootvodjashchemu to a path before gas purification. Here these questions are not considered and pylegazovyj a stream which is taken out from the oven, is considered as a cumulative phase.
Taking into account spent above the assaying, it is enough such simplified description for formation of the mathematical apparatus describing dynamics of behaviour of sulphur in oven ROMELT.
Process of a sulphur removal of drops of metal (6.12) includes some consecutive stages, each of which can be limiting.
Considering high intensity massoobmennyh processes in bubbled slag, it is possible to consider, that sulphur diffusion in slag does not limit speed of process as a whole. Sulphur diffusion in drops also cannot be a limiting stage of process owing to as enough the high contents of sulphur in drops, and them concerning the small size. It is possible to assume, that sulphur removal process proceeds either in mixed, or in a kinetic mode. Then speed of process (6.12) can be described following expression:
d [S] _ [S]
Where To} - a constant of speed, kg/m2* with; F ^ - a specific surface of sweat balls, м2*кг; [S] and (S) — concentration of sulphur in metal and slag, accordingly.
Integrating (6.14) in breaking points from [S] c to [S] and from 0 to t, we will receive:
[5] = Ю0ехр (-^0 (6.15)
Where [S] c - initial concentration of sulphur in svezhevosstanovlennyh "primary" drops; t — time of stay of drops in slag, with.
At a constant furnace production rate (R, kg/c) and the contents of drops in slag (Cfc, kg/m3) speed of their sedimentation is equal (km/s):
R R
V — V = ^
r s-t OR V ^ (6.16)
Gv^k Uк
Where Fei - the area of cross-section section of a bosh, м2; Ru - a specific duty of the oven,
Kg / (м2*с).
Considering, that formed drops pass a way equal to height of a course of bubbled slag (h,), time of their interaction with slag melt we will define as:
On
t =
r (6.17)
At
Substituting (6.17) in (6.15), we will receive for the sulphur contents in pig-iron following expression:
Constant of speed of process:
Kj^K^expt-Ei/RT),
Where Kj "- predeksponentsialnyj a multiplier; Ej - an activation energy, Dzh/MOLE; T - temperature, To; R - a gas constant. The equation (6.18) allows to analyse influence of some parametres on the sulphur contents in final metal.
The sulphur contents in slag on a course of melt is defined from the equation of a burden balance of sulphur.
Arrival of sulphur with raw materials is equal PCSC, kg/with, where Rs - the raw materials expense in a bosh minus entrainment, kg/with; Sc - the sulphur contents in raw materials, % of weights.
Arrival of sulphur will make of iron drops:
[S] 0 [l-exp (-/f, kg/island
Speed of process of disposal of sulphur in a gas phase is defined by expression:
d (S) _ Pt (S)
Where К.2 - a constant of speed of reaction; Rk - the expense of the oxygen submitted on blowing-off furmy, kg/with; Msh - weight of bubbled slag, kg.
Besides, there is a disposal of sulphur from the oven to tapped slag. Speed of this process at a continuous slag tap from the oven (the weight of slag in the oven is constant) is defined by expression PUm (S), where Rshchl - quantity of the slag formed in unit of time minus slag, entrained gazopylevoj a phase, kg/with. Reducing the received expressions in one, we will receive for the sulphur contents in slag:
RL + [5 0 [1 - exp (—Kl - ^V - K2Pk (5) - Pt „(5 (6.20) at (S) PV
The equation (6.20) describes behaviour of sulphur in oven ROMELT and allows at known values of constants of processes (6.12) and (6.13) to analyse influence of technical characteristics on process on the sulphur contents in metal, slag and py - legazovoj to a phase.
Constants of speeds of processes of transition of sulphur from metal in slag and from slag in a gas phase are integrated sizes and can be defined ground experimental data. Thus it is possible to use concrete values of constants with enough high reliability for calculations of distribution of sulphur at rather small deviations of parametres of process from values which they had in experiments by definition of constants.
As an example we will result a technique of definition of constants of speeds of processes (6.12) and (6.13) and energy activation at processing of slurries and aglorudy on installation ROMELT.
Ground the given skilled campaigns have defined a mass fraction of drops in slag, their particle-size distribution and concentration of sulphur.
For definition of a constant of speed and an activation energy of process (6.12) the data received at holding of six skilled campaigns on which provided the control of necessary parametres used.
The specific surface of sweat balls in a bubbled course is stable enough and made, 5 m2/kg. Basicity of slag was in narrow breaking points 0,9... 1,0. The temperature changed from 1320 to 1540 °s. Temperature of slag melt defined on size of a thermal stream on an oven wall.
On a course of melt seeded metal and slag samples in which defined concentration of sulphur. The initial contents of sulphur in svezhevosstanovlennyh sweat balls with-put [S] o=0,12 %; density of bubbled slag - 2700 kg/m3; height of a bubbled course - 1,8 m. of Value To; and initial data are resulted in tab. 27. On fig. 71, and dependence of a constant of speed of process (6.12) from temperature is presented,
0 3
On which values To, "= 315,5 kg/m with and Ei=260670 Dzh/MOLE are defined.
Table 27
Initial data for calculation and and values of constant Ru, kg / (м3*с) Sju kg/m3 (S), % IS], % t, to Ki, Kg / (м3*с) 1 0,11 30,0 0,08 0,035 1683 0,366 2 0,125 52,1 0,11 0,034 1663 0,370 3 0,119 51,3 0,13 0,037 1663 0,395 4 0,110 42,7 0,10 0,030 1720 0,398 5 0,098 26,2 0,11 0,048 1692 0,421 6 0,147 42,7 0,15 0,058 1730 0,419 7 0,169 24,0 0,11 0,041 1747 0,473 8 0,169 24,3 0,11 0,039 1743 0,476 9 0,162 30,0 0,13 0,072 1723 0,398 10 0,194 45,4 0,17 0,030 1703 0,169 11 0,187 54,5 0,11 0,042 1715 0,440 12 0,190 52,9 0,10 0,042 1703 0,419 13 0,198 20,8 0,08 0,048 1744 0,778 14 0,148 29,7 0,12 0,070 1718 0,359 15 0,137 32,7 0,12 0,038 1718 0,408 16 0,150 28,4 0,12 0,093 1659 0,176 17 0,146 34,0 0,14 0,097 1655 0,140 18 0,140 27,0 0,10 0,058 1717 0,421 19 0,155 37,5 0,11 0,061 1718 0,344 20 0,113 28,9 0,16 0,099 1653 0,132 21 0,160 27,0 0,13 0,090 1705 0,248 22 0,160 22,7 0,09 0,080 1715 0,289 23 0,152 25,4 0,11 0,092 1683 0,197 24 0,152 25,4 0,13 0,100 1693 0,156 | about and - about about About ' 8 • - about — - ° about
1 1 1 57 58 53 60 1/7 ' 10s and about about § - oo^j and
About oo 1 1 ch ^ In To,-12,0
-12,8-13,2-13, in
1пКг Z4 2,1 M 1,5 1,2
57
55
59
61 1/T-105 a Fig. 71. Dependence of constants of speeds of processes (6.12) - () and (6.13) - () from temperature
Constant of speed of process (6.13) defined on the experimental data received at holding of three skilled campaigns. Burden balances on the sulphur, allowed to define quantity of the sulphur deleted from the oven in gazopylevuju a phase have been made. Data are presented to tab. 28. Here initial data for calculation К2 are cited. Dependence of a constant of speed of process (6.13) from temperature is resulted on fig. 71; on it are defined: К2 ° = 3 5560,8 with "1 and Е2=120679 Dzh/MOLE. Initial data for calculation and znachennja constants
Table 28 in pylegazovuju a phase, *103 kg/with (S), % Rk, kg/with T, To к2, with 1 1 19,0 0,17 3,32 1623 3,37 2 20,7 0,15 3,32 1641 4,16 3 13,9 0,11 3,32 1692 5,45 4 20,3 0,10 3,32 1720 6,11 5 23,7 0,14 3,32 1643 5,10 6 23,8 0,13 3,38 1663 5,51 7 32,8 0,23 3,81 1593 3,74 8 35,0 0,18 3,81 1653 5,10 9 35,2 0,13 3,81 1723 7,11 10 35,6 0,12 3,81 1736 7,79 11 36,3 0,08 3,81 1765 11,90 12 38,4 0,25 3,81 1633 4,03 13 39,7 0,15 3,81 1693 6,95 14 42,8 0,13 3,81 1723 8,64 15 40,6 0,18 3,81 1723 5,92 16 41,5 0,16 3,81 1744 6,81 17 43,3 0,09 3,81 1793 12,63 18 43,2 0,10 3,81 1803 11,34 19 43,3 0,09 2,58 1913 12,63 20 21,6 0,14 ' 2,58 1623 5,98 21 20,6 0,13 2,58 1638 6,14 22 20,8 0,12 2,58 1663 6,72 23 23,7 0,10 2,58 1717 9,19 24 23,3 0,12 2,58 1718 7,53 25 21,9 0,105 2,58 1718 8,02 26 21,4 0,14 2,58 1628 5,92 27 20,3 0,14 2,58 1633 5,62 28 22,4 0,13 2,58 1633 6,68 29 22,4 0,125 2,59 1653 6,95 it is necessary to notice sulphur Entrainment, that the sulphur contents in metal and slag cannot be below equilibrium values, Therefore at calculation of the contents of sulphur in fusion products in the modes essentially differing from investigated, it is necessary to enter thermodynamic restrictions on balance metal - slag and slag - gas.
On fig. 72 the values of concentration of sulphur experimental and calculated on the offered equations in slag and metal are presented. Taking into account a small amount of experimental data, the big intervals of change of parametres and low accuracy of industrial gaugings it is possible to consider coincidence of settlement and experimental values satisfactory.

(S) p, % QfJ 0,11
0,09
0,07

Fig. 72 Comparison of experimental and settlement values of the contents of sulphur in
Slag () and in metal ()
0,07 0,09 0,11 0,13 {) 3, %
0,08 0,06 OHM 0,02