MODELLING AND EXPERIMENTAL STUDIES OF DIFFUSIVITY OF SULFUR AND ITS RELEVANCE IN OBSERVING SURFACE OSCILLATIONS AT THE SLAG METAL INTERFACE THROUGH
X-RAY IMAGING
Luckman Muhmooda, Nurni N Viswanathanb, Seshadri Seetharamanc
a K J Somaiya College of Engineering, Vidyavihar, Mumbai, India
b Indian Institute of Technology Bombay, India
c Royal Institute of Technology Stockholm, Sweden
ABSTRACT
A generic model was conceived for predicting the diffusion coefficient of species in slag. The diffusion coefficient of sulfur in CaO-Al2O3-SiO2 slag with low silica was measured using a combinational technique of the generic model and experiments. The uniqueness of the experiments was in the method of collecting samples. Another milestone was that the diffusion coefficient of sulfur in the slag was obtained through the sulfur levels in the metal (silver). Later the order of magnitude of the diffusion coefficient of sulfur in slag was used to estimate the time required for sulfur to reach the slag- metal interface of an iron drop immersed in CaO-Al2O3-FeO-SiO2 slag. This estimated time for arrival of sulfur at the interface was comparable to the actual observation. The current paper describes the challenges in measuring the diffusion coefficient of sulfur. It also describes the time estimates calculated based on the X-ray image for sulfur to reach the slag-metal interface.
INTRODUCTION
System dynamics pertaining to any process is difficult to assimilate due to its complexity.
The perfect understanding of any process is usually carried out by dissecting it into sub processes and apart from understanding these individual processes, the knowledge of the linkage between them also becomes critical. On a lab scale, significant studies have been made regarding processes/ phenomena involving the slag-metal interface like sulfur, phosphorous or oxygen transport 1-4. In most of these studies, there are extensive interactions at the slag-metal interface owing to which there is significant shape change of the drop(s). In the current study we look into the sulfur transport from the gaseous media to the metal via a slag phase. This involves dissociation of the sulfur dioxide gas used to sulfur gas, electrochemical reaction at the gas-slag interface by virtue of which it enters the slag as sulfur ions, its transport through the slag media , electrochemical reaction at the slag-metal interface
Advances in Molten Slags, Fluxes, and Salts: Proceedings of The 10th International Conference on Molten Slags, Fluxes and Salts (MOLTEN16) Edited by: Ramana G. Reddy, Pinakin Chaubal, P. Chris Pistorius, and Uday Pal TMS (The Minerals, Metals & Materials Society), 2016
where the sulfur ions are converted to sulfur atoms and finally transport of sulfur atoms in the metal media.
The aim of the study is to find the effect of sulfur on interfacial tension at the slag-metal interface. In the sub processes explained earlier, the rate determining step for sulfur to reach the slag-metal interface is the transport of sulfur through the slag and metal phases. In order to capture the dynamic effect of sulfur on the profile of the slag metal interface, the time required for the sulfur to reach the interface is of extreme importance.
As sulfur is in its ionic state in slag, its transport through slag would be a result of making and breaking of bonds and hence it should be slower in comparison to its transport in the metallic phase (where it prevails as an atom). This is reflected in the values obtained by various researchers for the diffusion of species in the metal as well as slag phases. As a rule of thumb, the transport of species in the ionic state is two orders of magnitude slower than the same species in its atomic configuration.
The paper describe in brief the experimentation required for calculating the diffusion coefficient of sulfur in slag as well as its help in x ray recording events occurring at the slag – metal interface due to the presence of sulfur.
SULFUR DIFFUSION COEFFICIENT IN SLAG – METHODOLOGY
Traditional experiments to determine the diffusivity of species in slag involves rapid quenching after sufficient equilibration time between the specie “rich” slag and the slag undergoing analysis 5,6. The concentration profile of the specie as a function of time and distance is indicative of the diffusivity. This method may not be accurate enough as rapid quenching could induce convective currents hence disturbing the actual readings. In this regard it was decided to go for insitu measurements of species in slag. The focus was given on sulfur diffusivity as this value would help in determining the time taken for sulfur to travel through a fixed slag height, enabling X-ray videography of the process.
The diffusivity of sulfur was determined using a unique combination of modelling and experiments. The prime assumption was that the concentration of sulfur in the metal phase is uniform. This depends on the coefficient of diffusivity in the metal with respect to slag. Two conditions of the model were considered; the first with the assumption that sulfur concentration was uniform in the metal and the second in which the diffusivity in both the metal and slag phase were considered. Comparison between these two conditions gives the error of the estimation of diffusivity using this approach.
In the model, real time parameters like partition ratio, sulphide capacity, density were used 7-
9. The only unknown was the diffusivity of sulfur in slag. This was assumed to have the order of magnitude of 10-6cm3/s which is typical for slags. The concentration profile of sulfur as a function of time was generated using the model and was later compared with actual sampling concentrations taken through experiments. This value was later refined so that the concentration points experimentally determined were closely located on the curve obtained
by the model. Further details on the model are available in previously published works by the authors 10.
EXPERIMENTAL HURDLES
The experimental evaluation of the sulfur diffusivity posed many challenges. The prime challenge was the crucible design. Since the methodology was to collect insitu samples of metal without disturbing the slag layer, the design and fabrication of the crucible was complicated. In the final design, it consisted of a central tube with holes at the bottom and this tube was surrounded by another crucible. Figure 1 shows the crucible design. The metal and the slag were loaded in the annular region at a height well-above the height of the holes in the central central tube. Once the metal was melted, it would fill the central chamber through which sampling was facilitated. Both the annular region as well as the central chamber were purged with argon. Armco iron was chosen as the crucible material to hold both the metal phase and the slag.
Figure 1: Schematic of the crucible design used for diffusivity measurements.
Once the material for the crucible was finalized, the next critical component to be decided was the metal. The metal should have low solubility for iron and vice versa. Since the maximum operational temperature was limited to about 50 degrees lower than the melting point of iron, a low melting metal was required. Silver was chosen as the metal. The solubility of Ag in Fe could be neglected.
Both sulfur as well as oxygen have a good tendency to dissolve in iron; hence the partial pressures of these needs to be controlled stringently. Using a gaseous combination proved impossible to meet these partial pressure requirements. After a thorough study, it was decided to use CaS as the source for sulfur. Since the density of CaS is lower than the metal and the slag, it would float on the slag surface providing a constant source for sulfur. At the temperature of interest CaS is solid.
The experimental set up showing the furnace, crucible along with other arrangements is shown in Figure 2. During the heating stage of the metal the sulfur source was kept away from the slag surface. Once the desired temperature is reached, the sulfur source was lowered down to have contact with the slag surface. This was taken as the zero time for the sulfur diffusion process. Samples are then taken at random time frames; they were then sent for sulfur analysis to NILAB AB and the concentration profiles are plotted. A detailed description of the set up as well as experimental procedure is given elsewhere 11.
Figure 2: Layout of the furnace, crucible and other related connections 11
RESULTS
The composition of the slag used is 51.5% CaO- 9.6% SiO2- 38.9% Al2O3. As mentioned in earlier section, the concentration of sulfur was measured in silver samples taken at various time intervals. The concentration profile using the model was also obtained 11. Sulfur concentration variation with time is shown in Table 1. The slag density and partition ratio at the slag metal interface was measured separately.9,10,11 The only unknown in the model was the diffusion coefficient of sulfur in slag. This term in the model was later fine-tuned to obtain a better agreement with the experimental results. Figures 3 show the concentration of sulfur in the metal as per the model curve and the experimental points at temperature 1723 K.
The order of magnitude was similar to that obtained by earlier researchers 5.
Table I. Sulfur concentration in silver metal during the diffusion experiments repeated at 1723 K. Sampling time is from the time CaS was introduced into the system.
Sampling time (seconds) Concentration of sulfur in silver metal (ppm)
First trial Second trial
18600 9.7 -
20100 16 15.6
21600 20.2 19.9
Figure 3: Concentration profile of sulfur in metal as a function of time; experimental (dots) and models values (curve) 11.
X-RAY CAPTURE AND CALCULATIONS
An independent experiment to study the effect of sulfur at the slag-metal interface was conducted. This involves the sulfur to be introduced in to the furnace in its gaseous form later dissolving in slag and slowly diffusing through the slag till it reaches the slag –metal interface. The slag-gas interface was a concave surface while the slag-metal interface was convex in nature. This leads to varying distances for the sulfur to travel till it reaches the slag- metal interface from the gas media. Since sulfur is a surfactant for the metal phase, as soon as it reaches the slag-metal interface, the interfacial tension decreases locally. This leads to the interface oscillations which could be observed using an X-ray set up in its video mode. Since there is a limitation in the minutes of video recording, it is required to know the approximate time at which the sulfur would reach the interface. From the X-ray image, it is possible to measure the thickness of the slag layer and hence, if one knows the diffusion coefficient, it is possible to estimate the time taken to reach the slag-metal interface. Figure 4(a) and (b) show the schematic of the process described as well as an X-ray image of the metal drop surrounded by slag 12.
In order to avoid change in slag composition during melting, the slag was saturated with Al2O3. The composition of the slag was taken as 22.9% CaO- 51.4% Al2O3- 18% SiO2- 5%
FeO.
Figure 4: (a) Schematic of sulfur movement from slag phase to metal phase. X-ray image of the sessile drop of iron surrounded by CaO-Al2O3- FeO-SiO2 slag at 1823K. The drop height was measured to be 5.16 mm and width was 9.03 mm respectively.
The slag layer height above the slag-metal interface was calculated to be approximately 2.23mm. Earlier, the diffusion coefficient of sulfur in CaO-Al2O3-SiO2 slag at 1723 K was evaluated to be 4.14 X 10-6 cm3/s. Assuming a similar order of magnitude of sulfur diffusion coefficient in the slag, the time taken for sulfur to travel this slag thickness and reach the slag-metal interface was estimated as 453 seconds. Figure 5 shows that the change in contact angle which is indicative of drop oscillations start roughly at 400 seconds. This is in line with the value predicted by earlier calculations.
Figure 5: Contact angle variation with respect to time from sulfur introduction into the system
12.
CONCLUSION
Diffusion coefficient of sulfur in CaO-Al2O3- SiO2 slag was evaluated using a combination of modelling and experimentation. The value of the diffusivity of sulfur in slag was the only unknown in the model. The model was later refined by a comparison between the concentration profile of sulfur and time both experimentally and as per the model. The order of magnitude of the value obtained was similar to that reported by others. This value was later used to record the surface velocity of sulfur at the slag-metal interface via X-ray videography observed by interfacial oscillations due to sulfur concentration variation at the slag-metal interface.
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