8. Advanced Viscosity Modelling Approach
8.4 Modelling Approach
Several slag samples were extensively investigated by
o viscosity measurements under reducing and oxidizing conditions, o a variation in shear rates,
o DTA-measurements to estimate the onset of crystallization and
o XRD-analysis of quenched slag samples to verify the amount and specie of minerals.
The flow behavior was explained on these results. Crystallization was identified as origin of changes in flow behavior for mostly all slags. Software tools are available to predict mineral content in slags as function of composition and temperature. The kinetic nature of crystallization complicates the adequate calculation of mineral formation. Either the begin of crystallization nor the consumption of slag components could be satisfyingly depicted. For that reason, a slag viscosity modelling approach is provided to
o support the selection of the best model, o calculate the SVF,
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8. Advanced Viscosity Modelling Approach 115 The developed a-factors can also be discussed from the point of slags, Table 19. Only slag S42 is completely covered by positive a-factors. Slags S36, S39 and S41 are violating the a-factor rule by one viscosity model. Sample S31 is mostly fitted by negative a-factors. For seven models, a negative a-factor must be applied. There is no clear evidence of B/A-ratio or formed mineral phases to explain the scattering on calculated negative a-factors. Elevated B/A-ratios seem to improve the a-factor fitting, S36 to S42. In contrast, the B/A-ratio of slag S40 is 1.857, but the fitted a-factors fall below zero for six viscosity models.
Table 19: Number of a-factor violations in view of slags.
The obtained a-factors show following properties which make it difficult to use a multi- parameter function, e.g. non-linear 3D-surface-fit:
o The slope of the fitted a-factors of several viscosity models can vary within a single slag (single B/A-ratio), Figure 83 a).
o The a-factor slope of a single viscosity model can vary for several slags (several B/A-ratios), Figure 83 b).
Violations
Rule a≥ Slag B/A on mass Model names
0 S42 2.497 -
1 S36 1.069 Bomkamp
1 S39 1.705 Lakatos
1 S41 2.126 Lakatos
2 S32 0.932 Streeter, ANNliq
4 S13 0.337 Bomkamp, Lakatos, Riboud, Duchesne
5 S35 1.046 S2, Bomkamp, Streeter, Duchesne,
ANNliq
6 S14 0.337 Watt-Fereday, Bomkamp, Shaw,
Streeter, Duchesne, ANNliq
6 S40 1.857 S2, Bomkamp, Lakatos, Urbain, BBHLW, Duchesne
7 S31 0.903 Bomkamp, Urbain, Riboud, Streeter, Kalmanovitch-Frank, Duchesne, ANNliq
8. Advanced Viscosity Modelling Approach 116
Figure 83: a-factors with different slopes of a) single slag (S42) and b) different slags (Bomkamp model).
8.4.2 Summary of Last Chapter
o The SVF is obtained from phase analysis taken from quenching experiments and XRD. To overcome temperature ranges without XRD information, the SVF is linear interpolated in steps of 10 K for a given slag in the range 1000-17000 °C. Linear interpolation is done with a look-up-table. The order is temperature, followed by B/A-ratio.
o Liquid slag composition is linear interpolated from same XRD datasets. The slag composition of extensively investigated slags was reduced by the components of formed minerals. The loss or the enrichment of slag components is indicated by factors below or above 1. The order is temperature, followed by B/A-ratio. o The a-factor is calculated on the results of interpolated SVF. Again, a look-up-
table is applied in the order shear rate, B/A-ratio and SVF.