Model of Inclusion Evolution During Calcium Treatment in the Ladle Furnace

Abstract

Calcium treatment of steel is typically employed to modify alumina inclusions to liquid calcium aluminates. However, injected calcium also reacts with the dissolved sulfur to form calcium sulfide. The current work aims to develop a kinetic model for the evolution of oxide and sulfide inclusions in Al-killed alloyed steel during Ca treatment in the ladle refining process. The model considers dissolution of the calcium from the calcium bubbles into the steel and reduction of calcium oxide in the slag to dissolved calcium. A steel–inclusion kinetic model is used for mass transfer to the inclusion interface and diffusion within the calcium aluminate phases formed on the inclusion. The inclusion–steel kinetic model is then coupled with a previously developed steel–slag kinetic model. The coupled inclusion–steel–slag kinetic model is applied to the chemical composition changes in molten steel, slag, and evolution of inclusions in the ladle. The result of calculations is found to agree well with an industrial heat for species in the steel as well as inclusions during Ca treatment.

Appendix: Volumetric Size Distributions of Inclusions

An automated inclusion analysis SEM technique, ASPEX, was used to obtain planar distribution of inclusion on the polished section. Particle sizes are divided into number of size groups after they are measured on plane sections. The number and size of particles in the plane section is determined, but to obtain the size distribution on a volume basis, the analysis of the obtained data is required. It is assumed that the particles are spherical so that equivalent sphere diameters or equivalent circle diameters can be considered. ASPEX measures equivalent circle diameters of inclusions which can be presented in a particle size distribution histogram.

The number of circles per unit area N_A as a result of N_V spheres per unit volume of diameter D is

$$ N_{\text{A}} = D \cdot N_{\text{V}} . $$

(AI)

So, larger spheres are more likely to be intersected by the plane of the polished section. Moreover, a sphere may be sectioned anywhere in its diameter. But, only largest spheres can lead to largest circle diameter at the sectioning surface. Therefore, the probability of spotting circles in this largest size group could be calculated and the residual probability distributed to the smaller size groups of circles. Then, circles from the next smallest size group of spheres are calculated and so on. Using this approach, the size distribution of spheres in the volume could be derived from the measurement of the size distributions of circles on the sectioning plane. The details of the method can be found in Reference 42. Schwartz[36] and Saltykov[43] developed a matrix of coefficients (α(i, j)) for the number of circles in size group (i) arising from spheres in size group (j) using probability distributions for sectioning randomly distributed spheres of sizes in k equal size groups. The number of spheres per unit volume in size group j from the numbers of circles in size groups i is

$$ N_{\text{V}} (j) = \frac{1}{\Delta }\left\{ {\alpha (j,\;j)N_{\text{A}} (j) + \alpha (j,\;j + 1)N_{\text{A}} (j + 1) + \cdots + \,\, \alpha (j,\;k)N_{\text{A}} (k)} \right\}, $$

(AII)

where j = 1 to k, Δ is the size interval used in the histograms and k is the number of size groups.