A Dynamic Flux Dissolution Model for Oxygen Steelmaking

Abstract

A modified model for prediction of flux dissolution in oxygen steelmaking process is presented in this study. The aim of this paper is to introduce a procedure for simulating the amount of dissolved lime with respect to the saturation concentration of CaO by coupling the existing thermodynamic and kinetic models simultaneously. The procedure is developed to calculate the saturation concentrations/solubility of CaO in slag using thermodynamic models namely FactSage™, Cell Model, and Thermo-Calc™. Total amount of dissolved lime is evaluated by integrating solubility values in the rate equation of lime dissolution over time taking into account the effects of physical properties and temperature of slag and particle size of flux additions and validated against industrial data available in literature. Comparison between measured and calculated undissolved lime shows a good agreement between them using any thermodynamic models even though there are some differences in the predictions of saturation concentration of CaO in slag. It has been shown that two distinct control mechanisms for lime dissolution in BOF slags exist and consideration of the free lime-controlled mechanism is essential for accurate prediction of dissolution rate of lime in slag.

Appendix A: Calculation Procedure of Saturation Concentration of CaO Using Cell Model[32]

Cell Fraction Determination

In this step, for a given slag composition, the combination of cells (R ^k _ii and R ^k _ij ) is determined such that the partition coefficient is maximized and hence yields the minimum value of free energy while satisfying the mass balance equations.

Calculation of Free Energy

The free energy of liquid slag may be approximated from the partition function as

$$ \begin{aligned} G^{\text{M}} = - RT\ln \varOmega \\ = - RT\left( { - \frac{{E_{\text{tot}} }}{RT} + \ln g} \right) \\ = (E_{\text{tot}} + E_{\text{int}} ) - RT(\ln (P) + \ln (U) + \ln (U^{*} )) \\ \end{aligned}, $$

(A1)

where G ^M is the free energy of mixing, R is the ideal gas constant, T is the temperature, E _form is the energy necessary for the formation of asymmetric cells from symmetric ones, E _int is the parameter introduced to describe the energy of interaction between different cells, P the total number of possible permutations of anions and cations, U is the total number of randomly distinguishable permutations, and U* is the maximum number of randomly distinguishable permutations. The partition coefficient Ω, in the above equation is a measure of the number of states accessible to the system at a given temperature was defined as

$$ \varOmega = \sum\limits_{i} {g_{i} } e^{{ - e_{i} /k_{\text{B}} T}}, $$

(A2)

where g _i is the degeneracy factor and refers to the number of states having energy e _i . The above equation is simplified by considering the ‘most probable’ energetic arrangement that maximizes the partition function

$$ \varOmega = g(E)e^{ - (E/RT)}. $$

(A3)

Component Activity Determination

Component activities referred to their pure liquid standard states are determined by computing the partial molar free energy of mixing for each slag component as

$$ RT\ln (a_{i} ) = G^{\text{M}} + \sum\limits_{j = 2}^{m} {\left( {\delta_{ij} - X_{j} } \right)} \left( {\frac{{\partial G^{\text{M}} }}{{\partial X_{j} }}} \right), $$

(A4)

where δij is Kronecker’s symbol (δij = 1 for i = j and δij = 0 for i ≠ j).

Calculation of Saturation Concentration

The saturation of CaO is calculated by iteratively calculating the activities of a system at different compositions until one of the stoichiometric components had precipitated as a solid phase. At initial upper and lower saturation points for a component (WT_high = 100 wt pct; WT_low = 0 wt pct), the cell fractions (R ^k _ij ), free energy (G ^M), and slag activities were recursively calculated until the upper and lower bounds have converged to within 0.01 wt pct. CaO saturation was assumed at a component activity (solid reference) of 0.9995 in order to ensure algorithm convergence at the true saturation point.