Dynamic Model of Basic Oxygen Steelmaking Process Based on Multi-zone Reaction Kinetics: Model Derivation and Validation

Abstract

A multi-zone kinetic model coupled with a dynamic slag generation model was developed for the simulation of hot metal and slag composition during the basic oxygen furnace (BOF) operation. The three reaction zones (i) jet impact zone, (ii) slag–bulk metal zone, (iii) slag–metal–gas emulsion zone were considered for the calculation of overall refining kinetics. In the rate equations, the transient rate parameters were mathematically described as a function of process variables. A micro and macroscopic rate calculation methodology (micro-kinetics and macro-kinetics) were developed to estimate the total refining contributed by the recirculating metal droplets through the slag–metal emulsion zone. The micro-kinetics involves developing the rate equation for individual droplets in the emulsion. The mathematical models for the size distribution of initial droplets, kinetics of simultaneous refining of elements, the residence time in the emulsion, and dynamic interfacial area change were established in the micro-kinetic model. In the macro-kinetics calculation, a droplet generation model was employed and the total amount of refining by emulsion was calculated by summing the refining from the entire population of returning droplets. A dynamic Fe_tO generation model based on oxygen mass balance was developed and coupled with the multi-zone kinetic model. The effect of post-combustion on the evolution of slag and metal composition was investigated. The model was applied to a 200-ton top blowing converter and the simulated value of metal and slag was found to be in good agreement with the measured data. The post-combustion ratio was found to be an important factor in controlling Fe_tO content in the slag and the kinetics of Mn and P in a BOF process.

Appendix

A.1 Mass Transfer Coefficient in Hot Metal and Slag

The mass transfer coefficient in the hot metal has been calculated by the following relationship,[23]

$$ \log k_{\text{m}} = 1.98 + 0.5\log \left( {\frac{{\varepsilon H^{2} }}{100L}} \right) - \frac{125,000}{2.3RT}, $$

(40)

where k_m is the mass transfer coefficient in metal phase (cm/s); ε is the stirring energy (W/t); H and L are the bath depth (cm) and diameter of the furnace, respectively; and T is the temperature in the impact zone (K). The total stirring energy was calculated by using the combined effect of the top and bottom gas injection in the BOF.[67]

The slag phase mass transfer coefficient was given by[7]:

$$ k_{s} = a\exp \left( { - \frac{37,000}{RT}} \right) \cdot \varepsilon^{\text{b}} , $$

(41)

where k_s is the mass transfer coefficient in slag phase (cm/s); R gas constant (J mol⁻¹ K⁻¹); and a and b are the empirical parameters, assumed to be 1.7 and 0.25, respectively.[7]

A.2 Calculation of Cavity Height and Radius

The height and radius of the individual cavity formed by the top jet can be expressed as follows:

$$ \begin{array}{*{20}c} {h = 4.469 \dot{M}_{h}^{0.66} L_{h} ,} \\ \end{array} $$

(42)

$$ \begin{array}{*{20}c} {r_{\text{cav}} = 0.5 \times 2.813L_{\text{h}} \dot{M}_{\text{d}}^{0.282} } \\ \end{array} , $$

(43)

where L_h is the lance height (m) and the dimensionless momentum flow rate and is defined as

$$ \begin{array}{*{20}c} {\dot{M}_{\text{h}} = \frac{{\dot{m}_{\text{n}} \cos \left( {\text{nangle}} \right)}}{{\rho_{\text{m}} gL_{\text{h}}^{3} }}} \\ \end{array} , $$

(44)

$$ \begin{array}{*{20}c} {\dot{M}_{\text{d}} = \frac{{\dot{m}_{t} (1 + \sin ({\text{nangle}}))}}{{g\rho_{\text{m}} L_{\text{h}}^{3} }}} \\ \end{array} , $$

(45)

where $\dot{m}_{\text{n}}$ is the momentum flow rate of the each nozzle, which is related to the total momentum flow rate, $\dot{m}_{t}$ by the following equations:

$$ \begin{array}{*{20}c} {\dot{m}_{\text{n}} = \frac{{\dot{m}_{t} }}{{n_{\text{n}} }}} \\ \end{array} . $$

(46)

Total momentum flow rate:

$$ \begin{array}{*{20}c} {\dot{m}_{t} = 0.7854 \times 10^{5} \times n_{\text{n}} \times d_{\text{th}}^{2} \times P_{\text{a}} \left( {\frac{{1.27P_{0} }}{{P_{\text{a}} }} - 1} \right)} \\ \end{array} , $$

(47)

where n_n is the number of nozzles in the lance tip; nangle is the nozzle angle (rad); d_th is the throat diameter of the lance (m); P₀ is the top supply pressure (Pa); and P_a is the ambient pressure (Pa).

A.3 Calculation of Equilibrium Distribution Ratios

Silicon distribution ratio[42]

$$ L_{\text{Si}} = \left\{ {\begin{array}{ll} {1 - \frac{{({\text{pct}}\;{\text{FeO}})}}{40} }, & {({\text{pct}}\;{\text{FeO}}) \le 40}, \\ {0 }, & {({\text{pct}}\;{\text{FeO}}) > 40}. \\ \end{array} } \right. $$

(48)

Manganese distribution ratio[43]:

$$ \log k^{\prime}_{\text{Mn}} = - 0.0180[\left( {{\text{wt}}\;{\text{pct}}\;{\text{CaO}}} \right) + 0.23\left( {{\text{wt}}\;{\text{pct}}\;{\text{MgO}}} \right) + 0.28\left( {{\text{wt}}\;{\text{pct}}\;{\text{Fe}}_{\text{t}} {\text{O}}} \right) - 0.98\left( {{\text{wt}}\;{\text{pct}}\;{\text{SiO}}_{2} } \right) - 0.08\left( {{\text{wt}}\;{\text{pct}}\;{\text{P}}_{2} {\text{O}}_{5} } \right)] + \frac{7300}{T} - 2.697, $$

(49)

where the apparent equilibrium constant k ^’_Mn is defined as follows

$$ k^{\prime}_{\text{Mn}} = \frac{{({\text{wt}}\;{\text{pct}}\;{\text{MnO}})}}{{({\text{wt}}\;{\text{pct}}\;T \cdot {\text{Fe}}) \times \left[ {{\text{wt}}\;{\text{pct}}\;{\text{Mn}}} \right]}} = \frac{{L_{\text{Mn}} \times \frac{{M_{\text{Mn}} }}{{M_{\text{MnO}} }}}}{{({\text{wt}}\;{\text{pct}}\;T \cdot {\text{Fe}})}}. $$

(50)

T. Fe denotes total Fe and M_Mn and M_MnO are the molar mass (g/mol) of Mn and MnO, respectively.

Phosphorus distribution ratio

The phosphorus equilibrium distribution ratio at the slag–metal interface can be written as[68] follows:

$$ L_{p} = \frac{{K_{p} f_{p} h_{\text{o}}^{2.5} }}{{C\gamma_{{{\text{PO}}_{2.5} }} }}, $$

(51)

where K_p is the equilibrium constant; f _p is the activity coefficient of P; h_o is the Henrian activity of oxygen; C is the conversion factor which related (pct P) with the mole fraction of PO_2.5; and γ_P2O5 is the activity coefficient of PO_2.5.

The equilibrium constant for the phosphorus oxidation reaction can be expressed as[63]

$$ \log \left( {K_{p} } \right) = \frac{17,060}{T} - 8.51. $$

(52)

Here ho is the Henrian activity of oxygen, determined by assuming FeO-O equilibrium.

$$ h_{o} = \frac{{\gamma_{FeO} }}{{X_{FeO} K_{F} }}. $$

(53)

K_F is the equilibrium constant for reaction [Fe] + [O] = (FeO), ΔG^o = -128,090+57.99 T.[63] γ_Feo and γ_P2O5 are the activity coefficients of FeO and PO_2.5, determined by Regular solution model proposed by Ban-Ya.[40] Henrian activity coefficient f _p was determined by employing the first-order interaction parameter.$\log \left( {f_{p} } \right) = e_{p}^{\text{p}} \left[ {{\text{pct}}\;{\text{P}}} \right] + e_{p}^{\text{c}} \left[ {{\text{pct}}\;{\text{C}}} \right],$where e ^p _p  = 0.063 and e ^c _p  = 0.19.[7]