# Dynamic Modeling and Simulation of Basic Oxygen Furnace (BOF) Operation

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Mass and Energy Balances

_{2}forming CO

_{2}(Equation (6)).

_{3}O

_{4}) that is reduced to FeO by carbon in the metal bath (Equation (7)).

_{2}, N

_{2}/Ar and unreacted oxygen O

_{2}form the off-gas stream. Owing to the high temperatures, the residence time for the gases is assumed to be negligible in this work. A mass balance for the metal bath gives:

- The gas hold up in the slag and metal bath is negligible
- The gas exits the furnace at the slag temperature
- The temperature of the slag-metal-emulsion and metal bath is uniform
- A fraction ${\alpha}_{l}^{p}$ of all the heat generated is assumed to be lost to the environment and the remainder is assumed to be absorbed by the slag.

#### 2.2. The Impact Zone

#### 2.3. Scrap Melting

#### 2.4. Iron Ore Dissolution

#### 2.5. Flux Dissolution

#### 2.6. Decarburization in the Emulsion Zone

- All droplets decarburize immediately after they are ejected from the impact zone
- The carbon content of the metal droplets in the emulsion zone is approximated as the average carbon content of the individual metal droplets
- Except for carbon, the mass of other elements in the metal droplets stays constant whilst the droplet travels through the emulsion zone

#### 2.7. Implementation

- Equations of the form:$$y\left(a\right)=\frac{1}{a}$$$$y\left(a\right)=\frac{1}{a+\u03f5}$$
- Piecewise functions of the form:$$y\left(c\right)=\left\{\begin{array}{cc}{y}_{1}\left(c\right)\hfill & a>b\hfill \\ {y}_{2}\left(c\right)\hfill & a\le b\hfill \end{array}\right.$$$$\tilde{y}\left(c\right)={y}_{1}(0.5tanh\left(\gamma (a-b)\right)+0.5)+{y}_{2}(0.5tanh\left(\gamma (b-a)\right)+0.5)$$
- Flux additions: Flux and iron ore can be added at anytime during a blow, and each individual addition is modeled as shown in Section 2.5. To model the indiviudal flux additons a new variable ${t}_{ij}$, where i is the flux type (lime, dolomite, iron ore) and j is the addition number (first, second, third), is defined for the flux addition time. Given the radius ${r}_{ij}$ of the flux added at time ${t}_{ij}$, Equation (41) for lime dissolution rate can be reformulated as:$$\frac{d{r}_{ij}}{dt}=\left\{\begin{array}{cc}0\hfill & t<{t}_{ij}\hfill \\ {k}_{L}\frac{{\rho}_{s}}{100{\rho}_{L}}(\%Ca{O}_{s}-\%Ca{O}_{sat})\hfill & t\ge {t}_{ij}\hfill \end{array}\right.$$

## 3. Results and Discussion

#### 3.1. System Parameters and Input Data

#### 3.2. Simulation Results for Cicutti’s Operations

- Period I: As the silicon content of the metal bath decreases, the decarburization rate increases
- Period II: Decarburization rate stays approximately constant
- Period III: Decarburization rate is controlled by mass transfer of carbon in the metal bath

#### 3.3. Simulation Results for Plant A Operations

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Schematic representation of the melting of scrap. (

**a**) Schematic representation of a plate. (

**b**) Schematic representation of temperature gradient between hot metal and a cold metal plate.

**Figure 8.**(

**a**) Total decarburization rate and decarburization rate at the emulsion zone and (

**b**) composition of the off-gas stream exiting the BOF.

**Figure 9.**(

**a**) Control profile for Cicutti et al. [13]’s data and (

**b**) scaled control profiles for a heat from Plant A.

**Figure 10.**Evolution of slag composition for the Cicutti data [13] and model prediction: (

**a**) FeO, (

**b**) SiO

_{2}, (

**c**) CaO, (

**d**) MgO.

**Figure 12.**Average process and predicted values for the end-point slag composition in weight percentage.

**Figure 13.**Average and standard deviation of the model predictions and process data for the end-point (

**a**) carbon content of the liquid metal and (

**b**) temperature of the liquid metal.

**Figure 14.**Evolution of: (

**a**) Carbon content of liquid metal and final carbon content C

_{C,f}of the metal droplets, (

**b**) silicon content of liquid metal, (

**c**) slag and metal bath temperature and (

**d**) slag composition. The values have been scaled for proprietary reasons.

**Table 1.**The values of model parameters for simulation and optimization. The heat transfer coefficients h are given in Wm${}^{-2}$K${}^{-1}$, and ${\alpha}_{Fe}^{p}$ is given in kgm${}^{-2}$Pa${}^{-1}$s${}^{-1}$. All the other parameters are dimensionless.

Parameters | Cicutti | Plant A |
---|---|---|

${\alpha}_{l}^{p}$ | 0.2 | 0.07 |

${\alpha}_{{O}_{2}}^{p}$ | 1 | 1.16 |

${\alpha}_{Si,C}^{p}$ | 10 | 2 |

${\alpha}_{C{O}_{2}}^{p}$ | 1 | 1 |

${\alpha}_{{C}_{c}}^{p}$ | 3 | 3.07 |

${\alpha}_{DG}^{p}$ | 1 | 1 |

${\alpha}_{Fe}^{p}$ | 7 × 10${}^{-6}$ | 2.0 × 10${}^{-5}$ |

${\alpha}_{Si}^{p}$ | 7 | 7 |

${\alpha}_{L}^{p}$ | 30 | 30 |

${\alpha}_{D}^{p}$ | 20 | 20 |

${\alpha}_{\mu}^{p}$ | 0.5 | 0.5 |

${h}_{L}$, ${h}_{D}$ | 1000 | 1000 |

${h}_{ore}$ | 2500 | 2500 |

${h}_{s-b}$ | 80,000 | 80,000 |

**Table 2.**Mass and composition of hot metal and scrap types added to the BOF, and average scrap thickness [22].

Input | Hot Metal | Heavy Scrap | Light Scrap | Pig Iron | External Scrap |
---|---|---|---|---|---|

Mass (kg) | 170,000 | 3570 | 10,000 | 12,140 | 4284 |

Thickness (mm) | - | 100 | 25 | 200 | 500 |

C (%) | 4 | 0.08 | 0.08 | 4.5 | 0.05 |

Si (%) | 0.33 | 0.05 | 0.05 | 0.5 | 0.001 |

Mn (%) | 0.52 | 0.3 | 0.3 | 0.5 | 0.2 |

P (%) | 0.066 | - | - | - | - |

S (%) | 0.015 | - | - | - | - |

**Table 3.**Simulation time for Cicutti et al. [13]’s data required in different studies.

Model | Computer | Software | Solution Time |
---|---|---|---|

Dogan et al. [6] | Pentium (R) 4 CPU 3.00 GHz and 3GB of RAM | Scilab | 240 min |

Sarkar et al. [8] | Not given | Matlab | 27 min |

Rout et al. [9] | Intel(R) Core(TM) i5-4570 CPU @3.20 GHz and 8 GB RAM | Matlab | 20 min |

Present study | Intel(R) Core(TM) i7-7700 CPU @3.16GHz and 16.0 GB RAM | Python 3.7 | 0.036 min |

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**MDPI and ACS Style**

Dering, D.; Swartz, C.; Dogan, N.
Dynamic Modeling and Simulation of Basic Oxygen Furnace (BOF) Operation. *Processes* **2020**, *8*, 483.
https://doi.org/10.3390/pr8040483

**AMA Style**

Dering D, Swartz C, Dogan N.
Dynamic Modeling and Simulation of Basic Oxygen Furnace (BOF) Operation. *Processes*. 2020; 8(4):483.
https://doi.org/10.3390/pr8040483

**Chicago/Turabian Style**

Dering, Daniela, Christopher Swartz, and Neslihan Dogan.
2020. "Dynamic Modeling and Simulation of Basic Oxygen Furnace (BOF) Operation" *Processes* 8, no. 4: 483.
https://doi.org/10.3390/pr8040483