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Although there have been a numerous number of studies on mathematical model of hot metal desulfurization by deep injection of calcium carbide, the research field as a whole is not well integrated. This paper presents a model that takes into account the kinetics, thermodynamics, and transport processes to predict the sulfur levels in the hot metal throughout a blow. The model could be utilized to assess the influence of the treatment temperature, rate of injection, gas flow rate, and initial concentration of sulfur on the desulfurization kinetics. In the second part of this paper an analysis of the industrial data for injection of calcium carbide using this model is described. From a mathematical model that describes the characteristics of a system, it is possible to predict the behavior of the variables involved in the process, resulting in savings of time and money. Discretization is realized through the finite difference method combined with interpolation in the border domain by Taylor series.

Desulphurization of iron from the blast furnace is a well-established technology. There have been many studies on the desulfurization of hot metal and steel by injection of powdered agents in the literature [

As customers increase requirements for steel quality, plants need practices that will help them remove sulfur faster and at lower cost. One important factor in the cost of a particular process is the reagent consumption to reach the aimed at sulfur content. Among the different reagents used, calcium-carbide-based reagents and magnesium-based reagents are currently the most popular. Although many researchers have studied CaC_{2} desulfurization [

Powder, in dense phase, is pneumatically transported and injected into the liquid metal through a submerged lance; a jet is created at the outlet of the lance that penetrates into the melt until its momentum is dissipated. In such systems gas bubbles rising through the liquid enhance mixing, promote chemical reactions, and minimize temperature and chemical inhomogeneities in the melt. Also, the stirring caused in the injection process improves the top-slag desulfurization. The bubbles forming in the liquid rise upward due to buoyancy, and the kinetic energy at the nozzle exits. A number of complex phenomena take place during the injection process which require an investigation of the kinetics, thermodynamics, transport processes, and overall process dynamics to predict the dynamic removal of sulfur from hot metal [

The mechanism of desulphurization with calcium carbide was first studied by Talballa et al. [

In this paper, a mathematical model is developed to obtain design guidelines and to predict the influence of the main parameters on the desulphurization efficiency of the process that will be of great help for plant engineers to improve and optimize the desulphurization with calcium carbide.

One approach to predicting the mechanism of desulfurization is to use a dimensional model, which could be dynamically updated. The model takes into account the kinetics, thermodynamics, and transport processes to predict the sulfur levels in the hot metal. A sensitivity analysis is performed to aid in the optimal selection of operating parameters. The model results allow the selection of operating conditions to minimize the processing time for desulphurization.

As our first step toward developing an appropriate mathematical model for such injection phenomena, it was decided to consider the case of axisymmetric gas injection into cylindrical ladle. Then, in cylindrical coordinates, the governing differential equation can be written as follows:

The reaction is described as a first-order, diffusion-controlled reaction.

There is no variation of flow properties in the

The bubble rising is described by the radial velocity

Parameters

In order to evaluate the effect of the reactor shape, it was decided to consider the case of axisymmetric gas injection into spherical ladle. Then, in spherical coordinates, the governing differential equation is

Initial and boundary conditions are presented in

The differential equations were discretized using finite difference method for both cylindrical (

A cylindrical vessel of 15.7 m^{3} and a spherical vessel of 12.6 m^{3} were considered. The vessel contained molten iron, at 1300–1500°C. A stream of gas was injected vertically through an annular nozzle located centrally at the middle of the tank. The gas was injected with a uniform velocity of 100 m/s. The flow was assumed to be axisymmetric. Computations were performed in transient mode. A mesh system of 51 nodes was used (Table

Mesh distribution.

Node | Radium [m] | Node | Radium [m] | Node | Radium (m) |
---|---|---|---|---|---|

0 | 0.1 | 17 | 0.406 | 34 | 0.712 |

1 | 0.118 | 18 | 0.424 | 35 | 0.73 |

2 | 0.136 | 19 | 0.442 | 36 | 0.748 |

3 | 0.154 | 20 | 0.46 | 37 | 0.766 |

4 | 0.172 | 21 | 0.478 | 38 | 0.784 |

5 | 0.19 | 22 | 0.496 | 39 | 0.802 |

6 | 0.208 | 23 | 0.514 | 40 | 0.82 |

7 | 0.226 | 24 | 0.532 | 41 | 0.838 |

8 | 0.244 | 25 | 0.55 | 42 | 0.856 |

9 | 0.262 | 26 | 0.568 | 43 | 0.874 |

10 | 0.28 | 27 | 0586 | 44 | 0.892 |

11 | 0.298 | 28 | 0.604 | 45 | 0.91 |

12 | 0.316 | 29 | 0.622 | 46 | 0.928 |

13 | 0.334 | 30 | 0.64 | 47 | 0.946 |

14 | 0.352 | 31 | 0.658 | 48 | 0.964 |

15 | 0.37 | 32 | 0.676 | 49 | 0.982 |

16 | 0.388 | 33 | 0.694 | 50 | 1 |

Main operation parameters.

Parameter | Numerical value | Parameter | Numerical value | Parameter | Numerical value |
---|---|---|---|---|---|

0.0001 m^{2}/s | 0.02 s^{−1} | 0.1–1 m | |||

0.005 J/mol | 0.01% | 1800 s | |||

0.0004 J/mol | |||||

8.314 J/mol K | 0.001 m/s | Δ | 1 s | ||

1400°C | Nodes | 51 | 0.00001 |

Both expressions of continuity equation were tested by computational methods for the model verification. The numerical solution algorithm consists of the subroutines shown in Figure

Numerical solution scheme.

Figures

Sulfur elimination against time, node 10,

Sulfur elimination against time, node 20,

Sulfur elimination against time, node 30,

Sulfur elimination against time, node 40,

The desulphurization rate of the cylindrical model is greater than that of the spherical model especially during the calcium carbide injection, although both schemes have practically the same incubation period. The process reaches almost equilibrium at the end of injection.

Numerical model was also tested using experimental data reported by other investigators. Enríquez et al. [

Rellermeyer et al. [

Freissmuth et al. [

Meichner et al. [

Figueroa [

The proposed model reaches an elimination percent of 40% with an initial sulfur concentration of 0.01 and a final sulfur concentration of 0.005. The efficient process duration is around 13 minutes. One can see from the industrial data that the model prediction agrees fairly well with the practical results.

The industrial data shows that for the process of desulphurization using CaC_{2} it is possible to obtain approximately a 49.69% of sulfur elimination in a time range of 10–25 minutes. The temperatures in both cases are around 1400°C and the elimination profiles are very alike.

Based on the analyses of thermodynamics and kinetics, a mathematical model has been developed, particularly with the three basic parameters being taken into account, to simulate the variation of sulfur in hot metal with time. Model verification and simulation analyses were carried out, arriving at the following main conclusions.

The cylindrical model agrees fairly well with the spherical model.

The model prediction agrees well with the practical results.

The process reaches equilibrium mainly at 1500 seconds and has an incubation period of 150 seconds approximately.

_{A}

Sulfur concentration

_{AB}

Diffusion coefficient

Kinetics coefficient

Variation coordinate

Time

_{r}

Radial velocity

_{0}

Initial diffusion coefficient

_{0}

Initial kinetics coefficient

_{a}

Activation energy

Gas constant

Temperature

_{0}

Internal radium

_{1}

External radium

_{0}

Initial concentration

Concentration derivative discretization

Spatial coordinate discretization.

The authors would like to thank the Departamento de Metal-Mecánica of the Instituto Tecnológico de Saltillo for supporting this paper.

_{2}