Mathematical model of a blast furnace

1. Introduction
The blast furnace is a countercurrent packed-bed chemical reactor in which gases ascend and reduce descending iron oxide particles. Inputs to the blast furnace are the load (layers of coke and ore) and hot blast. Output from the furnace are blast furnace gas, slag and pig iron. The developed mathematical model is a tool for simulation of thermal and chemical processes, monitoring and control of the following processes:

• theoretical combustion temperature in front of blast tuyére,
• distribution of gas flow, temperature, and chemical composition,
• temperature profile of blast furnace load,
• position and shape of cohesive zone.

Results of the model will provide information about prereduction load, heat load of the furnace, central and wall gas flow, and non-standard situations.

2. Mathematical model
The structure of blast furnace model corresponds to the structure of load. Blast furnace load consists of one layers of coke and ore, sometimes only layers of coke. The load is further divided into sectors and intercircle areas. This division created elementary zones where index i signifes the number of load from the bottom of the furnace, index j is the number of intercircle areas from the furnace axis to furnace wall and index k is the number of sectors in clockwise direction around furnace axis. Every element is defined by the folowing properties:

• number of the element and its six adjacent elements,
• dimension, area and volume of element,
• mass, composition and temperature of load,
• volume, composition and temperature of gas,
• parameters for computation of resistance and value of vertical and horizontal resistance.

For each element following elementary balance is computed:

• balance of gas flow,
• balance of load and gas heat,
• balance of load and gas material.

3. Models of particular processes

From on going processes point of wiev the model is devided into the next particular models:

• generation of heat,
• convection of gas,
• transfer of heat,
• chemical processes,
• process of smelting.