Static Heat Energy Balance Mathematical Model for an Iron Blast Furnace

In this study a static heat energy balance analysis has been carried out for an iron blast furnace. The objective of this work is to provide a mathematical calculation model of the heat distributions for the various components of the blast furnace. The model presented, is also indicative to the amount of excess fuel being charged. To prepare a proper heat balance, the first step is to attain a proper mass balance calculation. To do so, each input and output materials has been analysed, and the respective elemental compositions have been calculated. All major components and reactions of a blast furnace have been included in the study. Each calculation has been done with sufficient details, to allow estimation of heat requirements, according to the working conditions of a blast furnace.


Introduction
Heat energy analysis is a very major study for the proper operation of a blast furnace. Heat balance is an account of the input and output of heat in a process, which follows the first law of thermodynamics. A proper heat balance not only helps to predict the efficiency of a furnace, but to also eliminate any excessive fuel wastages. Reduced fuel requirement not only reduces production costs, but more importantly saves a portion of our rapidly depleting natural resources. To get a proper heat balance, a proper material balance is a necessity. A material balance is simply an account of input and output of mass, governed by the law of conservation of mass. A proper material balance will provide accurate quantitative values, thereby simplifying calculations in each step of the heat balance. Besides this, a detailed study of each input and output components of the blast furnace has to be carried out, which includes: 1 A heat balance analysis for a continuous production blast furnace was presented by [1]. The authors gave a simplified model to calculate heat distributions for various components of the furnace. However, the authors did not provide any insight to the reactions occurring in the furnace. Also, no sub-divisions to the calculations were shown. Taking [1] as reference, the following study has been conducted to calculate exact heat distributions of each input and output component of the furnace, in detail. Various standard textbooks [2][3][4][5], and papers [11][12][13][14] have been referred to get an in-depth insight into the factors which should be taken into consideration, and the reactions taking place in the different regions of the furnace. The standard enthalpy of formation of compounds data has been taken from [6], the enthalpy data of elements and compounds at high temperatures has been taken from [7] and the heat of solution data has been taken from [8]. Composition analysis of all materials has been carried out using XRF analysis, and BF gas analysis has been carried out using Orsat absorption method.

Working of a Blast Furnace
A blast furnace is a huge, steel rack lined with refractory bricks, which is used to convert iron oxide into pig iron. The blast furnace is an example of a counter current reactor where solids descend and gasses ascend. The fuel (coke, coal, nut coke) and other raw materials (iron ore, sinter, dunite, dolomite, quartzite) are weighed, and charged into the furnace from the top.
Coke is a mixture of coals, crushed and then heated to remove most of the volatile matter. Coke has higher calorific values due to the presence of more carbon content. Nut coke is smaller in size and has a lesser calorific value than coke. Sinter is produced by agglomerating iron ore fines with other plant wastages, having some iron percentages, such as screened sinter fines, flue dust and sludge from the blast furnace, and scales from mills. Limestone and dolomite are added to maintain the required basicity of sinter. Coke fines are used in the coke oven plant, to heat the iron ore fines along with the flux material, to form lumps of sinter. The iron ore is found in mainly two forms, Hematite (Fe₂O₃) and Magnetite (Fe₃O₄).
Air is collected from the atmosphere and heated to 1200°C with the help of giant hot blast stoves. From the stoves the hot combustion air is given sufficient oxygen enrichment, and supplied into the furnace at high pressure, through the tuyeres, as hot blast. The coke descends to the bottom of the furnace and is ignited by the hot combustion air blast. The coke reacts to produce CO₂ and heat, raising temperatures of the combustion region to around 1900°C. The wustite ore, having a high melting point, melts in this region. The CO₂ produced again reacts with excess C, to produce CO gas. This hot gas then moves upwards in the furnace reducing the iron oxides and the other input materials. Other than reduction by CO gas (Indirect Reduction), other reducing processes are reduction by C (Direct Reduction) and reduction by H₂. Dunite, dolomite and quartzite are slag producing agents, which produce slag along with iron ore impurities such as alumina and silica, and help in the removal of elements like sulphur and phosphorus. The raw materials require around 6 to 8 hours to descend to the bottom of the furnace, as the final products: hot metal and slag. The hot metal and slag flow out of the blast furnace through the tapping hole. The hot metal flows through the runner and is collected in the ladles. The slag having a lesser density than that of the hot metal, separates out from the hot metal, as the slag runner is placed in a different direction. The slag is granulated by sprinkling water over it and later sent to cement factories, where it used as a raw material. During reactions, various other gases are produced at various levels inside the furnace. These gases leave the furnace and is known as Blast Furnace Gas (BF Gas). The BF gas carries small particulate matter (dust), which are removed by passing the gas through the Dust Catcher and then the Gas Cleaning Plant (GCP). The BF Gas carries significant amount of energy, and after removal of dust, is reused in various areas of the plant. The dust collected in the Dust Catcher and GCP is used as a raw material for sinter. Figure 1 shows a schematic diagram of a blast furnace plant.  All data for the study has been taken from the month of April 2017. A heat energy flow diagram is shown in Figure 2 for a demonstration of the calculations. (-) sign indicates components which release heat, whereas (+) sign indicates heat absorbing components.

Heat Balance Calculations
Hot Metal Production in April 2017= 48411 Tons

Fuel Analysis
The

Combustion Air or Hot Blast Analysis
Volume of Moist Blast= 1181 m³/THM It is taken that atmospheric air contains 21% Oxygen (O₂) and 79% Nitrogen (N₂). Also, 15 gm moisture is considered to be present per m³ of atmospheric air. Quantity

Composition Analysis
For simplicity in calculations, it has been assumed the input iron ore to be only in the form of Hematite (Fe₂O₃). The percentage compositions of the various input materials are studied using XRF analysis, which is carried out for every batch of input materials, on arrival. The values are of that input materials, used in the month of April 2017. Only the percentage composition of the elements, taken into consideration for this study, has been shown.

Sinter
Total Quantity Used= 53101 Tons The sinter composition analysis results is shown in Table 3.  Table 4.

Dolomite
Total Quantity Used= 324 Tons Moisture Content= 0% The dolomite composition analysis results is shown in Table 5. The quartzite composition analysis results is shown in Table 6. The coke and coke ash composition analysis results are shown in Table 7 and Table 8 respectively.   Table 9 and Table 10 respectively.  The nut coke and nut coke ash composition analysis results are shown in Table 11 and Table 12 respectively.

Hot Metal Analysis
Temperature of Hot Metal= 1464°C = 1737 K The hot metal composition analysis results is shown in Table 13.

Volatile Matter
Assuming all volatile matter to be phenol.

Blast Furnace Gas (BFG)
Quantity of BFG = 1702 m³/THM Calorific Value of BFG= 870 Kcal/m³ Temperature of Blast Furnace Gas= 179°C = 452 K The blast furnace gas composition analysis results is shown in Table 14.

Dust Analysis
Dust Formation Temperature= 1400K The dust formation temperature is taken as 1400 K as the reactants with the dust, undergo reaction only after reaching the desired temperature. Also, dust is produced after a reaction, hence the calculation for sensible heat of dust will take into consideration the temperature in which a reaction takes place. Other than the mentioned compounds, dust also contains nominal amounts of MnO, TiO₂, P₂O₅. The heat effects of these compounds can be neglected. Table 15 shows the composition analysis results for the dust collected in dust catcher, and Table 16 shows the composition dust analysis results for the dust collected in gas cleaning plant.

Dust Catcher
Quantity of Dust Collected in Dust Catcher= 728 Tons

Slag Analysis
Quantity of Slag Produced= 362.2 Kg/THM The blast furnace slag composition analysis results is shown in Table 17. The slag calculation is done taking reference from [1]. The values of [1] are selected, as the slag composition data is similar to that produced in the blast furnace, taken in the study.
Heat produced during slag formation= 362.  Table 18 shows the elements entering into the blast furnace for reactions, after excluding dust losses, carbon in hot metal and FeO in slag. The mentioned elements have been excluded in beforehand for more accuracy in results. The amounts excluded are taken from the respective composition sheets. The enthalpies of reactions, as shown in Table 19, are calculated according to the temperature in which the reaction takes place, by applying Kirchoff's equation (1).

Reactions
(∆H Reaction ) T2 = (∆H Reaction ) T1 + [∑ (∆H T2 -∆H T1 ) Products -∑ (∆H T2 -∆H T1 ) Reactants ] where, T2 is the temperature at which the reaction takes place and T1 is the standard temperature of 298K. Figure 3 shows the different temperature zones in a blast furnace. The CO produced, for the reduction of ores, is produced by the combustion of fuels at 1700 K.

2C(s) (23214) + O₂(g) (11607) → 2CO(g) (23214)
The values in brackets is the number of moles of the substance undergoing reaction according to the mass balance shown in Table 18.
After performing various calculations, the reduction percentages are taken to be 60% Indirect Type (CO) Reduction, 35% Direct Type (C) and 5% reduction by Hydrogen (H₂), as this yields the most accurate results, as shown in Table 19. These percentages vary according to the operating conditions of the furnace. The percentages can be estimated by taking into consideration the BF Gas analysis.  2CO(s) (1820) --------------------------------- Reaction X is the mass balancing equation to balance the excess C supplied (excess fuel).
Moles produced in the BF according to calculations: CO = 18660; CO₂ = 15144 But the moles leaving the furnace in BF Gas: CO = 18024; CO₂ = 15257 Difference in moles of CO =18660 -18024 =636 (Excess) Difference in moles of CO₂=15144 -15257 =113 (Less) This difference in the number of moles can be explained due to the other reactions taking place inside the furnace. It can be said that 113 moles of CO are reducing some other oxides (other than those taken in this study) to produce 113 moles of CO₂. Hence CO₂ balance will then be achieved. Excess CO (523) may be due to the following reasons: 1. Furnace having a lesser percentage of direct reduction (<35%).

Excess fuel supply (From reaction X)
Reaction X is indicative to the excess fuel supplied inside the furnace. Though some amount of excessive fuel is desirable in order, to maintain the working temperature of the furnace. High amount of excessive fuel would produce negative effects on the efficiency of the furnace. As from above, reaction X, is an endothermic reaction, so adding extra fuel will reduce the efficiency of the furnace and also disturb the CO/CO₂ gas balance, which is undesirable. In general, around 8-10 Kgs of fuel is supplied in excess to prevent cooling down of the furnace. However, any quantity more than this, is wastage of fuel and should be restricted.

Heat Energy Balance Sheet
The final heat energy balance sheet is shown in Table 20.

Conclusion
A static heat energy balance mathematical model has been developed in this study. The model takes into consideration all the factors which play a significant role, in the heat requirements of a blast furnace. The calculations of the balance presented in the study will help to estimate the heat requirements of a furnace, and eradicate any excessive fuel supply. Individual percentage composition of each input and output component, taken in the study, would help to alter the quantity of supply of any component, for improving the efficiency. From the above calculations, one can account for approximately 73% of the heat supplied [Table 20]. This result is in accordance with the literature of heat energy balance for a blast furnace [3][4][5]. The remaining 27% can be explained as other heat losses taking place in the tuyere region [9][10], conduction, convection, radiation etc.