BF_MODEL

A Blast Furnace Model to Optimize the Burden Distribution

G. Danloy (1), J. Mignon (1), R. Munnix (1), G. Dauwels (2), L. Bonte (2)

(1) Centre for Research in Metallurgy (CRM), Liège, Belgium, www.crm-eur.com

(2) Sidmar, Gent, Belgium, www.sidmar.be

Key Words : Blast furnace, Mathematical model, Burden distribution, Vertical probings, Gas tracing.

INTRODUCTION

Since several years, large efforts are made in the blast furnace field to increase the substitution of coke bycoal in order to meet changing economical and environmental conditions. The experience gained until nowshows that the increase of PCI rate induces important changes of gas distribution in the blast furnace whichinfluence the whole process, the performance and the service life. Gas flow monitoring is therefore regardedas one of the keys to high PCI rates.

Gas distribution being the result of numerous interacting phenomena, the best approach consists inestablishing a mathematical model of the gas flow inside the blast furnace.

DESCRIPTION OF THE BLAST FURNACE MODEL

Basic principles

The blast furnace is modelled in a steady state. Therefore, it is assumed to be charged and emptiedcontinuously. The liquid level is considered as horizontal and fixed ; however, it is a parameter. The layeredstructure is assumed to be fixed, which is allowed by the fact that the gas velocity is much higher than thesolids velocity.

Assuming an axial symmetry, the model is bi-dimensional and written in cylindrical co-ordinates. Thesystem of differential equations is solved by the finite differences method.

The input data are : the blast furnace geometry, the process data (blast conditioning, coal injection rate, toppressure, etc.), the chemical and physical properties of the raw materials, the chemical composition of hotmetal and slag and the complete description of ore and coke layers (thickness and grain size distributionalong the radius).

The model simulates the burden distribution inside the whole blast furnace, the gas flow through the layeredstructure, the solids flow, the liquids flow, the heat transfer between the different phases and with the walls,the ore softening and melting in the cohesive zone as well as the main chemical reactions.

The work has been restricted to the main phenomena of the blast furnace. Some sub-models like liquids flow

and softening-melting have been simplified ; the phenomena taking place in the raceway have been limitedto a classical heat and mass balance. Attempts were made to include a char transportation and consumptionsub-model, but it was finally concluded that a research project completely devoted to this problem would benecessary to approach a valuable solution.

The general architecture of the model is shown atfigure 1.

The modular structure makes the model moreunderstandable, allowing easy modifications andfurther improvements. But, due to the interactionsbetween the blast furnace phenomena, the differentmodules are integrated into a complex loopingprocedure.

The results of the model consist in a completedescription of each point of the blast furnace, i.e. thefields of temperature, pressure, velocity and chemicalcomposition of gas, solids and liquids, as well as thewall thermal losses distribution.

Geometry

The model has been applied to the geometry and theoperating conditions of the blast furnace B of Sidmar.The bottom of the calculation field corresponds to theliquid surface which is assumed to be fixed andhorizontal. The raceway and the dead man shapes havebeen fixed according to relevant literature.

The blast furnace must be divided into a great number of cells in order to obtain a correct description of thephenomena like the gas flow through the layers of materials. A compromise between the calculation timeand the quality of the results led to a grid of 20 x 120 cells. For a blast furnace of 10.5 m in hearth diameter,the mesh dimension is then 0.30 m x 0.23 m. On a Digital Personal Workstation 433 AU, the computationtime amounts generally to 3 hours. This time depends highly on the degree of severity imposed forconvergence detection. This model working off line, such a high computation time is not really a dramaticdrawback. Moreover, it could still be improved by using more rapid calculators. The program is written inFORTRAN.

Burdening model

Most plants already calculate the ore and coke layers geometry at the top with their own burden distributionmodel adapted to their individual situation. The modular conception of the present model allows a perfectintegration of these existing auxiliary models. In the present work, we use the Sidmar burdening model [1]which applies to a bell-less top. This model calculates the layers thickness as well as the grain sizedistribution along the blast furnace radius. It calculates also the radial distribution of the resistance to gasflow resulting from the Ergun's law.

The Sidmar burdening model (figure 2) takes into account the trajectory of each type of material for eachposition of the chute, the thickness of the material flow, the dynamic effects generated at the impact point ofthe materials on the burden surface, the grain size segregation (at the hoppers discharge, on the chute and onthe burden surface) and the percolation. The results are in good agreement with the microwave profilometermeasurements [2].

The structure and the properties of the layers are thenextended from the top to the bottom of the blast furnaceon the basis of the results of the solid flow sub-modelexplained below.

Gas flow

This sub-model calculates the gas velocity and pressureat any point of the blast furnace, being given the gas flowrate at tuyeres, the top pressure, the blast furnacegeometry and the layered structure of the burden.

In the dry zone, the voidage of each material is afunction of height and radial position. The values arebased on measurements [3] made on samples issued fromthe Mannesmann furnace quenched with nitrogen in1981. In the cohesive zone and in the dripping zone, thevoidage has been decreased to take into account thevolume occupied by the liquids.

The Ergun equation [4] which holds in a homogeneousfield, can be written in a vectorial form :

G ) |G| . f + f ( - = P 21∇

G gas flow vector, reported to the empty reactor section [kg/m2.s]P static pressure [Pa]f1 laminar flow resistance factor [s-1]f2 turbulent flow resistance factor [m2/kg]

The mass conservation of gas is described by :

∇. (G/M) = Cr_Gas

M molecular weight of the gas [kg/kmol]Cr_Gas rate of gas creation by chemical reactions

(carbon gasification by CO2 and H2O)[kmol/m3.s]

A preliminary study of the different resolution methodsallowed to select the Direct Differential Methodbecause it gives the best precision together with one ofthe shortest calculation times.

Figure 3 shows the calculated gas velocity field at theentrance of the cohesive zone. It can be seen that thegas velocities are greater in the coke layers than in theore layers. Moreover, to cross the cohesive zone, thegas tries to avoid the softening and melting ores byflowing mainly through the coke "windows" ; the smallpart of the gas which passes through the less permeableore layers follows a path as short as possible i.e. almostperpendicular to the interfaces.

Solids and liquids flows

The determination of the solids flow is based on is based on a potential model taking into account thevanishing of solids by melting and by gasification. The main hypotheses are the following :

- imposed dead man,- uniform distribution of solids velocity at the blast furnace

top,- the burning rate of coke in the raceway does not depend on

the radius.

The basic mass conservation equation is written as follows :

tBurnMeltGasif )

( b

−−−=ρ

∇ •S

S solids flow vector [kg/m2.s]bρ solids bulk density [kg/m3]

Gasif carbon gasification reaction rate by CO2 and H2O[m3/m3.s]

Melt ore melting rate [m3/m3.s]Burnt coke burnt in the raceway [m3/m3.s]

The solution is obtained through the introduction of a potentialfunction Ψ [m2/s] such that :

kv = −Ψ∇

v solids velocity [m/s]k resistance to gas flow [-]

The potential function is set at 0 on the raceway section. Thiselliptic problem is solved by the over-relaxation method.

Figure 4 shows an example of results. The layer thicknessdecreases progressively from the top to the tuyeres. In the upper part of the bosh, the coke layers have anaverage thickness of 0.08 m at the wall which can becompared to 0.21 m observed at the top. The inclinationangle of the layers decreases also : from 30° at the top, itreaches about 6° in the belly. From the start of meltingline to the end of melting line, the ore layers becomethinner and thinner which reflects the meltingphenomenon.

These results fit very well with the observations made onseveral dissected blast furnaces, as for example onHirohata n°1 BF of Nippon Steel (figure 5) [5]. Thisfigure highlights also a sharp inverted V shape cohesivezone with a very low root touching the wall and theraceway as in the model results. In the belly, the modelcalculates cohesive rings of 1.7 m width which can becompared to values ranging from 1.2 to 1.7 m on figure 5.

As concerns the liquids issued from the melting line, theyare supposed to flow vertically into the hearth.

Heat transfer

The main supplementary data required for the heat transfer description are the temperature of the gas issuedfrom the raceway and the standard heats of the chemical reactions. At steady state, the conservation ofenergy and the thermal transfers between the solids, liquids and gas phases are described by :

For liquids : - ∇ . (Hl . Gl) + ∇ . (kl ∇ Tl) - Qtr, l + Σ αl, i . Ri . ∆Hr, i = 0

For gas : - ∇ . (Hg . Gg) + ∇. (kg ∇ Tg) - Qtr, g + Σ αg, i . Ri . ∆Hr, i = 0

For solids : - ∇ . (Hs . Gs) + ∇ . (ks ∇ Ts) - Qtr, s + Σ αs, i . Ri . ∆Hr, i = 0

with, for each phase,

H enthalpy at temperature T [J/kg]G mass flow vector, reported to the empty reactor section [kg/m2.s]k thermal conductivity [J/m.EC]T temperature [°C]Qtr heat transferred to the other phases and to the cooling medium by convection and radiation [W/s]Ri rate of reaction i [kmol/m3.s]∆Hr, i heat of reaction i [J/kmol]αi proportion of the heat of reaction i absorbed by the considered phase [-]

The heat transferred by the liquids by conduction and radiation as well as the heat transferred by radiation bythe gas have been neglected.

The Kitaiev correlations [6] have been chosen to quantify the heat transfer coefficient between gas andsolids and to account for heat conduction inside the solid particles. However, like many authors, we haveapplied a correction factor to the heat transfer coefficient at temperatures higher than 1000°C.

The heat transfer coefficients gas-liquids and solids-liquids have been determined by calibration onindustrial data in order to produce hot metal and slag at the right temperature.

The boundary conditions are expressed by the wall temperatures, themselves calculated by the followingheat transfer equation :

) T - T ( . h = ) T - T ( . h wgwwatwp

hp global heat transfer coefficient wall-cooling water [W/m2.°C]hw global convection and conduction heat transfer coefficient granular bed-wall (W/m2.°C)Twat cooling water temperature (°C)Tg gas temperature at the wall (°C)Tw wall surface temperature (°C)

The global heat transfer coefficient wall-cooling water has been determined in function of the height bycalibration on industrial data from BF B of Sidmar. The coefficient hw is calculated following the method setup by Yagi and Kunii [7].

Cohesive zone sub-model

The cohesive zone starts where the solids reach 1200°C and ends where the ore is completely melted. Theore melting degree is calculated from the available heat resulting of heat transfer. It is calculated by meansof an under-relaxation procedure which continues until convergence i.e. until the assumed and calculatedvertical positions of both isotherms don't differ more than a half mesh, which means about 0.12 m in height.

Chemical reactions sub-model

The model considers the following reactions :

FexOy + CO = FexOy-1 + CO2 (reaction 1)

CO2 + C = 2 CO (reaction 2)

FexOy + H2 = FexOy-1 + H2O (reaction 3)

C + H2O = CO + H2 (reaction 4)

CO + H2O = CO2 + H2 (reaction 5)

The gas composition and flow rate are known at the tuyere tip. It is supposed that in a given cell thechemical reactions develop without any interference and that no diffusion of chemical species occur fromone cell to the others. Iron and slag are supposed to reach their final composition as soon as they are formedin the cohesive zone.

In each cell, and for each chemical species, the continuity equation is expressed by

∇ . (Fi) = Ri

Fi flux vector of the i species expressed on the empty section of the reactor [kmol/m2.s]Ri difference between generation and consumption rates of the i species [kmol/m3.s].

A single stage reduction model applied to porous spherical particles is used [8, 9]. The reactions are of firstorder relative to the partial pressures of the gas components. The diffusion inside the particles is consideredbut the diffusion through the boundary layer outside the particles is neglected, as it is of minor importance.

Various expressions of the reaction rate constant can be found in literature. We adopted the following value[m/h] which is based on reduction tests performed in the 80ies in CRM laboratory :

k = 475 . exp [ - 10000 / ( 1.987 . T)]

The value was obtained from the application of the preceding equations to experimental results. Theequilibrium is calculated according to the results of Darken and Gurry [10].

For coke gasification by CO2, a gasification model applied to porous spherical particles is used [9]. Thereaction rates are of first order relative to the partial pressures of CO2 and CO. The diffusion of gas throughthe external boundary layer as well as through the pores of coke is taken into account. We use the reactionrate constant determined by Heynert [11].

The kinetics of reaction 4 is assumed proportional to the kinetics of reaction 2. Reaction 5 is assumed atequilibrium above 850°C ; below this temperature, it is neglected.

CALIBRATION OF THE MODEL AND ILLUSTRATION OF THE RESULTS

The calibration of the model is based on experimental data obtained by vertical probings and by gas tracingat blast furnace B of Sidmar. The results are illustrated below.

The burden consisted of 88 % sinter and 12 % pellets. The coke rate was 287 kg/thm (including 27 kg/thmof nut coke charged together with sinter) with a coal rate of 178 kg/thm. The production level was 65thm/m2.day or 2.7 thm/m3.day.

The measured and calculated temperature profiles are reported at figures 6 and 7. The long thermal reservezone observed on probes 1 to 4 is reproduced by the calculations but some tuning is still necessary toimprove the fitting. The drying of solids shown by probe 1 below 5 m needs also to be improved in thesimulation. Between 1000°C and 1300°C, area of reactions 2 and 4, the patterns of calculated temperatureprofiles are similar to those measured. Results concerning probes 5 and 6 can be regarded as good.

Experimental and calculated results concerning the progress of chemical reactions are compared on aChaudron diagram at figures 8 and 9. On both figures, the gas path shows a similar behaviour which leads tothe conclusion that the chemical phenomena are fairly well simulated.

The calculated radial profiles of top gascomposition and temperature are also in goodagreement with the measured ones, as can beseen at figure 10.

At figure 11, the pressure profiles calculatedalong the wall compare well to the pressureprofiles measured during the vertical probingsboth by the wall probe and by the wall pressuretappings. A pressure loss of 0.300 bar has beensubstracted from the pressure measured in thehot blast main to obtain the experimental valueof the pressure at tuyere nose.

Transfer times of gas from the tuyeres to the top are measured on blast furnace B of Sidmar by gas tracingwith helium [12]. These measurements can also be used to calibrate the model. Figure 12 compares theexperimental measurements to the results of the model. Despite small differences attributed to a systematicerror in the measurement of gas transfer time through the sampling line, the profiles are almost parallel,indicating that the gas distribution in the blast furnace is correctly simulated. This result is worth to behighlighted, as gas distribution is the main objective of the present model.

These comparisons lead to the conclusion that the mathematical model simulates correctly the mainphenomena involved in the blast furnace process.

SIMULATION OF THE INFLUENCE OF THE BURDEN DISTRIBUTION PATTERN

The charging procedure being the most important means to influence the gas distribution, we selected bymeans of the Sidmar burdening model three typical charging procedures promoting without any doubt acentral, a peripheral and an intermediate gas distribution. The layers configurations resulting from theSidmar burdening model appear at the top of figure 13, as well as the radial distribution of the coke volumicfraction and of the resistance to gas flow.

With charging pattern n°1, the coke volumic fraction reaches 100 % at the blast furnace center and only22 % at the wall ; as a consequence, the resistance to gas is very low at the center and relatively high at thewall. With charging pattern n° 2, coke and ore are distributed in such a way to obtain a uniform distributionof the resistance to gas flow. It is interesting to observe that the coke proportion is higher at the wall than atthe centre because it is necessary to compensate for the grain size segregation effect. Charging pattern n° 3has been designed to create a low resistance zone at the furnace periphery ; at the wall, the coke proportionreaches 54 %.

The operation data have been described in the preceding chapter. In order to highlight the influence of theburden distribution, all the parameters of the model are kept constant for the three simulations.

Figure 13 shows the gas temperature map and the calculated cohesive zone in the three cases. These resultsare in good agreement with industrial experience. It is also worth mentioning that the cohesive zone is muchthinner with charging pattern n° 1.

In the dry zone, the three pressure profiles are almost superposed, but they differ greatly in the cohesive anddripping zones. The calculated pressure drops are respectively 0.99 bar, 2.19 bar and 1.38 bar for thecharging patterns n° 1, 2 and 3. Such a classification agrees well with experience.

In practice, the characteristic curve of the blower willimpose the operating conditions, so that chargingpatterns n° 2 and 3 will result into lower blast andproduction rates. To obtain a pressure loss of 0.99 bar inthe three cases, the model calculates that theproductivity will be respectively 64.8, 46.1 and 52.6thm/m2.day (i.e. 100 %, 71 % and 81 %).

At figure 14, the three radial profiles of top gastemperature are compared. They fully agree to whatmight be expected. With charging pattern n° 1, the hightemperatures observed at the centre allow to purge by thetop a significative fraction of the alkalies load, as alreadyreported industrially [13].

The radial profiles of top gas oxidation degree (figure15)are coherent with the top temperature profiles. Theaverage value of the top gas CO2/(CO+CO2) ratio isrespectively of 0.488, 0.525 and 0.527 for the chargingtypes n° 1, 2 and 3.

The profiles of heat losses through the walls highlightalso the great differences between the three chargingpatterns that are mainly due to the different wall

temperature profiles. As expected, the heat losses are lower with then°1 charging pattern. After integration on the whole wall surface, heatlosses of respectively 141 MJ/thm, 197 MJ/thm and 212 MJ/thm arecalculated for cases n° 1 to 3 (i.e. 9130 kW, 12780 kW and13760 kW).

The main results of these calculations are summarized in table I.

The three typical charging patterns applied here above result inextremely different blast furnace operations. But much smallercharging modifications, more frequently encountered in the industrialpractice, can also result in appreciable modifications of the blastfurnace inner state and performance (figure 16). In this respect, themodel can certainly help the operator to choose the most appropriateburden distribution pattern in function of the desired effect on theblast furnace results.

Table I – Calculated results relative to the three charging types.

Charging typeUnit

1 2 3Pressure loss bar 0.99 2.19 1.38

Productivity for a pressure loss of 0.99 bar thm/m2.24 h%

64.8100

46.171

52.681

Heat losses through the walls MJ/tHMkW

1419130

19512780

21213760

Top gas CO2 / (CO + CO2) - 0.488 0.525 0.527Top gas temperature at BF centre °C 818 161 46

SIMULATION OF THE INFLUENCE OF THE PRODUCTION RATE

The influence of the production rate on the blast furnace performance has been simulated for two differentcharging patterns, one leading to a central operation and one leading to a uniform operation. Figures 17 and18 illustrate the effects observed on the cohesive zone.

DISCUSSION OF THE RESULTS

The model results show that the gas flow pattern and the cohesive zone are mainly dictated by the burdendistribution.

The change of gas distribution from the lower shaft tothe upper shaft level is illustrated on figure 19 where thegas flow rates on both sections have been related to anormalized section divided into 10 rings of equal area.The change of gas distribution implies that some gas ismoving from the central region towards the wall but thephenomenon is rather limited. Considering that, in thepresent simulation, the central part of the furnace isoccupied by coke only, the gas distribution in the uppershaft appears very flat as the fraction of gas passingthrough the rings varies only in the range of 13 % to9 %. This result is totally different from the commonfeeling of a very high gas flow rate at the centre, feelingbased on the usually measured top gas temperatureprofiles. In conclusion, the temperature profile is mainlyrelated to the gas velocity profile but gives a poorindication on the gas flow rate profile.

The validity field of the model could be enlarged by the modelling of other phenomena such as thebehaviour of unburnt coal particles, voidage modifications, grain size alteration, channelling, accretion,scaffolding and peeling. As it includes the main phenomena involved in the blast furnace process and theirinterrelations, the present model is an appropriate frame to the development of such additional modellingwork.

CONCLUSIONS

A mathematical model has been developed which simulates the main phenomena involved in the blastfurnace process at steady state. It has been calibrated with experimental data obtained by vertical probingsand by gas tracing at blast furnace B of Sidmar.

The model results show the strong influence of the burden distribution pattern on the gas distribution and onthe different operating results such as the pressure drop, the productivity, the shape and position of thecohesive zone, the top gas temperature profile and the heat losses through the wall. As a consequence, it canbe used to simulate and to forecast the influence of the burden distribution changes which are made by theoperator. Therefore, it is a powerful tool to help him to choose the proper burden distribution pattern infunction of the desired effect on the blast furnace results.

Sidmar has decided to implement the model for an industrial use.

ACKNOWLEDGEMENTS

This research has been carried out with financial support from the Belgian Public Authorities and from theECSC.

REFERENCES

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