Computational Model for Estimation of Refractory Wear and Skull

Deposition in Blast Furnace Hearth Wall

Abhinav Mithal, Member, IEEE, and Toma Hentea, Senior Member, IEEE

Abstract- Knowing how much refractory remains in the

hearth is critical to the assessing when a blast furnace hearth

needs to be relined. In this work a computational model coupled

with a finite state machine and a neural network pattern

recognition block has been developed for the blast furnace

hearth to determine the thickness of two refractory layers and

formation of protective layer of solidified metal (skull). A neural

network was also used for data correction. The results provide

estimation of wear of the hearth refractory lining and insight to

the erosion profile formed inside the blast furnace hearth. The

walls and the floor of the hearth have embedded thermocouples

to monitor the temperatures of the furnace walls. Based on the

temperature readings of the thermocouples one can determine

the heat flux through the wall. This heat flux is used in the

computational model, based on heat flow and conservation of

energy, to determine the skull deposition and refractory wear.

I. INTRODUCTION

One of the most critical areas of the blast furnace is the

hearth. It is the lowest part of the furnace where molten

metal and liquid slag is collected. Due to the complex

chemical, mechanical and thermal impact a hearth of the

furnace is sensitive to erosion. The erosion rate is very

strong, especially at the wall near the tap holes. If this

erosion process continues unrestrained the walls of the

hearth can be so severely damaged that a break out of the

molten iron through the hearth wall is possible. Therefore,

carefully monitoring the condition of the hearth lining during

the campaign is required. Due to hostile conditions in the

hearth, no direct measurements of the remaining hearth

lining thickness are possible, therefore, indirect

measurements, such as thermocouple readings are used to

estimate it.

There are many factors that cause strong erosion in the

brick lining, e.g. chemical reaction between the hearth

material and liquid iron, abrasion and friction caused by

solid coke particles present in the hearth, thermo-mechanical

stress, and fluid induced shear stress. Erosion done by any of

these factors will cause a rise in the temperature of outer

surface of the walls of the hearth. This is because as the

This work was supported in part by the Indiana 21 sl Century Research and technology Fund.

Abhinav Mithal was with Purdue University Calumet, Hammond, IN 46323, USA. . He is now with Nokia Co., Boston, MA 01752, USA; e­mail: abhinavmithal@gmail.com .

Toma Hentea was with Purdue University Calumet, Hammond, IN 46323, USA . He is now with Grand Valley State University, School of Engineering, Grand Rapids, MI 49504, USA phone 616-745-3672, fax 616-331-7215.e-mail: henteato@gvsu.edu.

978-1-4244-8126-2/10/$26.00 ©2010 IEEE

thickness of the refractory reduces the thermal resistance of

the refractory reduces or the thermal conductivity increases

and there will be a lesser temperature drop between the inner

surface of the wall and the outer surface in steady state for

constant heat flux. Therefore, computational models can be

developed based on the variation of the temperature drop

between the inside of the hearth to the outer walls of the

hearth which determines the thermal resistance from inside

to the outside which in term is the measure of the thickness

of the of the refractory and the solidified protective metal

deposited on the inner surface of the refractory.

Groth et al (Nov 1999), developed a model to detect

inefficient cooling on the shell and to understand irregular

,,elephant-shaped" erosion profiles. Their model is based on

calculation of maximum and average temperatures. These are

fed to a two dimensional heat transfer program which

produces two solidification isotherms. These isotherms

detect the refractory wear and skull deposition.

Preuer et a!. (1992), investigated the cause of the

"mushroom effect" wear profile in the blast furnace hearth.

Clark and Cripps et al (1985) and Kurpisz et al (1988)

studied the thermocouples positioned in the refractory to

determine the temperature distribution and hence the location

of the 1150°C isotherm, which approximates the hot metal

eutectic temperature and hence the maximum possible extent

of the hearth erosion or the variation of the buildup.

Hearth wear mechanism

The life span of a blast furnace is determined mainly by

the erosion process within its hearth. Thermo-mechanical

wear mechanisms start at relatively low temperature levels

and increase, often exponentially, at elevated levels. Well

known thermo-mechanical wears mechanisms include:

• Erosion and dissolution of carbon in hot metal

• Hot metal penetration in pores-resulting in much

higher thermal expansion

• Stress cracking-cracks through refractory causing

thermal shoot

• Spalling-intemal cracks in single refractory bricks

II. COMPUTATIONAL MODEL

A method is developed to estimate the width of the

refractory and skull deposition in a Blast Furnace hearth.

This method estimates the erosion and skull inside the hearth

using one dimensional steady-state heat transfer. It is

assumed that the system is in steady state. When there is a

temperature gradient within a body, heat energy will flow

from the region of high temperature to the region of low

temperature. This phenomenon is known as conduction heat

transfer, and is described by Fourier's Law

q = -kfiT ( 1)

This equation determines the heat flux vector q for a given

temperature profile T and thermal conductivity k. The minus

sign ensures that heat flows down the temperature gradient.

Heat flux q, is the rate of heat flowing past a reference

datum. Its units are W/m2• Thermal conductivity k, is a

material property that describes the rate at which heat flows

within a body for a given temperature difference. Its units are

W/m-k.

The side wall structure can be divided up into four

sections, as shown in Figure 1. The heat flux through a

cylinder of radius r, and length L written as:

dT q = -kA-, where A = 27iY L (2) dr

Equation 2 is used to calculate the heat flux in the side

walls of the blast furnace hearth. The data from a blast

furnace consist of readings from about 280 thermocouples

situated near the periphery of the hearth either at a deep

location (l25mm inside the periphery) or shallow location

(25mm inside the periphery). It also includes the readings for

hot metal temperature inside the hearth. Figure 1 shows the

nomenclature for temperature measured by shallow

thermocouple (T s), temperature measured by deep

thermocouple (T D) , thermal conductivities kCB' kFB and kskull

and radii of various layers in the hearth wall. The side wall is

composed of three materials or layers which are the carbon

brick (CB), fire brick (FB), and skull. The skull may or may

not be present at any given time. T HF and rHF are the

temperature and radius of the hot face (where hot metal

exists in liquid! semi liquid form), respectively. T HF

essentially is the hot metal temperature at that point.

Similarly, T FB and rFB are the temperature and radius of the

fire brick interface, respectively and T CB and rCB are the

temperature and radius of carbon brick interface,

respectively. rD and rs are the distance to the deep and

shallow thermocouple respectively from the center of the

hearth.

Center line

Fig. 1 Side wall structure

kCB and kFB are known values while kskull has been assumed

anywhere between 1.3 and 13 by different authors.

Therefore, various values of kskull were tried and results

obtained were matched with the actual skull deposits

measured in the blast furnace hearth and those predicted by

using 3-D approach and CFO models.

Applying the principle of conservation of flux, and

assuming that all fire brick, carbon brick and skull exist, the

radius of the hot face rHF is computed by eq. 3.

rFB

rHF

= ----,,-(-

THF

_-TD)(-kSi.'ll

l-

n[ rs )---'-"-] ----,;-

exp ___ -'-- k_C_B __ rD----'-- ksi.1I11 In[ rCB )_ ks(,ll

In[�) (TD - Ts) k FB rFB kCB rCB

(3)

If the skull is not present, rHF is computed by eq. 4.

Similarly, when only the carbon brick exits with skull

deposited over it, rHF is computed by eq. 5. Finally if only

the carbon brick exist the radius of the hot face can be found

by computed by eq. 6.

(5)

Using Equations 3, 4, 5 and 6 the thickness of the

protective, solidified metallic layer (skull) deposited on the

side walls of the blast furnace hearth and the remaining

width of the refractory (hearth wall layers) can be

determined at any given time.

The erosion process is monitored using a 4-state model.

State 1 is entered when carbon brick, fire brick, and the

skull, exist together. The process exits this state and enters

State 2, when skull deposited on the fire brick gets

completely dissolved. State 2 is maintained while carbon

brick and fire brick exist and the skull is not present. The

process exits state 2 and enters State 1, when skull is

deposited on the fire brick or it enters State 4 when fire brick

gets completely eroded in which case the process never

comes back to State 1 or State 2.

State 3 is entered when carbon-brick with skull deposited

over it exists and fire-brick is not present. Process exits this

state and enters State 4, when skull deposited on the carbon

brick gets completely dissolved.

State 4 is maintained while carbon-brick exists and fire­

brick and skull is not present thereby exposing the carbon

brick directly to the hot metal inside the hearth. The process

exits this state and enters State 3, when skull is deposited on

the carbon brick.

While the finite state model allows the use of physical

models for the estimation of wear, its utilization implies an

accurate knowledge of the thermal conductivity parameters.

An alternative approach consists in using a pattern

recognition block to determine the state of the wear process.

We developed a neural network classifier based on the

sensitivity of the deep and shallow wall temperatures and the

molten iron temperature.

The neural network classifier was implemented on a two

layer feed forward network with five hidden neurons. The

results of the classifier were used for fine tuning of the

computational model.

III. EXPERIMENTAL RESULTS

Twelve thermocouple pairs (deep and shallow

thermocouples) were selected for experiment purposes. The

location of thermocouples was such that four thermocouple

pairs were aligned almost vertically one under the other and

we picked up three sets of such vertically aligned

thermocouples at three different angles, summing a total of

12 thermocouple pairs. The three sets were picked up from

three widely spaced angles (9 = 39°, 157°, 220°) on the blast

furnace hearth wall to give an approximate understanding of

amount of erosion in different directions of the hearth wall.

1oo.-----�------�------�----�------�

1<10

120

100

00

'deep'TC ',hallow'TC ',hell'TC

Fig. 2: Plot of all three thermocouple temperatures for one set at level TEB

The three sets of thermocouples, a pair each at different

angles (denoted by anglel, angle2 and angle3) pointing away

from the center of the hearth and a pair at each angle had 4

levels (level TEB, TEA, TEVI and TEV) depicting the

height of the thermocouples in the set. It should be noted that

the height of thermocouples in different sets but one level is

same. TEV is the bottom most level and level TEB is the

topmost.

The last thermocouple level in each set was deliberately

picked up such that they lie little below the bottom of the

hearth. This was done in order to check the validity of the

program and the derived equations. Since there will be no

erosion (almost never) below the bottom of the hearth for a

long time, this can help us determine invalidity of the model

if at any time (particularly for high temperature when erosion

is occurring in most of the places) the model predicts erosion

at the level 4 thermocouples.

The data obtained from the blast furnace had many

erroneous readings and missing data points. Erroneous

readings include negative readings from the thermocouples

which are clearly not possible. Other erroneous readings had

large abrupt changes. Therefore, it was necessary to clean the

data by removing the outliers and filling in the gaps.

A two step process was used for cleaning the data. They

are:

1) Remove the outliers and put a gap in place of that data.

So, now our program assumes it to be a missing data point.

2a) For small gaps use interpolation to get the missing

values (data).

2b) For large gaps built a neural network to fill in the

missing data. The neural network was built using available

good data at approximately the same level of temperature

and thermocouple location.

Figure 3 shows the graph of the estimated total width of

the side wall of the blast furnace hearth over a period of 18

months. Estimated Wall Radius atLevel TEB Angle 1

- CB+FB+Skuli - CB+FB • NO Skull

6.5 - CB+Skuli • NO FB CB· NO FB & Skull

- Deep Te Temp

3.50 21m 4000 6000 800J 10000 121m 14000 16000

Fig. 3: Estimated total wall radii at 39° angle at level TEB.

This figure shows the variation of the total wall width at

level TEB but at different angles. The plot also shows the

variation in the deep thermocouple temperature with time.

The deep thermocouple temperature plot is reduced to scale

to fit in the plot with other wall width data. The main

purpose of this plot is to see the variation in the shape of the

plot during erosion and skull deposition. This has helped in

the sensitivity analysis discussed later in this section. It

should be noted that the plot of estimated total width versus

time changes color at many places; it starts with red and then

turns green at some places and go back to red and finally it

becomes yellow for a small amount of time and then turns

blue and never becomes red thereafter. Red color in the plot

shows the state when carbon brick, fire brick and skull, all

three are present inion the hearth walls. Green portion of the

plot shows the period of time when skull was completely

dissolved but fire brick and carbon brick were still present.

These two colors keeps on toggling in the graph until the fire

brick is completely eroded and at time the color of the plot

changes to yellow to show a state were the carbon brick is

completely exposed to the hot molten metal in the blast

furnace hearth. Finally when erosion stops and skull is

deposited on the once exposed carbon wall the color of the

plot changes to blue and now plot color would keep toggling

between yellow and green for the rest of the campaign of the

furnace until a relining is done for the hearth. Figures 4, 5,

and 6 show actual thicknesses of the carbon brick, the fire

brick and the skull deposited on the walls of the blast furnace

hearth varying with respect to time in different directions at

TEB level. The green line shows the width of the carbon

brick at any given time. Notice that it starts at 2.075 meter

and gets depleted due to erosion over time. The blue line

shows the width of fire brick which is 0. 114 meter thick. The

red curve indicates the thickness of the skull deposited on the

carbon or fire bricks. The time axis is in number of days.

Esl,maloorl of Refraclory Wear and Sui Thickness 1: L ....... I TE:6 Anglel 28

2.7

25

24

23

22

:2 1

20�---- 1�00------XO�-----300�-----ALoo------&O�----�&O

Fig. 4: Estimated Refractory wear and skull thickness at 39° angle at level TEB.

2.9 Esllma110n of Rehcto,)' We �d S\<ulJ Thickness al Level TEB N11l1e2

2.8

2.7

2.6

25

2.4

2.�

2.2

2.1

20 100 200 300 d.OO 500 600 Fig. 5: Estimated Refractory wear and skull thickness at 157°

angle at level TEB.

ESlim31iorl of Refractory We r nd Skull Thickness at lowel TE8 Angle3 2.8

2.7

2.1

20 100 200 300 400 50) 600 Fig. 6: Estimated Refractory wear and skull thickness at 220°

angle at level TEB.

To validate the computational model, we performed a sensitivity analysis. It is expected that when the walls of the hearth get eroded the thermocouples on the outer surface of the heath become more reactive to the change in hearth temperatures. This is due to the fact that there will be less thermal resistance and consequently less heat dissipation from inside to the outer surface of the hearth. As a result, in an eroded wall, the change in deep thermocouple temperature with respect to some change in hot metal temperature would be much larger than in an un-eroded segment of the wall.

The sensitivity studies were merged with the refractory

wear results to see what happens to sensitivity at times when

refractory erosion occurs. It is interesting to note that when

carbon brick and fire brick erosion takes place there is a

sudden rise in the sensitivity and as skull builds up the

sensitivity decreases. Also, after the fire brick is completely

eroded the thermocouples become much more reactive to

change in hearth temperatures.

IV. CONCLUSIONS

A computational model has been developed for the blast

furnace hearth that determines the thickness of two refractory

layers and formation of protective layer of solidified metal

(skull) on the refractory in the walls of the blast furnace

hearth at any time during the campaign. The results provide

estimation of wear of the hearth refractory lining and insight

to the erosion profile formed inside the blast furnace hearth.

Results from the model show (numerically and

graphically) that severe erosion occurred in the blast furnace

during the period under study. It also reveals that an

elephant''s foot erosion profile is present in the blast furnace

hearth.

Further work can be done in this area. A complete 3-D

profile can be created if data from all the levels in the hearth

is available. Using the simplicity and speed of this model 3-

D profiling can be easily done.

REFERENCES

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[3] Takeda, K., Watakabe, S., Sawa, Y, Itaya, H., Kawai, T., and Matsumoto, T., 1999, "Prevention of Hearth Brick Wear by Forming a Stable Solidified Layer," Ironmaking Conference Proceedings, Vol. 58, pp. 657-665.

[4] Brannbacka, 1., et al., 2003, "Model Analysis of the Operation of the Blast Furnace Hearth with a Sitting and Floating Dead Man," ISIJ International, Vol. 43, No. 10, pp. 1519-1527.

[5] Huang, F., Fang Van, Predrag Milovac, Pinakin Chaubal, Chenn Q. Zhou, "Numerical Investigation of Transient Hotmetal Flow in a Blast Furnace Hearth", AIST 2005.

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