Formation Process of Brittle Layer in Carbon Brick and Kinetic Analysis of Dendritic Penetration

Abstract

In order to explore the formation process of brittle layer, the dissection investigation of actual BF was analyzed, the penetration experiments were carried out, the cause of brittle layer formation in carbon brick was summarized. The mechanism of dendritic penetration of molten iron was clarified, the kinetic model of penetration was established combined with the penetration mechanism. The results show that: The brittle layer is observed on the hot face of carbon brick, there are a lot of striated gaps in the brittle layer near the hot face. The penetration depth of molten iron increases with the increase of temperature and penetration time, the penetration velocity is relatively high at the beginning, then gradually decreases. The dendritic penetration of molten iron is a key common problem in carbon brick, it is easier to form at the junction of two phases in carbon brick. There are three paths for each branch of dendritic penetration, the penetration of the third path is extremely destructive to carbon brick owing to the elongation of penetration in this path is relatively large. The essence of the meniscus is the confrontation between the cohesion of molten iron itself and the adhesion between molten iron and carbon brick. The model calculation indicates that the adhesion force is relatively small, the key to prevent the penetration is to control the adhesion force between molten iron and carbon brick. The maximum penetration depth of molten iron can be evaluated through the penetration model.

1. Introduction

The long process production dominated by blast furnace (BF) accounts for more than 90% of steel output in China, which is still the mainstream production process at present.^1,2,3) At the end of BF campaign, the erosion of carbon brick in hearth is intensified, and the heat flow intensity of hearth continues to increase, which seriously affect the efficient and stable operation of BF.^4,5,6) The maintenance at the end of BF campaign will increase fuel consumption and carbon emissions, which is not in line with the current development trend of “carbon peak”.^7,8) Therefore, the erosion of carbon brick attracts great interest from ironmaking scholars and operators.

In the course of numerous dissection investigations, the brittle layer has been found on the hot face of residual carbon brick.^9,10) The brittle layer is mostly loose and easy to peel off, which seriously affect the performance of carbon brick in hearth. On one hand, the brittle layer reduces the strength of carbon brick, which is easy to be swept away by the circulation of molten iron. On the other hand, there are a lot of air gaps in the brittle layer, the thermal conductivity of air gaps is too low, which will break the heat transfer balance of hearth.^11,12,13) All these will accelerate the erosion of carbon brick and reduce the service life of BF. Previous studies related to the brittle layer have involved the hazards of brittle layer, the formation process of brittle layer, and the relevant influencing factors of brittle layer. However, there are many views and no consensus in early works, the opinions are divergent on the formation of brittle layer.^14,15,16) The formation mechanism of brittle layer has not been sufficiently understood, and the kinetic analysis of dendritic penetration has been rarely reported.

In the current paper, characteristics of brittle layer in carbon brick were analyzed based on the dissection investigation of actual BF. The penetration experiments were carried out in the laboratory, the cause of brittle layer formation in carbon brick was summarized. The mechanism of dendritic penetration of molten iron was clarified based on the obtained results, the kinetic model of penetration was established combined with the penetration mechanism.

2. Experimental

The samples of brittle layer were obtained from the dissection investigation of commercial BFs. The parameters of two commercial BFs for dissection investigation are depicted in Table 1. The BFs at the end of the campaign were shut down as planned, the materials in hearth were removed after the residual iron was discharged, so the hot face of carbon brick was clearly exposed in hearth. Then, the dissection investigation was carried out by the way that researchers entered the hearth. The brittle layer on the hot face of carbon brick was photographed, measured and sampled along different heights and different radial directions. The samples were cut and embedded in the resin, the SEM (Scanning Electron Microscope) and EDS (Energy Dispersive Spectrometer) analysis was conducted on the samples.

Table 1. The parameters of two commercial BFs for dissection investigation.

Item	Started	Shut down	Volume	Hearth	Salamander	Tuyere	Taphole
1BF	2007.12	2015.08	1780 m3	9.8 m	2.1 m	26	2
2BF	2010.01	2022.06	4000 m3	13.5 m	3.0 m	36	4

The experiments of molten iron penetrating into carbon brick were also carried out in the laboratory. The original carbon brick was cut into thin slices, the molten iron sample was placed on the thin slice, and the thin slice was pushed into a horizontal tube furnace for experiment. The carbon content in carbon brick was tested to be 82.3%, the SiO₂ content was 8.75%. The apparent porosity of carbon brick was detected as 18.86%, the average aperture was 1.083 μm. The carbon content in molten iron was controlled at 4.5%, which was consistent with the actual hearth. The design parameters of penetration experiments are listed in Table 2. The temperature was raised to the required temperature, and high purity argon gas was used for protection during the whole experiment. The penetration depth of molten iron was measured by SEM, and other valuable information was also collected after the experiment.

Table 2. The design parameters of penetration experiments.

Item	Carbon content in molten iron	Temperature	Penetration time
1	4.5%	1450°C	5 min, 10 min, 15 min, 20 min
2	4.5%	1500°C	5 min, 10 min, 15 min, 20 min

3. Results and Discussion

3.1. Macro Morphology of Brittle Layer in Hearth

The macro morphology of carbon brick hot face in hearth is presented in Fig. 1. As shown in the figure, the carbon brick have been eroded in the circumferential direction of hearth below the center line of taphole. The carbon brick is incomplete compared with the original one, carbon brick with small residual thickness has fallen off and exposed a new surface of another carbon brick, due to small carbon bricks are lined in this BF. The performance of carbon brick on eroded hot face is obviously different from that of other parts, some of the carbon brick are very loose, which will fall off from the original carbon brick when touched by hand. Some of the fallen carbon brick become a small piece, and some even become powder, which indicates that the embrittlement is relatively serious. The actual erosion profile of hearth does not conform to the monitoring model, which also proves the existence of brittle layer.

Fig. 1. Macro morphology of carbon brick hot face in hearth. (Online version in color.)

The brittle layer which is taken from the hot face of carbon brick is presented in Fig. 2. The hot face of brittle layer is uneven and has a certain radian, which is generally consistent with the erosion profile, some areas are bonded with molten iron. There are a lot of striated gaps in the brittle layer near the hot face. These striated gaps are arranged orderly along the radial direction of the hearth, and each gap has a certain length. Some gaps are arranged in parallel, while some gaps are interlaced to form larger gaps. These striated gaps will not only affect the heat transfer of carbon brick, but also seriously affect the strength of carbon brick. When the brittle layer is in direct contact with molten iron, it is easy for molten iron to sweep away a piece of the front brittle layer due to the high density and large inertia of molten iron.

Fig. 2. Macro morphology of brittle layer in carbon brick. (Online version in color.)

3.2. Micro Characteristics of Brittle Layer in Carbon Brick

The micro analysis results of brittle layer are shown in Fig. 3. The penetration of molten iron is found in front of the brittle layer, which corresponds to the molten iron found on the hot face of carbon brick. The dendritic penetration of molten iron is observed (Fig. 3(a)). The penetration of molten iron shows an obvious direction, from the hot side to the cold side (from the right side to the left side). As presented in Fig. 3, a main channel is formed after molten iron penetrates along the pores of carbon brick under the action of static pressure of molten iron. A secondary channel appears near the main channel due to some pores are connected in carbon brick, and there is a tendency to continue to penetrate around the main channel (Fig. 3(b)). The dendritic penetration of molten iron will expand the original pores in carbon brick, which will make the carbon brick form brittle layer.

Fig. 3. Dendritic penetration of brittle layer in carbon brick. (Online version in color.)

The penetration depth of penetration experiments is depicted in Fig. 4. As shown in the figure, the penetration depth increases with the penetration time. The penetration velocity is relatively high at the beginning, then gradually decreases. The penetration depth is almost unchanged at the last moment of experiment. The lager penetration depth is obtained at higher temperature. The micro analysis results of the penetration experiments are presented in Fig. 5. The penetration of molten iron has entered the interior of carbon brick, and continues to penetrate the interior of carbon brick. A large amount of penetration makes the position of carbon phase in carbon brick replaced by molten iron (Fig. 5(b)), which changes the structure of alternating arrangement of carbon phase and silica phase in the original carbon brick (Figs. 5(c) and 5(d)). This will inevitably change the strength and other performance parameters of carbon brick, leading to the appearance of brittle layer in carbon brick. As shown in the upper right corner of Fig. 5(a), the dendritic penetration of molten iron is also formed in the experiment, which is consistent with the results found in the dissection investigation. This indicates that the dendritic penetration is a key common problem in the formation of brittle layer in carbon brick. What’s more, the dendritic penetration is easier to form at the junction of two phases owing to the pores here are larger than other parts in carbon brick.

Fig. 4. The penetration depth of penetration experiments. (Online version in color.)

Fig. 5. Micro analysis results of penetration experiments. (Online version in color.)

3.3. Cause of Brittle Layer Formation in Carbon Brick

As mentioned above, the formation of brittle layer is closely related to the penetration of molten iron. After the molten iron directly contacts with carbon brick, the molten iron will penetrate into the carbon brick along the pores. The penetration presents a dendritic shape under the action of static pressure of molten iron, and the dendritic penetration is easier to form at the junction of two phases in carbon brick. Once the dendritic penetration is formed, it will continue to penetrate along the main channel to the spatial direction. This will expand the original pores in carbon brick, so the through gap is generated in carbon brick. Moreover, the tapping of BF is periodic in the normal production process, which will cause the frequent fluctuation of molten iron level in hearth. The frequent fluctuation of the liquid level makes the temperature of the hot face of carbon brick change greatly. This will make the carbon brick withstand the influence of thermal stress, which will make the through gap grow and expand. In addition, alkali metal vapor and zinc vapor in BF will enter the gap, react and deposit in the gap, which accelerates the expansion of the gap.¹⁷⁾ When there are enough through gaps, the brittle layer is finally formed. Hence, the penetration of molten iron is the essential reason for the formation of brittle layer.

4. Kinetic Analysis of Dendritic Penetration of Molten Iron in Carbon Brick

4.1. Mechanism of Dendritic Penetration of Molten Iron

The dendritic penetration of molten iron is the main reason for the formation of brittle layer. The mechanism of dendritic penetration of molten iron is shown in Fig. 6. The penetration occurs under the action of pressure. The molten iron penetrates along the pores inside the carbon brick, the dendritic penetration is formed. There are three paths for each branch of dendritic penetration. The first path is almost vertical along the cold side, the penetration depth of this path is the maximum, the penetration of this path is the basic condition for other penetrations. The second path becomes narrow enough to prevent the further penetration, the penetration depth of this path is the minimum. While, the third path changes the direction of penetration, the final penetration even points to the hot side. Although, the penetration depth of this path is not the maximum, it is extremely destructive to carbon brick owing to the elongation of penetration in this path is relatively large. Moreover, the dendritic penetration is also related to the pore size since a lower pressure is required to penetrate into a larger pore.

Fig. 6. The mechanism of dendritic penetration of molten iron. (Online version in color.)

Actually, the dendritic penetration is formed in three-dimensional space although Fig. 6 is two-dimensional, which will lead to the penetration in each direction of carbon brick, and finally lead to the formation of brittle layer. Therefore, the elongation of penetration is proposed to evaluate the penetration behavior:

  

$$\phi =\sum _{i=\mathrm{1....}n}\frac{S_i}{L_i}$$(1)

where φ denotes the elongation of penetration; i is a main branch of the dendritic penetration; S_i represents the sectional area of the end of dendritic penetration perpendicular to the direction i, mm²; L_i refers to the penetration depth along the i direction, mm.

As described in Eq. (1), the elongation of penetration increases with the sectional area of the end of dendritic penetration, so the effect of the third path is relatively large. The elongation of penetration is generally 0.3–0.5, the carbon brick will pulverize when it exceeds 0.7. The destructive effect of penetration on carbon brick will be strengthened with the increase of the elongation of penetration. Furthermore, the formation of elongation is related to the penetration velocity and the maximum penetration depth, so the kinetic model should be established.

4.2. Kinetic Model of Dendritic Penetration of Molten Iron

The penetration of molten iron is related to many factors. Properties of molten iron (surface tension and viscosity) and properties of carbon brick (pore size and pore structure) will affect the penetration depth and penetration velocity of molten iron. The penetration will be affected by the contact angle as well. The kinetic model should be established to explore the penetration process. However, the pore shape of carbon brick has great influence on the model. In the current study, the pores in carbon brick are approximately regarded as rectangular to clarify the penetration behavior of molten iron.

The model is established based on the following assumptions:^18,19) (1) The pores in carbon brick are approximately regarded as rectangular; (2) The pores have sufficient depth in carbon brick; (3) The pore size is the same and the distribution is uniform in carbon brick; (4) The carbon content of molten iron is saturated, there is no dissolution of carbon during the penetration. Namely, the properties of the molten iron are unchanged, and the pore structure in carbon brick remains unchanged.

When penetration does not occur, the interface between molten iron and carbon brick should be as shown in Fig. 7(a). A meniscus on the pore is taken as a micro element for force analysis as presented in Fig. 7(b). The meniscus will be subject to the pressure of hot air, static pressure of molten iron, the residual pressure in the pore and the pressure generated at the meniscus. When the penetration does not occur, a balance should be maintained between all pressures:²⁰⁾

  

$$P_h+P_m=P_r+P_b$$(2)

where P_h P_m P_r P_b are the pressure of hot air, static pressure of molten iron, the residual pressure in the pore and the pressure generated at the meniscus, respectively, Pa.

Fig. 7. Force analysis model of the meniscus. (Online version in color.)

The pressure of hot air and the residual pressure in the pore are relatively smaller. So, whether the penetration occurs depends on the relative relationship between the static pressure of molten iron and the pressure generated at the meniscus. What’s more, the depth of salamander is a fixed value in hearth, the change of liquid level fluctuation can be ignored, so the static pressure of molten iron is constant for a certain BF.^21,22) Therefore, the situation depends on the pressure generated at the meniscus. The essence of the meniscus is the confrontation between the cohesion of molten iron itself and the adhesion between molten iron and carbon brick. The cohesive force of molten iron is a manifestation of its cohesive effect.²³⁾ The adhesion between molten iron and carbon brick exists due to the wetting between molten iron and carbon brick.^24,25) The maximum pressure that the meniscus can withstand depends on the relatively small one of the two actions.

(1) The point on the meniscus will be torn when the cohesion force of molten iron is small, then the penetration will occur.

As shown in Fig. 7(b), the static pressure of molten iron at point A on the meniscus is (the direction of force is to point out of the arc along the radius direction OA):

  

$$\rho gh+\rho grcos{\alpha }_A$$(3)

where ρ refers to the density of molten iron, kg/m³; g corresponds to the acceleration of gravity, m/s²; h denotes the depth of salamander in hearth, mm; r refers to the radius of curvature of the meniscus, mm; α_A is the angle between the point of the meniscus and the vertical direction, °.

The horizontal component of the force is (ρgh+ρgr cosα_A)×sinα_A, the vertical component of the force is (ρgh+ρgr cosα_A)×cosα_A. In the vertical direction, the shear of the meniscus by the static pressure of molten iron is limited due to the small height difference, so the horizontal stretching is the main reason for the tear of the meniscus. The accumulation of the force of molten iron in the horizontal direction can be calculated by integration:²⁴⁾

  

$$\underset{0}{\overset{\alpha }{\int }}(\rho gh+\rho grcos\alpha )\times sin\alpha \times lr(1-cos\alpha )d\alpha$$(4)

The result of the integration is:

  

$$\rho ghrl\times [{(1-cos\alpha )}^2/2+r/h\times (1+2{cos}^3\alpha -3{cos}^2\alpha )/6]$$(5)

where α corresponds to the angle between the whole meniscus and the vertical direction, °; l is the length of pore, mm.

In the actual production, there is r<<h, then Eq. (5) can be simplified as:

  

$$\rho ghrl\times {(1-cos\alpha )}^2/2$$(6)

For the wetting angle and triangle in Fig. 7(b), there are the following relationships:

  

$$\beta =\alpha +\pi /2$$(7)

  

$$sin\alpha =d/2r$$(8)

where β corresponds to the contact angle between molten iron and carbon brick, °; d is the width of pore, mm.

Equation (9) can be obtained from Eqs. (7) and (8):

  

$$r=-d/2cos\beta$$(9)

The accumulation of the force of molten iron in the horizontal direction can be obtained by Eqs. (4), (6) and (9):

  

$$-\rho ghdl\times {(1-sin\beta )}^2/4cos\beta$$(10)

The condition that it is not penetrated by molten iron is:

  

$$-\rho ghdl\times {(1-sin\beta )}^2/4cos\beta \le \sigma l$$(11)

where σ refers to the surface tension of molten iron in hearth, N/m.

(2) The static pressure of molten iron will overcome the pressure generated at the meniscus when the adhesion force between molten iron and carbon brick is small, then the penetration will occur.

The pressure generated at the meniscus can be expressed as:²⁰⁾

  

$$P_b=\sigma \times (1/r_d+1/r_l)$$(12)

where r_d r_l are the radius of curvature of the meniscus along the pore width, the radius of curvature of the meniscus along the pore length, respectively, mm.

Equation (12) can be simplified due to r_d<<r_l:

  

$$P_b=\sigma \times 1/r_d$$(13)

Equation (13) can be obtained from Eqs. (9) and (13):

  

$$P_b=-2\sigma cos\beta /d$$(14)

The condition that it is not penetrated by molten iron is:

  

$$\rho gh\le -2\sigma cos\beta /d$$(15)

Then, the cohesion force of molten iron, the adhesion force between molten iron and carbon brick are compared. Equations (11) and (15) are transformed to obtain:

  

$$hd\le -2\sigma cos\beta /\rho g\times 2/{(1-sin\beta )}^2$$(16)

  

$$hd\le -2\sigma cos\beta /\rho g$$(17)

The right side of Eq. (16) is significantly larger than the right side of Eq. (17), which indicates that the adhesion force between molten iron and carbon brick is relatively small. Therefore, the penetration of molten iron in carbon brick is caused by the adhesion force reaching the limit first. The key to prevent the penetration is to control the adhesion force between molten iron and carbon brick.

(3) The pores in carbon brick can be simplified from rectangle to circle in order to obtain the maximum penetration depth of molten iron. The pore structure is simplified to be a cylindrical capillary, the length and width of the pore are the diameter of the cylinder. Then, the penetration model is simplified and easy to be evaluated.

The kinetics of penetration can be evaluated by the penetration velocity:²⁸⁾

  

$$d{D}_P/dt=R^2/8\eta D_P\times (P_h+P_m+2\sigma cos\beta /R-\rho g{D}_P)$$(18)

where D_P represents the penetration depth of molten iron, mm; t refers to the penetration time, s; R corresponds to the radius of cylindrical pores, mm; η denotes the viscosity of molten iron, Pa·s.

While, the pores are not always vertical in actual carbon brick, the pore structure in carbon brick is usually complex. So, the labyrinth coefficient is introduced to modify the equation. The labyrinth coefficient is related to the specific pore distribution in the actual carbon brick. Some carbon bricks have Z-shaped pore structure, some have S-shaped pore structure, and some have other shapes. The specific value of labyrinth coefficient is also different. Here, the empirical formula of labyrinth coefficient is employed:²⁸⁾

  

$$\zeta =0.04+0.238\epsilon$$(19)

where ζ refers to the labyrinth coefficient; ε corresponds to the apparent porosity of carbon brick, %.

Equation (18) is refined as:

  

$$d{D}_P/dt=R^2/8\eta D_P\times [\varsigma \times (P_h+P_m+2\sigma cos\beta /R)-\rho g{D}_P]$$(20)

The maximum penetration depth of molten iron can be calculated by making the penetration velocity zero:

  

$$D_P=(0.04+0.238\epsilon )\times [(P_h+P_m)/\rho g+2\sigma cos\beta /\rho gR)]$$(21)

The penetration velocity can be evaluated through Eq. (20). The penetration velocity is relatively high at the beginning, then gradually decreases, which is consistent with the results of the penetration experiment as Fig. 4. The maximum penetration depth at 1500°C is calculated to be 1206 μm according to Eq. (21), which is smaller than the experimental result. The penetration will be affected by the contact angle at the interface, further penetration will take place if the contact angle decreases.

Therefore, the maximum penetration depth of molten iron in carbon brick can be evaluated through the properties of carbon brick, the properties of molten iron, BF design and operation parameters. Moreover, the measures to control the dendritic penetration of molten iron can be proposed to reduce the influence of brittle layer,^29,30) so the erosion of carbon brick can be alleviated. Last but not the least, the pore structure in the actual carbon brick is very complex, the actual carbon content in molten iron is undersaturated, and more work should be done to explore the penetration behavior.

5. Conclusions

In order to explore the formation mechanism of brittle layer, characteristics of brittle layer in carbon brick were investigated based on the dissection investigation of actual BF and penetration experiments. Our findings are as follows:

(1) The brittle layer is observed on the hot face of carbon brick, there are a lot of striated gaps in the brittle layer near the hot face, these striated gaps will not only affect the heat transfer of carbon brick, but also seriously affect the strength of carbon brick.

(2) In the penetration experiments, the penetration depth increases with the penetration time, the lager penetration depth is obtained at higher temperature. The penetration velocity is relatively high at the beginning, then gradually decreases. The penetration depth is almost unchanged at the last moment of experiments.

(3) The dendritic penetration of molten iron has been found in both dissection investigation and penetration experiments, the dendritic penetration of molten iron is the essential reason for the formation of brittle layer. There are three paths for each branch of dendritic penetration, the elongation of penetration is proposed to evaluate the penetration behavior, the penetration of the third path is extremely destructive to carbon brick.

(4) Whether the penetration occurs depends on the confrontation between the cohesion of molten iron itself and the adhesion between molten iron and carbon brick, the penetration of molten iron in carbon brick is caused by the adhesion force reaching the limit first. The maximum penetration depth of molten iron can be calculated based on the penetration model through the properties of carbon brick, the properties of molten iron, BF design and operation parameters.

Acknowledgments

The Project Supported by Tangshan Science and Technology Research and Development Plan (22130203H) and Open Fund of The State Key Laboratory of Refractories and Metallurgy (G202005).

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