effects of temperature, refractory composition and mass

$: Effects of Temperature, Refractory Composition and Mass$
ISIJ International, Vol. 57 (2017), No. 4

© 2017 ISIJ697

ISIJ International, Vol. 57 (2017), No. 4, pp. 697–705

* Corresponding author: E-mail: [email protected]: http://dx.doi.org/10.2355/isijinternational.ISIJINT-2016-583

1. Introduction

The reaction between refractories and iron or steelmak-ing slag, namely, corrosion, is one of the main forms of chemical damage of fired refractories used in ironmaking and steelmaking processes. For example, in the steelmaking ladle, the lining structure of the slag line refractory gener-ally comprises a wear refractory (in many cases, MgO–C brick, etc.), safety brick (in almost all cases, two layers) and the steel shell. Taking the corrosion behaviour of slag line refractories in the steelmaking ladle as an example, it is necessary to consider the reaction between the wear refrac-tory and the slag in stable normal operation. However, if the wear refractory has fallen away for some reason, it is necessary to consider the reaction between the slag and the safety bricks. At this time, it is very important to under-stand the reaction behaviour between several types of slag and refractories, such as the wear refractory and the safety bricks, in order to establish countermeasures to prevent cor-rosion of the refractories by slag and to predict the corrosion rate in advance.

In the past, there have been many studies on the reac-tion between slag and refractories.1–19) To introduce some examples of research to date, the main objects of research were the reaction between steelmaking slag and MgO system refractories such as MgO–C brick (mainly wear

Effects of Temperature, Refractory Composition and Mass Transfer Rate on Corrosion Rate of Al2O3–SiO2 System Bricks into CaO–SiO2–Al2O3–MgO Slag

Yuta HINO,* Hisahiro MATSUNAGA and Keiji WATANABE

Slag & Refractories Research Dept., Steel Research Laboratory, JFE Steel Corporation, Chiba, 260-0835 Japan.

(Received on October 4, 2016; accepted on December 6, 2016)

The corrosion rate of Al2O3–SiO2 system bricks, which are practical fired bricks, into CaO–SiO2–Al2O3–MgO slag was investigated, and the effects of temperature, refractory composition and mass transfer rate in slag on the corrosion rate of the bricks were discussed. As a result, the corrosion rate decreased as the alumina content in the brick increased. The corrosion rate increased with increasing temperature. The corrosion rate decreased with decreasing rotational speed, that is, mass transfer of Al2O3 and SiO2 in the slag phase. Corrosion proceeded at the rate of 1.3 mm/min even when the rotational speed of the refrac-tory sample was 0 rpm. Based on an analysis of the experimental results from the viewpoint of transport phenomena, under the conditions of this study, it is estimated that the reaction proceeds under a condi-tion in which natural convection is rate-controlling for mass transfer when the rotational speed is lower than 44 rpm, in a transition region, that is, a mixed condition of natural convection and forced convection, at speeds of 44–133 rpm, and under a condition in which forced convection is rate-controlling when the rotational speed is over 133 rpm.

KEY WORDS: corrosion; fired brick; temperature; mass transfer; natural convection; forced convection.

refractories) in reports by Z. Yu et al.11) and K. Matsui et al.1) and the reaction between single-component materials and slag, for example, alumina ceramic refractories and steelmaking slag, represented by the report by K. Sandhage et al.,8,9) among others.

However, there are few examples of reports on the reac-tion behaviour between practical fired refractories such as Al2O3–SiO2 system bricks, which are used as safety bricks, and multi-component slags, as represented by steelmaking slag, in spite of the importance of this subject. In particular, there are virtually no examples of reports on the wear rate of Al2O3–SiO2 system fired bricks in the presence of slags with comparatively high concentrations of FeO or MnO, such as the slag at tapping of rimmed steels.

In addition, the effects of operational factors such as temperature and the stirring condition of the slag and mol-ten metal, and the effect of the refractory material, namely, the chemical composition of the refractory on the corrosion rate of the refractory, which is the object of this study, have not yet been elucidated. In the future, it is thought that a more quantitative analysis of these factors will be needed in order to clarify the phenomena responsible for corrosion behaviour.

From the above, for the purpose of clarifying the basic factors which affect the reaction rate between steelmak-ing slag and bricks, the reaction rate of Al2O3–SiO2 bricks and CaO–SiO2–Al2O3–MgO slag was investigated, and the effects of temperature, the chemical composition of the refractory and the slag mass transfer rate (mass transfer


© 2017 ISIJ 698

of the slag phase) on the corrosion rate of the bricks were studied from the viewpoint of reaction kinetics.

2. Experimental Method

The experimental method will be explained in this chap-ter. Figure 1 shows a schematic diagram of the experimen-tal method. Metal and slag were introduced into a MgO crucible and melted by heating to the experimental tem-perature. After melting, a refractory sample, which had been processed to a cylindrical shape (φ40 mm × 160 mm), was set directly above the MgO crucible and preheated by hold-ing for 20 min. Then, the refractory sample was immersed in the metal, and the refractory was reacted with the molten slag by rotating the sample at a certain rotational speed for a fixed time. At this time, the temperature during the experi-ment was controlled with a thermocouple, which was set on the wall of the MgO crucible (the temperature of the metal was assumed to be the same as that of the thermocouple). After the experiment, the refractory sample was taken out and the amount of reaction with the slag was evaluated from the change in the sample diameter. In addition, with some samples, the vicinity of the refractory/slag interface before and after the experiment was observed by scanning electron microscopy (SEM), and the composition of the slag and refractory phases was checked by EDX.

Table 1 shows the experimental conditions. As the metal, 1.8 kg of industrial pure iron was melted. The temperature in this study was varied between 1 823 K and 1 923 K so as to investigate the effect of temperature on the corrosion rate of the refractory. The rotational speed of the refractory sample was varied between 0 rpm and 300 rpm for the purpose of investigating the effect of the mass transfer rate of the slag phase on the corrosion rate. The holding time of the sample immersed in the slag and metal was set to 4 min.

The slag used in this study was a synthetic slag that was prepared by compounding various high-grade reagents (CaO, SiO2, Al2O3 and MgO (over 99.9%)). The composi-tion of the slag is also shown in Table 1.

Table 2 shows a list of the refractories used in this study. These samples are all general-purpose fired bricks. Two

types of high-alumina bricks, which are categorized as H–1 and H–3 in JIS,20) fire clay having an Al2O3 content of 40% class and agalmatolite bricks were used.

3. Experimental Results

Figure 2 shows a photograph of a refractory sample after the experiment. A decrease of sample diameter due to corrosion was observed at the position of contact with the

Fig. 1. Experimental apparatus.

Table 1. Experimental conditions.

Metal Weight 1.8 kg

SlagComposition

CaO 50 wt%

SiO2 20 wt%

Al2O3 25 wt%

MgO 5 wt%

Weight 0.5 kg

RefractoryMaterial Al2O3–SiO2 system brick

Shape φ 40 mm × 160 mm

Temperature 1 823 K–1 923 K

Rotational number 0–300 rpm

Holding time 1–4 min

Table 2. List of refractories used in this study.

H1 H3 Fire clay Agalmatolite

Type of brick

High alumina

High alumina Fire Clay Pyrophylite

SiO2 12.7 % 36.5 % 51.9 % 81.4 %

Al2O3 86.3 % 62.7 % 43.3 % 18.4 %

CaO 0.6 % 0.3 % 0.3 % 0.1 %

MgO 0.4 % 0.5 % 0.2 % 0.1 %

Phases

Corundum Mullite Mullite SiO2 (quartz)

Mullite Corundum SiO2 (Cristbalite)

SiO2 (quartz)

SiO2 (Cristobalite) Mullite

Apparent porosity 21.7% 22.7% 16.0% 18.0%

Bulk density 2 710 kg/m3 2 370 kg/m3 2 290 kg/m3 2 200 kg/m3

Fig. 2. Photograph of refractory sample after experiment.


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molten slag. Based on the results of the measurement of the sample diameter before and after the experiment, the change of sample diameter, as shown in Eq. (1), was defined as the “degree of corrosion,” and the corrosion rate was defined as shown in Eq. (2) and calculated. The obtained corrosion rates were evaluated under each condition.

∆D D Df= −0 .............................. (1)

∆∆ ∆D

t

D D

tf=

−0 .............................. (2)

where, D0 (mm) means sample diameter before the experi-ment, and Df (mm) means sample diameter at the corrosion zone after the experiment. Δt (min) means the elapsed time. The sample diameter at the corrosion zone after the experi-ment was determined as follows: First, the refractory sample was divided into two equal parts in the height direction. The diameter of corroded sample at the corrosion zone was then measured at 10 mm intervals, and the average value of the diameter was adopted as a Df. Figure 3 shows the comparison of the corrosion rates of the respective refrac-tory samples.

A decreasing tendency in the corrosion rate could be seen as the Al2O3 content in the bricks increased. A list of the mineral phases of the bricks used as samples in this study is shown in Table 2. Here, as a noteworthy phenomenon, the corrosion rate tended simply to change monotonously depending on the Al2O3 content, independent of differences in the mineral phases making up the bricks.

Figure 4 shows the relationship between the corrosion rate and the rotational speed of the sample. The corrosion rate decreased with decreasing rotational speed. Further-more, it was found that corrosion proceeded at the rate of 1.3 mm/min even when the rotational speed was 0 rpm.

Figure 5 shows the results of a study of the effect of tem-perature on the corrosion rate. The corrosion rate increased with increasing temperature. Arranging (analysing) these data by a Arrhenius plot, and assuming a linear relation-ship between the results of the analysis, if the apparent activation energy is evaluated from the inclination of the regression line, the value of 331 kJ/mol is obtained. This apparent activation energy was also compared with other reported data. Table 3 shows a list of the apparent activa-tion energies obtained from the corrosion rates of solid Al2O3-based materials (mainly Al2O3 ceramics) into slag, which were evaluated previously,4–6) together with the tem-perature dependence of the diffusion coefficient of Al2O3

in CaO–SiO2–Al2O3–MgO slag.21) The apparent activation energy obtained in this study was similar to the previously-reported values.

From the dependence of the corrosion rate on the rota-tional speed and temperature mentioned above, there is considered to be a strong possibility that the rate-controlling step of the corrosion rate of Al2O3 system refractories in CaO–SiO2–Al2O3–MgO slag (in the range of this experi-ment) is diffusion of Al2O3 or SiO2 in the slag phase. Fur-thermore, the possibility that the temperature dependence of the corrosion rate is attributable to the temperature dependence of the diffusion coefficient or the temperature dependence of the viscosity coefficient of Al2O3 or SiO2 in the slag phase is conceivable.

Fig. 3. Corrosion rates of refractory samples.

Fig. 4. Relationship between corrosion rate and rotational speed of sample.

Fig. 5. Temperature dependence of corrosion rate in Al2O3–SiO2 brick.

Table 3. List of apparent activation energies of corrosion rate of solid Al2O3-based materials and temperature depen-dence of diffusion coefficient.

Slag system E (kJ/mol)

S. Taira et al.CaO–SiO2–Al2O3 338–356

CaO–SiO2–Al2O3–MgO 220–440

Handbook of properties of molten iron and molten slag

CaO–SiO2–Al2O3–MgO (Diffusion of Al2O3)

356

CaO–SiO2–Al2O3–MgO (Diffusion of SiO2)

220–376


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4. Discussion

4.1. Determination of Rate Controlling StepA reaction model was constructed, and the corrosion

behaviour of the Al2O3–SiO2 system bricks was studied from the viewpoint of reaction kinetics in order to analyse the experimental results of this study more quantitatively and explain the results more scientifically.

The reactions taken into consideration in this study are shown in Eqs. (3), (4) and (5).

Al O s Al O in slag2 3 2 3( ) ( )= ..................... (3)

SiO s SiO in slag2 2( ) ( )= ....................... (4)

3 3 22 3 2 2 3 2Al O SiO s Al O in slag SiO in slag⋅ = +( ) ( ) ( ) ... (5)

Generally, the following factors are conceivable as the rate-controlling step of the reaction rate when a solid oxide dissolves in a liquid-phase slag:

1. Chemical reaction at molten slag/solid interface2. Mass transfer of elements or compounds between

solid/liquid interface and bulk slagThe rate-controlling step was studied as follows.Some reports have been noted that the formation of inter-

mediate compounds was observed at the reaction interface in the dissolution reaction of a number of Al2O3 system solid oxides into slag. First, this point was studied. Figure 6 shows the phase diagram of a CaO–SiO2–Al2O3–MgO system (isothermal section at 1 923 K).6) The black circle (point 1) shows the initial slag composition at the start of the experiment, and the white circle (point 2) shows the point at which the slag and the refractory are completely mixed. Both exist as liquid phases at the experimental temperature (1 923 K), and formation of new intermediate compounds cannot be seen. Based on this, in the refractory/slag system observed here, it is considered that reactions in which the refractory simply dissolves in the slag have occurred as shown in Eqs. (3), (4) and (5). Figure 7 shows a photograph of the area around the slag/refractory interface after the experiment in this study. Neither a solid phase, which would be considered to be a reaction product, nor an interfacial layer caused by the reaction was observed. This same phenomenon was also observed with the other types of refractories in this study (see Table 2).

Furthermore, the apparent activation energy estimated in this study from the result of the Arrhenius plot in Fig. 5 (331 kJ/mol) showed a value similar to the temperature dependence of the diffusion coefficient of alumina and silica in the CaO–SiO2–Al2O3–MgO system slag listed in Table 3. Moreover, because the effect of the rotational speed, namely the mass transfer rate of the slag phase (although this is a relative rate) on the corrosion rate of the refractory sample was large in the results in Fig. 4, there is considered to be high possibility that the mass transfer of reaction products between the bulk slag and the reaction interface is the rate-controlling step.

On the other hand, the possibility that the chemical reac-tion at the reaction interface is the rate-controlling step was also examined. First, if the formation of an intermediate compound at the reaction interface were observed, the com-pound-forming reaction would be the rate-controlling step,

but because the formation of an intermediate compound was not observed in this study, this possibility can be rejected.

Next, the reactions shown in Eqs. (3)–(5) were examined. Assuming these reactions were the rate-controlling step, the temperature dependence of the reaction rate, namely, the apparent activation energy, would be expected to be larger than the apparent activation energy if mass transfer in the slag phase were the rate-controlling step.22) The temperature dependence (apparent activation energy) of the dissolution rate of alumina into CaO–SiO2–Al2O3–MgO system slag is 440 kJ/mol at most, and the temperature dependence of the dissolution rate of silica was estimated as 234 kJ/mol from the report by B. N. Samadder et al.17) Further, the apparent activation energy of the dissolution rate of mullite into a slag, which is shown in Eq. (5), has been estimated as 52–396 kJ/mol.18,19) In all the reported values mentioned above, it was assumed that the rate-controlling step of the reaction rate was the mass transfer of the object oxide between the bulk slag and the reaction interface. The apparent activation energy obtained in this study is in the range of these reported values. From this, the possibility that a chemical reaction at the solid/liquid interface is the rate-controlling step is considered to be extremely low.

Therefore, in the following, the dissolution rate of the

Fig. 6. Phase diagram of CaO–SiO2–Al2O3–MgO system at 1 923 K calculated by thermodynamic calculation.

Fig. 7. Photograph of area around interface between slag and refractory sample.


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refractory evaluated here was studied assuming that mass transfer of Al2O3 and SiO2 between the solid/liquid interface and the bulk slag is the rate-controlling step in all the reac-tions shown by Eqs. (3)–(5).

4.2. Kinetics Analysis by Reaction Model4.2.1. Outline of Model and Assumptions

A schematic illustration of the reaction model discussed in this study is shown in Fig. 8.

The assumptions used in analysing the reaction rates of these reactions (i.e., in construction of the reaction model) are as follows.

a) Because the aim of this research was to investigate the dissolution reaction of Al2O3–SiO2 system refrac-tories into CaO–SiO2–Al2O3–MgO system slag, it was assumed that the refractories comprised only Al2O3, SiO2 and mullite (effects of impurities were negligible).

b) Based on assumption a), it was assumed that the corrosion rate of the refractories is the sum of the corrosion rates of Al2O3, SiO2 and mullite.

c) Based on the results in the previous section, a bound-ary layer model was applied to the analysis of the corrosion rate, and the rate-controlling step was assumed to be the mass transfer of Al2O3 and SiO2 between the bulk slag (liquid phase) and the solid/liquid interface.

d) The Al2O3 and SiO2 concentrations (liquid phase formed by chemical reaction; denoted by the asterisk * in the figure) at the slag/refractory reaction interface were assumed to be pure.

Numerical analyses were carried out based on these assumptions.

4.2.2. Reaction EquationsThe reaction rate equations used in this study are

explained in this section.First, if it is assumed that the amount of weight reduction

of the refractory due to the decrease of sample diameter per unit time is equal to the amount of reaction, Eq. (6) can be derived from the mass balance.

γ π ρ ε= ⋅ −( ) ⋅2 1rldr

dtR ....................... (6)

where, γ (kg/s) is the amount of mass weight reduction of the refractory per unit time, ρR (kg/m3) is the bulk density of the refractory material, l (m) is the immersion depth of the refractory sample into the molten slag, r (m) is the radius of the refractory sample and ε is the porosity of the refractory (− ).

On the other hand, the dissolution reaction rates shown by Eqs. (3)–(5) (mass transfer rates in molten CaO–SiO2–Al2O3–MgO slag) can be expressed as follows for Al2O3, SiO2 and mullite.

N

Al O

Al O Al Orl

k X X

Al OA

A M

slag

Al Al O A

2 3

2 3

2 3

2 3 2 3

2=( )

( ) + ( )⋅ −

%

% %

*

π ρ

ll O2 3( ) ....... (7)

NSiO

SiO SiOrl k X XSiO

S

S M

slag Si SiO SiO2 2 2

2

2 2

2=( )

( ) + ( )⋅ −( )%

% %*π ρ

.......................................... (8)

NAl O

Al O Al Orl

k X

MulliteM

A M

slag

Al Al O

=( )

( ) + ( )⋅ −

%

% %

*

2 3

2 3 2 3

2

2 3

π ρ

XX

SiO

SiO SiOrl k X X

Al O

M

S M

slag Si SiO Si

2 3

2

2

2 2

2

( )+

( )( ) + ( )

⋅ −%

% %*π ρ OO2( )

.......................................... (9)

where, (%Al2O3)A is the alumina (corundum) particle con-tent in the refractory, (%SiO2)S is the silica particle content in the refractory, (%Al2O3)M is the alumina content con-tained in the mullite phase in the refractory and (%SiO2)M is the silica content contained in the mullite phase in the refractory, and N (kg/s) shows the reaction rates (mass transfer rates) of each component. X is the percentage con-centration of each element, kAl (m/s) is the mass transfer coefficient of Al2O3 in slag, kSi (m/s) is the mass transfer coefficient of SiO2 in slag and ρslag (kg/m3) is the density of slag. Combining Eqs. (7), (8) with (9), the overall reaction rate can be expressed by Eq. (10).

N N N

rl k X X k X

Al O SiO Mullite

slag Al Al O Al O Si Si

2 3 2

2 3 2 32

+ +

= ⋅ −( ) +π ρ *OO SiOX2 2

* −( ){ } ... (10)

From Eqs. (6)–(10), the overall reaction amount is shown by Eq. (11).

γ γ γ= + = + +Al O SiO Al O SiO MulliteN N N2 3 2 2 3 2 ....... (11)

At this time, from assumption d) in the previous section, XAl O2 3

* and XSiO2

* were assumed to be the unity.The mass transfer coefficients of Al2O3 and SiO2 in the

mass transfer rate equations were calculated by consider-ing the JD-factor. The JD-factor for the cases of a turbulent

Fig. 8. Schematic illustration of reaction model discussed in this study.


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flow and a laminar flow can be expressed as Eqs. (12) and (13), respectively.23–25) Here, the critical Reynolds number is approximately 15 000.

J St ScD = ⋅ = −

2

3 0 20 037. .Re .................. (12)

J St ScD = ⋅ = −2

3 0 50 0664. .Re ................. (13)

where, St is the Stanton number, Sc is the Schmidt number and Re is the Reynolds number. These can be expressed by Eqs. (14)–(16) by using the mass transfer coefficient k (m/s), representative length d (m), diffusion coefficient D (m2/s), density of slag ρslag (kg/m3), relative velocity between a solid and liquid v (m/s) and viscosity of slag μ (Pa·s).

Stk

v= ................................... (14)

ScDslag

=µ

ρ .............................. (15)

Re =ρµ

slagvd .............................. (16)

Table 4 shows a list of the values used in the calculation of non-dimensional numbers.26–33) In this study, the immer-sion depth of the refractory sample in the slag was used as the representative length. The value of the diffusion coeffi-cient was determined by calculation from the inter-diffusion coefficients of Al2O3–CaO and Al2O3–SiO2 in Al2O3–SiO2–CaO–MgO system slag.26,27)

Based on the above, the corrosion rate of the Al2O3–SiO2 system refractory was calculated from Eqs. (6)–(16), and the results of this calculation were compared with the experi-mental results.

4.3. Comparison of Calculation Results and Experi-mental Results

In the following, the comparison of the calculation results and the experimental results is discussed.

Figure 9 shows the comparison of the calculation results and the experimental results for each refractory. Figure 10 shows the same comparison for the temperature dependence of the corrosion rate.

In both figures, the calculation results were approximately consistent with the experimental results, and it was found

that the effects of the refractory material and temperature on the corrosion rate of Al2O3–SiO2 system bricks can substan-tially be reproduced by these calculations.

Here, the calculation results in Fig. 9 will be considered in more detail. Among the mass transfer rate equations in the reaction model constructed in this study, Fig. 11 shows the comparison of the calculation results for the mass trans-fer rate of Al2O3 with the results for SiO2. In these calcula-tions, it was found that the mass transfer rate of SiO2 was about 2.0 times larger than that of Al2O3. It is presumed that this difference is attributable to the difference of the mass transfer coefficients of the various components in the slag. When the respective mass transfer coefficients were com-pared, it was found that the mass transfer coefficient of SiO2 in slag was high, being 2.0 times larger than that of Al2O3. In other words, it is thought that the corrosion rate increased when the SiO2 content in the brick increased because SiO2 dissolves and diffuses in molten slag more readily. As the rate-controlling step of the corrosion rate of the refractory in this study, it was also determined that the mass transfer of Al2O3 and SiO2 between the reaction interface and the bulk slag was rate-controlling for the reactions described in Eqs. (3)–(5). In this study, it was found that the calculation results were approximately consistent with the experimental

Table 4. List of properties used in calculation of non-dimensional numbers.

Terms Symbol Unit Value

Viscosity of slag μ (Pa∙s) 0.071

Difuusion coefficient D =D0∙exp(−Ea/RT)

Al2O3D0 (m2/s) 0.000537

Ea (kJ/mol) 251

SiO2D0 (m2/s) 0.0095499

Ea (kJ/mol) 293

Density of slag ρslag (kg/m3) 2 700

Representative length d (m) 0.02

Fig. 9. Comparison of calculation results and experimental results of corrosion rates of bricks.

Fig. 10. Comparison of calculation results and experimental results of temperature dependence of corrosion rate.


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results for the corrosion rates of various refractories with different Al2O3 contents, and the mass transfer rate of SiO2 was larger than that of Al2O3. Based on these facts, it is pre-dicted from the calculations that the overall corrosion rate will increase if the SiO2 content in the refractory increases. Thus, from the results of this analysis, it can be thought that the corrosion rate of Al2O3–SiO2 bricks into CaO–SiO2–Al2O3–MgO slag is determined simply by the sum of the mass transfer rates of Al2O3 and SiO2. From above discus-sion, assumptions b) and c) are considered valid.

Furthermore, in this study, the Al2O3 and SiO2 at the slag/refractory reaction interface were assumed to be pure at the instant of decomposition, and these substances dissolved into the molten slag. Concerning the decomposition reaction of mullite, the Al2O3 and SiO2 at the slag/refractory reaction interface were also assumed to be pure in this reaction. The amount of corrosion of each type of refractory was calcu-lated based on these assumptions. The results of the calcu-lations were similar to the experimental results. Because it was possible to reproduce the corrosion rates of Al2O3–SiO2

system refractories with different mineral phases by calcula-tion, assumption d) can also considered to be basically valid.

The results of a detailed comparison of the temperature dependence of the corrosion rates in the calculation results and experimental results are shown in Fig. 12. The physical properties which change accompanying changes in tem-perature are the viscosity coefficient and the diffusion coef-ficient. Therefore, calculations were made for three cases: (1) the case of changing only the viscosity of the slag, (2) the case of changing only the diffusion coefficient and (3) the case of changing both the viscosity coefficient and the diffusion coefficient.

As a result of those calculations, it was found that the effect of the viscosity coefficient on the temperature depen-dence of the corrosion rate is essentially nil, and it was confirmed that the corrosion rate can be explained almost entirely by the temperature dependence of the diffusion coefficient. It may be noted that the temperature dependency of the inter-diffusivities of CaO–Al2O3 and CaO–SiO2 in CaO–SiO2–Al2O3–MgO system slag have roughly similar

Fig. 11. Comparison of mass transfer rates of alumina and silica calculated by reaction model in this study.

values of 251 kJ/mol and 292 kJ/mol, respectively.21) From this, however, it was not possible to distinguish whether the temperature dependence of the diffusion coefficient of Al2O3 or that of SiO2 was the controlling factor for the temperature dependence of the corrosion rate in this study.

Figure 13 shows the comparison of the calculation results and the experimental results for the relationship between the corrosion rate and the sample rotational speed. In both cases, the calculation results showed good agreement with the experimental results when the rotational speed was over 150 rpm. Under this condition, it can be understood that the rate-controlling step of the corrosion rate is the mass transfer of Al2O3 and SiO2 in slag.

However, below the rotational speed of 150 rpm, the calculation results were no longer consistent with the experi-mental results. In particular, at 0 rpm, the calculated corro-sion rate was 0 mm/min. As the reason for this, since the calculations in this analysis were made using a mass transfer rate equation that assumed a condition of forced convec-tion, this result indicates that it is necessary to consider a

Fig. 12. Results of detailed analysis of temperature dependence of corrosion rate.

Fig. 13. Comparison of calculation results and experimental results of relationship between corrosion rate and rota-tional speed.


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different reaction mechanism when the rotational speed is less than 150 rpm.

4.4. Reaction Mechanism at Low Rotational SpeedFirst, therefore, the reaction behaviour at 0 rpm was dis-

cussed. In this condition, it is thought that the rate-control-ling step is the mass transfer of Al2O3 and SiO2 in slag by natural convection. The mass transfer coefficient under natu-ral convection can be calculated from Eqs. (17)–(19).23–25)

Sh Gr Sc= ⋅0 653 0 25 0 25. . . ..................... (17)

Shkd

D= ................................. (18)

Gr

g dR slag slag=

− ⋅ ⋅ρ ρ ρ

µ

3

2.................. (19)

The corrosion rate at the rotational speed of 0 rpm was recalculated by applying these equations and the above-mentioned Eqs. (6)–(10). As results of those calculations, a comparison of the experimental results and calculation results of the corrosion rate is shown in Fig. 14. The experimental results and calculation results are substantially in agreement. Accordingly, these calculations clarified the fact that the mass transfer of Al2O3 and SiO2 in slag under natural convection becomes the rate-controlling step when the rotational speed of the sample is 0 rpm.

Next, the phenomena that occur under the conditions between 0 and 150 rpm were examined. In considering the reaction behaviour under these conditions, the authors hypothesized the existence of a transition region between natural convection and forced convection (i.e., a mixed condition in which both natural and forced convection exist simultaneously).

H. Tanaka et al. carried out a heat transfer analysis of the flow in a vertical pipe under conditions of natural and forced convection.34) In that research, the existence of a transition region between natural convection and forced convection was assumed. The boundary condition for the transition from natural convection to the transition region was expressed by Eq. (20), and that from the transition region to forced convection was expressed by Eq. (21).

Re = 16 5

8

21. Gr ............................ (20)

Re = 50

8

21Gr.............................. (21)

Originally, these equations define the boundary condi-tions among natural convection, the transition region and forced convection with regard to heat transfer. However, in transfer phenomena theory, an analogy between heat trans-fer and mass transfer exists. Therefore, in this study, the authors attempted to calculate the transition region condi-tions, assuming that Eqs. (20) and (21) are also applicable to the analysis of mass transfer.

Figure 15 shows the result of the derivation of the transi-tion region by applying Eqs. (20) and (21) on the previous Fig. 13. The rotational speed corresponding to the threshold between natural convection and the transition region was

calculated to be 44 rpm, and the threshold between the transition region and forced convection was calculated to be 133 rpm. From the above, under the experimental conditions in this study, it is estimated that the reaction in which mass transfer of Al2O3 and SiO2 in slag is the rate-controlling step will proceed under the condition of natural convection at rotational speeds lower than 44 rpm, under the condition of the transition region at speeds of 44–133 rpm and under the condition of forced convection at speeds over 133 rpm.

5. Conclusions

The reaction rate (corrosion rate) between Al2O3–SiO2 system bricks, which are general-purpose fired bricks, and CaO–SiO2–Al2O3–MgO system slag was investigated, and the effects of temperature, the composition of the refractory and the mass transfer rate in slag (mass transfer of the slag phase) on the corrosion rate of the bricks were investigated.

(1) The corrosion rate decreased as the Al2O3 content in the brick increased. The corrosion rate changed approxi-mately linearly, depending simply on the Al2O3 (Al2O3/(Al2O3+SiO2)) ratio, and did not depend on differences in the component phases of the bricks.

(2) The effect of temperature on the corrosion rate of Al2O3–SiO2 system bricks was clarified quantitatively.

(3) The corrosion rate decreased with decreasing sample rotational speed, that is, decreasing mass transfer of

Fig. 14. Comparison of calculation results and experimental results of corrosion rate at 0 rpm.

Fig. 15. Result of derivation of transition region (shown on Fig. 13).


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Al2O3 and SiO2 in the slag phase. However, corrosion pro-ceeded at the rate of 1.3 mm/min even when the rotational speed of the refractory sample was 0 rpm. Regarding this phenomenon, it is thought that the reaction proceeds under a condition of natural convection at low rotational speeds.

(4) From an analysis of the experimental results from the viewpoint of transport phenomena theory, with the experimental system in this study, it is considered that the reaction proceeds under a condition in which natural convection is rate-controlling for mass transfer when the rotational speed is lower than 44 rpm, in a transition region between natural and forced convection when the rotational speed is 44<R≦133 rpm and under a condition in which forced convection is rate-controlling for mass transfer when the rotational speed is over 133 rpm.

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effects of temperature, refractory composition and mass

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