Gas Permeability Evaluation of Granulated Slag Particles Packed Bed during Softening and Melting Stage with Fanning’s Equation

Abstract

Negative effect from low coke rate operation at cohesive zone is obvious because it makes thinning of coke slit thickness. Correct knowledge about gas permeability of cohesive layer is becoming more and more important. In order to precisely understand cohesive behaviour, a softening and melting simulator under rapid heating and quenching conditions was applied for clarify a determinant factor of gas permeability behaviour. To focus on softening and melting behaviour, granulated slag particle bed layer without iron oxide was prepared as packed bed sample layer can show softening and melting. The packed bed slag samples in graphite crucible were rapidly heated up to 1200°C, and then gradually heated up to 1500°C with 10°C/min under inert gas atmosphere and 0.1 MPa load. Gas pressure drop and shrinkage degree of the sample layer were measured during the softening and melting test, and quenched sample was made at certain temperature when the maximum gas pressure drop was measured. The CT observation of the quenched sample provided 3D shape information of gas path shape in sample packed bed. Gas pressure drop was estimated with fanning’s equation with the gas path information. The estimation values were shown positive correlation with measured maximum pressure drop. The CT observation also gave triple line length among molten slag, graphite, and gas. Combination the triple line length and molten slag surface tension could use for evaluation of static force balance when maximum pressure drop obtained.

1. Introduction

Toward to “Zero carbon steel”, suppression of greenhouse gas emission from ironmaking process should be one of the most important issue. Low carbon blast furnace operation¹⁾ is an effective action for mitigation of CO₂ emission from ironmaking. The low carbon operation has many agendas to achieve highly efficient and stable operation as normal operating condition. One of the biggest problems from them is a thinning of coke layer thickness due to decreasing coke charging ratio into blast furnace. Especially at cohesive zone, the coke layer has an important role as coke slit for smooth gas flow through softening and melting region of iron burden layer. When melt from iron burden generates gas impermeable part in the zone, gas can only flow through the coke slit between molten iron ore layers. In this case, the shape of the cohesive zone would has a strong effect on blast furnace operating condition. Therefore, detail knowledge of cohesive zone formation mechanism is essential to deliver the low carbon operation. Iron burden reduction test under load condition^2,3,4) was well developed for understanding of the cohesive zone formation mechanism. This method fits to estimate practical property of iron burden for blast furnace operation. However, the result from this test is too complex to estimate directly the formation mechanism, because it normally includes whole part of iron burden hysteresis from reduction behaviour to softening and melting behaviour. To focus only the deformation behaviour of iron burden’s structure, a novel softening and melting simulator was developed.⁵⁾ The simulator can control temperature of a packed bed sample with rapid heating and rapid quenching over 1000°C/min. This capability can skip reduction reaction temperature range and directly focus on the temperature range of softening and melting behaviour.

In our previous work,⁶⁾ granulated slag particles packed bed was applied to understand the softening and melting behaviour as first step. From the quenched sample’s cross-section observation, the slag packed bed showed maximum pressure drop when the slag particles fused each other and held-up in sample layer as shown in Fig. 1. In this stage, gas pressure drop of sample layer cannot estimate using Ergun’s equation⁷⁾ as shown in Eq. (1), because slag agglomerate didn’t remain particle shape any more.   

$$\frac{\mathrm{\Delta }P}{L}=150\frac{{(1-\epsilon )}^2}{{\epsilon }^3}\frac{\mu u}{{(\phi D_p)}^2}+1.75\frac{(1-\epsilon )}{{\epsilon }^3}\frac{\rho u^2}{\phi D_p}$$(1)

Fig. 1.

Relationship between maximum pressure drop and fusing slag layer formation behavior.⁶⁾

Here, ΔP is the pressure drop, L is the total height of the bed, u is the superficial velocity, μ is the viscosity of gas, ε is the porosity of the bed, φ is the sphericity of the particles in the bed, D_p is the diameter of the volume equivalent spherical particle.

In order to truly understand the cohesive zone formation mechanism, gas permeability evaluation method of this stage is also necessary. Purpose of this study is direct evaluation of gas pressure drop from gas path shape in hold-up slag layer without Ergun’s equation.

2. Experimental Methodology

2.1. Experimental Apparatus

A “softening and melting simulator” can achieve to high speed temperature control over 1000°C/min of sample packed bed by combination of infrared gold image furnace heating and dry-quenching chamber as shown in Fig. 2. The infrared furnace has a cylindrical isothermal area as 35 mm diameter and 40 mm height. A sample holder is designed as 36 mm outer diameter and 43 mm height using a special designed graphite crucible. Temperature distribution in the crucible, 30 mm inner diameter and 40 mm inner height, was confirmed within ±5°C during radiation of infrared. In quenching step for avoid effect of sensible heat from reaction tube, the sample holder can move down to dry-quenching chamber located just below the infrared furnace after stopping of infrared radiation. A stainless wall of the chamber is cooled by cooling water. A cooling rate of the sample holder was confirmed as over 1000°C/min in temperature range from 1000°C to 1500°C.

Fig. 2.

Schematic illustration of softening and melting simulator.

As measurement devices, the simulator equips gas pressure sensors at gas-inlet and gas-outlet, and a sample thickness displacement sensor builded in a loading device, located top of the simulator. A pressure drop through sample layer and a shrinkage degree of sample and can be obtained by the gas pressure sensors and the displacement sensor, respectively.

2.2. Experimental Samples

In order to focus on softening and melting behavior without reduction reaction, granulated slag particles were prepared as softening and melting sample materials. 6 kinds of slag samples were synthesized in gradual cooling condition to avoid making glassy slag as shown in Table 1. All of them didn’t include iron oxide to avoid reduction reaction. Although slag samples have a variety of composition, their temperature ranges of molten slag formation are almost same as from 1200°C to 1400°C. The slag samples were crushed and granulated into 4 mm–5 mm diameter.

Table 1. Experimental slag compositions.

	CaO	SiO2	Al2O3	MgO	CaO/SiO2
	mass%	mass%	mass%	mass%	―
Slag I	33.7	56.5	7.8	2	0.60
Slag II	28.3	47.9	21.8	2	0.60
Slag III	44.1	44.1	9.8	2	1
Slag IV	32.8	38.7	26.5	2	0.85
Slag V	46	37	15	2	1.25
Slag VI	49	39.2	9.8	2	1.25

2.3. Experimental Procedure

The granulated slag samples were charged into the sample holder of the softening and melting simulator as shown in Fig. 3. The sample holder has 30 mm inner diameter and 35 mm inner height. The holder has 19 holes with 3 mm diameter for gas flow in to sample layer. The slag sample layer was inserted between graphite ball, 5 mm diameter, layers as prepared as coke layer in cohesive zone. A graphite lid was placed on upper graphite layer for add load 0.1 MPa as same as cohesive zone condition. The lid also has 12 holes with 3 mm diameter for gas flow.

Fig. 3.

Schematic illustration of experimental sample setup in sample holder.

The sample layer was heated up to 1200°C with 1000°C/min. After reach to 1200°C, a heating rate was changed to 10°C/min. During heating experiment, 0.1 MPa load was added to the sample layer from top part through the lid and N₂ gas was flowed from bottom side with 1 NL/min as inert atmosphere. Displacement amount of the sample layer thickness and gas pressure drop were measured for evaluation of softening and melting behaviour.

In order to evaluate a gas permeability when the sample layer shows maximum pressure drop, 2 steps experiment procedures were applied as follows.

In step 1, sample’s softening and melting behaviour was evaluated up to 1500°C. Through evaluation results in step 1, maximum pressure drop could be recognized, and the temperature of this condition could be estimated for each slag samples. This temperature is recognized as Quenching Temperature, T_max (Fig. 4(a)). In step 2, same heating condition as Step 1 for the sample was applied until T_max. When the sample heated up to the temperature, the sample was immediately quenched with 1000°C/min (Fig. 4(b)). For estimation of gas path shape in the sample layer, the quenched samples were provided to micro computed tomography scanning observation with SKYSCAN1172, BRUKER.

Fig. 4.

Schematic illustration of quenched sample preparation procedure.

3. Results and Discussions

3.1. Pressure Drop Estimation with Fanning’s Equation

Figure 5 shows typical result of the sample layer shrinkage degree and the pressure drop variation with time. The pressure drop began to increase when the shrinkage degree was over than 50%. Similar trend was observed in all types of the slag samples. From variation of the shrinkage degree, temperature, T_max, when the pressure drop reaches maximum value could be estimated. Table 2 shows values of pressure drop and shrinkage degree at T_max for each slag. At the T_max, the quenched samples each slag were prepared. Prepared “Quenched Sample” was observed by micro CT scanning technique. This observation provided inner structure of fusing slag sample layer with non-destructive imaging. As shown in Fig. 6, inner structure of fusing sample layer could be obviously distinguishable into slag, pore, graphite due to deference of X-ray transmission abilities among consist materials. With this structure analysis method, effective gas path shape was evaluated from sequential cross-sectioning observation. Effective means the gas path was categorized as open pore in fusing slag sample layer and the path continuously connected from bottom to top. The CT images were checked every 0.5 mm thickness from the bottom to the top, and the continuous gas paths were tracked, and their locations and sizes were measured as shown light blue area in Fig. 7. Information about the location and pore size were used for pipe approximation in each 0.5 mm thickness. Results from this evaluation provided length and diameter of unit gas path, which locates between each sliced layer. Summation of the unit gas paths from bottom to top could be assumed piping shape of whole part of the effective gas path as shown in Fig. 8.

Fig. 5.

Variations of shrinkage degree and pressure drop of Slag II with time.

Table 2. Pressure drops and shrinkage degrees at T_max.

	Tmax	Pressure drop at Tmax	Shrinkage degree at Tmax
	°C	kPa	%
Slag I	1334	8.1	47.8
Slag II	1394	6.6	81.1
Slag III	1312	5.9	74.0
Slag IV	1319	7.1	55.7
Slag V	1395	5.9	64.2
Slag VI	1448	5.0	64.8

Fig. 6.

Inner structure observation of slag fusing layer using micro CT scanning technique. (Online version in color.)

Fig. 7.

Schematic images of sequential cross-sectioning observation every 0.5 mm thickness from the bottom to the top. (Online version in color.)

Fig. 8.

Schematic illustration of piping shape estimation of whole part of the effective gas path.

Basic equation to estimate gas pressure drop in pipe flow is well known as Fanning’s equation⁸⁾ as shown in Eq. (2).   

$$\mathrm{\Delta }P=\left(\frac{2L_P}{D}\right)({\rho }_f{\overline{u}}^2)f$$(2)

Here, ΔP is the pressure drop, L_P is the length of pipe, D is the diameter of the pipe, $\overline{u}$ is the flow velocity in the pipe., ρ_f is he density of the gas, f is the Fanning friction factor of the pipe.

Combination of effective gas path shape and Fanning’s equation can give a calculated maximum gas pressure drop value in fusing slag sample layer. The effective gas path actually existed not only one in the slag sample layer but also several numbers and it might have some numbers of branch as shown in Fig. 9.

Fig. 9.

Schematic illustration of gas path shapes in in fusing slag sample layer.

In that case, following assumptions were applied for calculation of maximum gas pressure drop value in fusing slag sample layer; gas flow is distributed under the condition that each gas flow path causes same pressure drop; the distributed gas volumes to each gas path becomes same and minimum value. These assumptions gave gas volumes in each effective gas path. Information of the gas volume in the gas path decided gas flow rate, and every gas flow was confirmed in lamellar state, Re < 500, and f = 16/Re is applied as a friction coefficient in this study’s condition.

Before comparison between measured maximum pressure drop values from softening and melting simulator and the calculated values, the measured values needed to be excluded effect from upper and bellower graphite particles layers because gas pressure measurement devices locate at gas inlet and gas outlet as shown in Fig. 10. To calibrate for effect from other part, pressure drop measurement without slag sample layer was carried out and the pressure drop without slag was subtracted from the measured values with slag sample layer as shown in Fig. 11. Figure 12 shows the calibrated measured values and the calculated values are shown good positive correlation. Reason of deviation between these values might be from difficulty of the pipe shape estimation. Although improvement is necessary of this method, it is revealed from this discussion that a combination of fanning’s equation and 3D information of effective gas path shape is expediency for estimation of gas pressure drop.

Fig. 10.

Schematic illustration of effect from upper and bellower carbon particles layers on measured pressure drop values.

Fig. 11.

Schematic illustration of methodology for exclude of graphite particles layer’s effect.

Fig. 12.

Comparisons between calibrated measured maximum pressure drop values from softening and melting simulator and the calculated values.

3.2. Static Force Balance between Molten Slag and Graphite Particle Layer

From previous work,⁶⁾ it was found liquid slag phase clogged in sample layer when the sample showed maximum pressure drop at once. And then, the molten slag moved through the upper graphite layer due to upward gas flow. This situation recovered smooth gas flow in the sample layer as shown in Figs. 1(c) to 1(d). From this result, it could be thought slag clogging behavior has a dominant effect on the maximum pressure drop value. For correct comprehension about slag clogging behavior, it is necessary to understand static force balance between molten slag and graphite particle layer. When capillary force balance is assumed as a main mechanism of slag holding against gas updraft at under graphite layer as shown in Fig. 13, surface tension is one of the directly related value to static force balance in slag physical properties.

Fig. 13.

Schematic illustration of static force balance between molten slag and graphite particle layer.

Information of T_max and initial slag composition of the samples were used for liquid phase composition estimation when temperature shows maximum pressure drop. The estimation was based on FactSage calculation with FToxid Database. Slag’s surface tension values of each sample were calculated using Nakamoto’s estimation formula⁹⁾ as shown in Table 3.

Table 3. Estimated values of surface tension from calculated liquid phase compositions at T_max with Nakamoto’s estimation formula.

	Tmax	Liquid phase ratio at Tmax	CaO	SiO2	Al2O3	MgO	CaO/SiO2	Surface Tension
	°C	mass%	mass%	mass%	mass%	mass%	―	mN/m
Slag I	1334	82.7	30.7	57.5	9.4	2.4	0.53	401
Slag II	1394	90.5	29.2	48.4	20.2	2.2	0.60	445
Slag III	1312	82.9	43.2	42.6	11.8	2.4	1	439
Slag IV	1319	79	34.7	39.0	23.8	2.5	0.89	451
Slag V	1395	100	46	37	15	2	1.25	486
Slag VI	1448	100	49	39.2	9.8	2	1.25	458

Figure 14 shows relationship between slag surface tension and measured maximum pressure drop value, and they show negative correlation. This is opposite trend from slag static holdup’s point of view as reported as Eq. (3).¹⁰⁾ This equation shows increasing of surface tension value gives increasing of slag holdup. Normally, increasing of the static hold up makes difficult of gas flow and increases the pressure drop.   

$$\begin{array}{c}{h}_s=9.96{(C{p}_m)}^{-1.38}\\ C{p}_m={\displaystyle \frac{\rho g{\left\{{\displaystyle \frac{d_p\phi \epsilon }{(1-\epsilon )}}\right\}}^2}{\left|\sigma cos\theta \right|}}\end{array}$$(3)

Here, h_s is the static holdup, Cp_m is the modified capillary number, ρ is the density of the slag, g is the gravitational acceleration, d_p is the diameter of the coke, φ is the sphericity of the coke particles, ε is the porosity of the bed, σ is the density of the slag, θ is the contact angle of slag against coke.

Fig. 14.

Relationships between slag surface tensions and calibrated measured maximum pressure drop values.

It was thought this disagreement of trends about slag holdup came from idea lack of triple line length. Triple line length among molten slag, graphite and gas was roughly estimated from 3D scanning observation as shown in Fig. 15. Top level of molten slag layer, which contact with the upper graphite layer, was decided using cross-section observation in vertical direction from 3D scanning observation. From horizontal cross-section at the level, contact length between slag and graphite, included crucible inner surface, was measured as the triple line length. Figure 16 shows relationship between the contact length between slag and graphite, L_{slag–graphite}, and measured maximum pressure drop value. They show a good positive correlation, except Slag III. Deviation of Slag III might be caused from difficulty for estimation of L_{slag–graphite}.

Fig. 15.

Schematic illustration of methodology for estimation of contact length between slag and graphite. (Online version in color.)

Fig. 16.

Relationships between contact lengths between slag and graphite and calibrated measured maximum pressure drop values.

Although contact angle values between each molten slag and graphite are necessary for precise evaluation of the capillary force balance, the contact angle simply fixed 120° as non-wetting condition because previous reports¹¹⁾ about the contact angle indicated the value could be bigger than 90°. Figure 17 shows relationship between capillary force decided by slag’s surface tension, σ∙cosθ∙L_{slag–graphite}, and measured maximum pressure drop value. Increasing trend of maximum pressure drop is found with increasing of capillary force value. It could be explained increase of capillary force caused increasing of holdup slag amount as gas flow prevention region in sample layer. For accuracy improvement, deeper study on wettability of slag against carbonaceous materials is necessary in future work.

Fig. 17.

Relationships between capillary forces and calibrated measured maximum pressure drop values.

4. Conclusions

Effective gas path shape evaluation technique was developed to estimate gas pressure drop value during softening and melting of particle packed bed by combination of quenched sample and 3D-CT scanning observation. It was revealed that the pressure drop could be estimate using Fanning’s equation combined with the effective gas path shape. The 3D observation of the quenched sample gave information about molten slag’s distribution and contact situation against graphite in sample layer. Capillary force balance between molten slag and graphite showed strong relationship with maximum pressure drop.

Acknowledgements

Authors express their gratitude to a financial support by Grants-in-Aid for Scientific Research “KAKENHI” (15H04168) and scientific advices from the research group of “Control of Cohesive Phenomena in Blast Furnace to optimize Gas Permeability” established in ISIJ.

References

• 1)   T.  Ariyama and  M.  Sato: ISIJ Int., 46 (2006), 1736.
• 2)   K.  Ono,  K.  Yamaguchi,  A.  Shigemi,  N.  Nishida and  K.  Kanbara: Tetsu-to-Hagané, 65 (1979), 505 (in Japanese).
• 3)   K.  Mori,  R.  Hidaka and  Y.  Kawai: Tetsu-to-Hagané, 66 (1980), 1287 (in Japanese).
• 4)   H.  Hotta and  Y.  Yamaoka: Tetsu-to-Hagané, 71 (1985), 807 (in Japanese).
• 5)   A.  Kemppainen,  K.  Ohno,  M.  Iljana,  O.  Mattila,  T.  Paananen,  E.  Heikkinen,  T.  Maeda,  K.  Kunitomo and  T.  Fabritius: ISIJ Int., 55 (2015), 2039.
• 6)   K.  Ohno,  T.  Maeda,  K.  Kunitomo,  Y.  Morita,  K.  Sunahara,  K.  Nishimura and  K.  Higuchi: Proc. 8th Int. Cong. on Science and Technology of Ironmaking (ICSTI 2018), ASMET, Leoben, Austria, (2018), 86, USB.
• 7)   S.  Ergun: Chem. Eng. Prog., 48 (1952), 89.
• 8)   J. T.  Fanning: A Practical Treatise on Hydraulic and Water-Supply Engineering, D. Van Nostrand Company, New York, (1893), 254.
• 9)   M.  Nakamoto,  A.  Kiyose,  T.  Tanaka,  L.  Holappa and  M.  Hämäläinen: ISIJ Int., 47 (2007), 38.
• 10)   H.  Ohgusu,  Y.  Sassa,  Y.  Tomita,  K.  Tanaka and  M.  Hasegawa: Tetsu-to-Hagané, 78 (1992), 1164 (in Japanese).
• 11)   M.  Hayashi,  S.  Sukenaga,  K.  Ohno,  S.  Ueda,  K.  Sunahara and  N.  Saito: Tetsu-to-Hagané, 100 (2014), 211 (in Japanese).