Influence of Channeling Factor on Liquid Hold-ups in an Initially Unsoaked Bed

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1 , pp Influence of Channeling Factor on Liquid Hold-ups in an Initially Unsoaked Bed Hirotoshi KAWABATA, Kazuya SHINMYOU, 1) Takeshi HARADA 2) and Tateo USUI Department of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka Japan. 1) Formerly Graduate Student of Osaka University, now at Toyota Industries Corporation, 2-1 Toyoda-cho, Kariya-shi, Aichi Japan. 2) Graduate Student of Osaka University, Department of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka Japan. (Received on June 15, 2005; accepted on August 10, 2005) One of the important factors for minimum energy consumption and CO 2 emission of a blast furnace (BF) is to elucidate the liquid flow phenomena and liquid hold-ups in the dripping zone of BF. Liquid hold-ups were studied by using a cold model of a fixed bed soaked prior to experiments (hereinafter called initially soaked bed), but the existing correlation equations derived from liquid hold-ups under initially soaked bed do not agree with liquid hold-ups under initially unsoaked bed such as the dripping zone of BF. In the present study, correlation equations for liquid hold-ups in initially unsoaked bed were experimentally derived by a new approach, in which channeling factor (F c ) was proposed and defined as follows: F c is the ratio of the number of liquid paths per one horizontal line to the number of voids between particles per the same horizontal line, and was measured by using the moving image of liquid paths photographed by a CCD video camera. By using empirical equation for F c, hold-ups in initially unsoaked bed were described as the following correlation equations. 1 Static hold-up H S(I-UB) (%) 0.9 H S(I-SB) F c 0.8 Nc m 0.5 Dynamic hold-up H d(i-ub) (%) 0.9 H d(i-sb) F c Total hold-up is the sum of H S and H d H t (%) H S H d where, Nc m 1 (cosq) 3, and subscripts I-SB and I-UB designate quantities associated with initially soaked and unsoaked beds, respectively. The comparison with the previous liquid hold-ups shows that the estimated hold-ups are in good agreement with the experimental values for any particle diameters used and both contact angles of 10 and 70 under initially unsoaked bed. KEY WORDS: channeling factor; empirical equation; initially unsoaked bed; liquid hold-up; liquid path; blast furnace. 1. Introduction Many researchers have been studying to develop an innovative blast furnace (BF) with minimum energy consumption and CO 2 emission. One of the important factors for their developments is to elucidate the liquid flow phenomena and liquid hold-ups in the dripping zone of BF. Liquid hold-ups in a packed bed have been investigated by using a cold model of a fixed bed which was soaked prior to experiments (hereinafter called initially soaked bed). 1 5) The characteristics of liquid hold-ups for BF, however, should be investigated by using a bed unsoaked prior to experiments (hereinafter called initially unsoaked bed), because the burden is not completely wetted in the lower part of BF. Recently, it has been elucidating that liquid hold-ups for initially unsoaked bed 6 10) were different from those for initially soaked bed. Conclusions obtained in our latest paper 10) with one-dimensional model (1D model) are as follows: In initially soaked bed, total, static and dynamic hold-ups under bad wettability condition increase monotonically as particle size decreases, which means the specific surface area increases. Liquid hold-ups in initially soaked bed agree with the existing correlation equations, for example Fukutake and Rajakumar s 3) equation. On the other hand, in initially unsoaked bed, total and static hold-ups under bad wettability condition indicate maximum values at particle diameter of about 10 mm and decrease abruptly in proportion to decrease in the particle size, despite an increase in the specific surface area. Thus, the influence of the initial bed condition, soaked or unsoaked, on liquid hold-ups is great under bad wettability condition. In the present study, correlation equations for liquid hold-ups in initially unsoaked bed were derived experimentally by a new approach, in which channeling factor (F c ) was proposed and defined as follows: F c is the ratio of the number of liquid paths per one horizontal line to the num ISIJ 1474

2 ber of voids between particles per the same horizontal line, and was measured by using the moving image of liquid paths photographed by a CCD video camera. 2. Experimental 2.1. Visualization of Liquid Paths through Initially Unsoaked Bed The visualization method was used in order to investigate liquid flow behavior and to measure F c in initially unsoaked bed. A packed vessel for visualization was two-dimensional model (2D model) with a rectangular parallelepiped made of transparent acrylic resins as shown in Fig. 1. The size of the packed bed is 400 mm in width, 100 mm in depth and 175 mm in height. A liquid distributor of the visualization model installed above the packed bed was composed of 773 injection needles of 0.5 mm I.D. and 25 mm in length to disperse liquid uniformly on the top surface of the packed bed. The filtered tap water was dyed with red ink for easy visualization of liquid paths. Liquid flow behavior and liquid paths were photographed continuously from the front of the packed bed by using a CCD video camera. A digital camera was also used. Solid/liquid contact angles (q) of tap water were about 70 and 10 for fluorine-coated particles and non-coated particles, respectively. In the visualization model, both q decreased to about 65 and 5, respectively, because the water was dyed with red ink, which is a surface-active agent. To reduce the wall surface effect of the packed column on the liquid flow distribution and hold-ups, the inner surface was coated with fluorine. Alumina balls of six sizes, 2.8, 5.0, 8.1, 10.3, 15.1 and 19.4 mm in diameter (D p ), were used as packing particles. As shown in Table 1, void fraction (e) increases from 0.35 to 0.40 and mean void diameter (d v [e/(1 e)] 1/3 D p ) increases from 2.3 to 16.9 mm as D p increases from 2.8 to 19.4 mm. Fig. 1. Table 1. Schematic layout of the two-dimensional model for visualization of liquid flow behavior and measurement of channeling factor (transparent acrylic resins). Particle diameter and void fraction of 2D visualization model (400 W 100 D 175 mm H ) Definition and Measurements of Channeling Factor As the new idea to derive correlation equations for liquid hold-ups in initially unsoaked bed, in the first place channeling factor (F c ) was proposed and defined as follows: F c is the ratio of the number of liquid paths (liquid droplets and/or liquid rivulets) per one horizontal line to the number of voids between particles per the same horizontal line, which means the ratio of effective particle contacted with liquid. The measurement method of F c is very easy as shown by a photograph of liquid paths in Fig. 2 in comparison to the direct measurement of the effective contact area. Red rivulets are liquid paths and spherical balls are the packed particles. The number of liquid paths and the number of voids between particles (nearly equal to the number of particles) were counted on the three horizontal lines (marked as A, B, C) which divided the packed height into quarters as shown in Fig. 2. Averaged value of the three ratios on the three horizontal lines was defined as F c. Actually, the moving image of liquid paths taken by a CCD video camera instead of a still picture photographed by a digital camera was used in order to measure F c in initially unsoaked bed. The recording period of the moving image was 10 min. However, the moving image from 5 min to 10 min in the period was used to count the number of liquid paths, because liquid flow became steady at about 5 min after the onset of water irrigation into the packed bed. The feeding rate of the moving image was increased up to four times on a screen of a personal computer, and the number of liquid paths was measured whether liquid flowed down or not in every void between particles on one horizontal line during the interval of 5 min. To increase the accuracy, those measurements were repeated twice or three times on three horizontal lines. 3. Results 3.1. Visualization of Liquid Flow Behavior through Initially Unsoaked Bed Figure 3 exemplifies visualization photographs in the case of bad wettability (q 65 ) for the packed particle diameters (D p ) of 2.8, 5.0, 10.3 and 15.1 mm under initially unsoaked bed with the liquid velocity (V L ) of about 0.1 mm/s. It is found that the restricted liquid paths and/or liquid rivulets 7,10) are formed within the packed bed of D p 2.8 and 5.0 mm even though liquid was dispersed uniformly on the top surface of the packed bed. Only four or five liquid paths for D p 2.8 mm can be seen, and for D p 5.0 mm, the number of liquid paths increases to be about ten. On the other hand, for D p 10.3 and 15.1 mm, liquid droplets and/or liquid rivulets are dispersed relatively in the void between particles and on the particle surface. The difference of color of alumina particles (light gray and light ocher) attributes to the use of two digital cameras ISIJ

3 ISIJ International, Vol. 45 (2005), No. 10 Fig. 2. Measurement method of channeling factor. Fig. 4. Fig. 3. Visualization of liquid flow behavior under initially unsoaked bed with good wettability (q 5 ). Visualization of liquid flow behavior under initially unsoaked bed with bad wettability (q 65 ). Figure 4 exemplifies visualization photographs in the case of good wettability (q 5 ) for Dp 5.0, 10.3, 15.1 and 19.4 mm under initially unsoaked beds with VL 0.1 mm/s. In the upper layer of the packed bed, liquid droplets and/or liquid rivulets wet the packed particles well and spread out in the void between particles and/or on particle surface in comparison to those for bad wettability condition (Fig. 3), because q decreased from about 65 to 5. For Dp 5.0 mm, liquid paths can be seen only three or four, and for Dp 10.3 mm, liquid paths increase about six or more. Liquid paths within the packed bed for good wettability condition are much less than those for bad wettabiliry condition. Furthermore, even though the packed particle size increases up to 15.1 or 19.4 mm, liquid droplets and/or liquid rivulets are not distributed enough within the whole packed bed and the restricted liquid paths are formed. Observed liquid flow behavior through initially unsoaked bed under good wettability condition implies that the liquid dispersed uniformly on the top surface of the packed bed 2005 ISIJ Fig. 12. Visualization of liquid flow behavior through two layer bed packed with different particle diameters in initially unsoaked bed (q 65 ). forms much localized streams and is difficult to spread out within the whole packed bed, even though the liquid spreads out easily on the solid surface in the case of good wettability. Li et al.11,12) also reported that In the hydrophilic small particle bed, with increasing attractive capillary force the liquid flows join easily together. As the 1476

4 result, the channeling liquid flows are generated in the small particle side. And for the small hydrophilic particle, there are some peaks in the liquid distribution, which shows the channeling flow caused by stronger capillary force of hydrophilic particle. Thus, the influence of wettability on liquid flow behavior is very large in initially unsoaked bed. 7,10) 3.2. Influence of Wettability on Channeling Factor in Initially Unsoaked Bed Usually, because e in close vicinity to wall surface is higher than e in the central part of the packed bed, much liquid flows down in the vicinity to wall and therefore liquid flow distribution is not uniform in the packed bed (so-called wall effect ). To investigate the effect of wall surface on F c, it was observed whether liquid was dripping or not from every hole (33 in width 10 in depth) drilled in the bottom plate of the packed bed (hereinafter called dripping hole and non-dripping hole, respectively). Dripping hole rate, which is the ratio of the number of dripping holes to the number of all holes for an array in the width direction (33 holes), is shown as the distribution for the array in depth (10 holes) in Fig. 5. Array No. 1 and No. 10 are near the wall. Liquid dripping distribution is comparatively uniform under the conditions of D p 10.3 mm, q 65 and V L 0.15 mm/s and wall effect can not be seen. Moreover it was ascertained that liquid dripping distributions were nearly uniform for other particle diameters under q 65. Thus, in the present experiments, e in close vicinity to the wall surface has little influence on F c in the packed bed, because the present packed bed is relatively large size with 400 mm in width, 100 mm in depth and 175 mm in height. Under q 5, however, in spite of the precise settling of the packed vessel perpendicularly, liquid dripping distributions within the packed bed scatter with every experiment even in the same packed particle. Figure 6 shows the measured values of F c for q 65 plotted against V L as a parameter of D p. Each plot is a mean value of two or three data. F c rises from about 0.1 to 1.0 as D p increases from 2.8 to 15.1 mm, while V L has little effect on F c except for the case of D p 2.8 mm. F c for D p 5.0 mm is nearly 0.5, and F c for D p 8.1 and 10.3 mm are almost 0.9, and F c for D p 15.1 mm is 1.0. Figure 7 depicts the measured values of F c for q 5 plotted against V L as a parameter of D p from 2.8 to 19.4 mm. Although each plot is an average value of two or three data, the dependence of V L on F c is not clear forq 5, because the variations of F c with V L for several particle diameters are different from each other. In the present work, for the sake of simplicity, an empirical equation for F c correlating with the particle diameter and wettability is derived on the assumption that V L has no effect on F c. That is F c is assumed constant for the same particle diameter and the same wettability, and evaluated as an averaged value over the present experimental range of V L Empirical Equation for Channeling Factor in Initially Unsoaked Bed Figure 8 indicates the relation between F c and the mean Fig. 6. Effect of liquid velocity on channeling factor under initially unsoaked bed with bad wettability (q 65 ). Fig. 5. Influence of wall surface on liquid dripping distribution (1: front side, 10: back side). Where, dripping hole rate is the ratio of the number of dripping holes to the number of all holes for an array in the width direction. Fig. 7. Effect of liquid velocity on channeling factor under initially unsoaked bed with good wettability (q 5 ) ISIJ

5 Fig. 8. Relation between channeling factor and mean void diameter under initially unsoaked bed. Fig. 9. in initially soaked bed. void diameter (d v ) in the packed bed under initially unsoaked bed as a parameter of q, where, d v [e/(1 e)] 1/3 D p. The reason why the use of d v instead of D p gives more accurate correlation for F c is considered as follows: (1) F c depends on the void scale rather than D p, because liquid droplets and/or liquid rivulets mainly flow down in the void space within the packed bed and the flow behavior is more affected by the void scale rather than D p. (2) e is taken into consideration in d v and varies from 0.35 to 0.40 with increasing D p from 2.8 mm to 19.4 mm in the present 2D visualization experiments as listed in Table 1. Since it is assumed that V L has no effect on F c, the averaged values of F c over the present range of V L shown in Figs. 6 and 7 are plotted in Fig. 8 for q 5 and q 65 as a function of d v. By taking into account the measured values of F c for both contact angles and asymptotic behavior of F c towards unity with increasing d v for any contact angle, the following empirical equation for F c can be derived as functions of d v and q by the regression analysis: F c 1 exp( Cp 0.75 /Nc 3.5 ) ( )...(1) where, Cp [r L g (d v ) 2 /s L ]: modified capillary number ( ), Nc 1 cosq : dimensionless interfacial force ( ), g :gravitational acceleration (m/s 2 ), r L : liquid density (kg/ m 3 ), s L : surface tension (N/m). Lines shown in Fig. 8 are the calculated values from Eq. (1) for several contact angles from 5 to 90. As a result, the calculated lines for q 5 and q 65 reproduce the measured values rather well. 4. Discussion 4.1. Derivation of Correlation Equations for Liquid Hold-ups in Initially Unsoaked Bed Modified Equation for Liquid Hold-ups in Initially Soaked Bed Liquid hold-ups data used in the present work are the modified ones as follows 10) : The measured value of static hold-up (H Sm ) was corrected by subtracting the liquid holdup H Sw which sticks to the inner surface of wall in the empty column and varies depending on the size of the packed vessel, namely the inner surface area and the superficial volume of the packed vessel. In the author s experiment, 10) the measured H Sw on the wall in the empty column was 0.41% in 1D model (200 mm in inside diameter 500 mm in packed bed height), and therefore H S was evaluated by subtracting 0.41 from H Sm. Consequently, the present equations for initially soaked bed is given by only a little modification of the equations of Fukutake and Rajakumar 3) as follows. Static hold-up for initially soaked bed (I-SB), H S(I-SB) (%) 100/( Cp 0.9 m )...(2) where, Cp m Cp s /Nc [r L g (D p ) 2 ]/[s L (1 cos q) (1 e) 2 ]; modified capillary number ( ), Cps [r L g (D p ) 2 ]/[s L (1 e) 2 ], modified capillary number ( ). Dynamic hold-up for initially soaked bed (I-SB), H d(i-sb) (%) Re m 0.7 Ga 0.48 Cp m s 0.1 Nc (3) where, Re m [r L V L D p ]/[(1 e) m L ]; modified Reynolds number ( ), Ga m [(r L ) 2 g (D p ) 3 ]/[(m L ) 2 (1 e) 3 ]; modified Galilei number ( ), m L ; viscosity coefficient of liquid (Pa s). Total hold-up is the sum of H S and H d as follows, H t (%) H S H d...(4) Figure 9 represents the comparison between experimental hold-ups 10) and the calculated ones from Eqs. (2), (3), and (4) under q 70 for initially soaked bed. A solid, a dotted, and a dashed lines show total, static and dynamic hold-ups under the condition of V L 0.2 mm/s, respectively. Measured hold-ups agree well with calculated ones from Eqs. (2), (3), and (4) over the present experimental range of particle diameter Correlation Equations for Liquid Hold-ups in Initially Unsoaked Bed Liquid hold-ups in initially unsoaked bed do not agree with the existing correlation equations. 3,6) Then correlation equations for liquid hold-ups in initially unsoaked bed were derived as follows. F c for initially unsoaked bed is greatly affected by q and d v as above mentioned, and the number of liquid paths within the bed of good wettability is much less than that of bad wettability as shown in Figs. 3 and ISIJ 1478

6 Furthermore, the decreasing ratio of static hold-ups for good wettability to those for bad wettability is more than the decreasing ratio of the number of liquid paths for good wettability to the one for bad wettability, because much liquid volume quickly flows down pulling each other by surface tension in a few liquid paths without standing on the particle surface and the void between the particles. On the basis of our experimental results, static hold-up H S(I-UB) and dynamic hold-up H d(i-ub) in initially unsoaked bed are considered to be mainly affected by F c and q. Therefore, correlation equations for H S(I-UB) and H d(i-ub) are derived by the regression analysis using the author s many hold-up values 9,10) as follows: Static hold-up in initially unsoaked bed (I-UB) is given by H S(I-UB) (%) 0.9 H S(I-SB) F c 0.8 Nc 1 m...(5) Dynamic hold-up in initially unsoaked bed (I-UB) is given by H d(i-ub) (%) 0.9 H d(i-sb) F 0.5 c...(6) And total hold-up is the sum of H S and H d as follows. H t (%) H S H d...(4) where, Nc m 1 (cos q) 3, and subscripts I-SB and I-UB designate quantities associated with initially soaked and unsoaked beds, respectively. Channeling factor F c used in the present study to derive these correlation equations for initially unsoaked bed could not consider the influence of liquid density and viscosity. To derive correlation equations with more accuracy, the further examinations on channeling factor have to be carried out, especially for the dependency of liquid density. Fig. 10. in initially unsoaked bed (influence of particle diameter) Comparison between Experimental and Estimated Hold-ups for Initially Unsoaked Bed Figure 10 represents the comparison between experimental and estimated hold-ups for initially unsoaked bed with q 70 as a function of V L. The estimated ones written by solid, dotted and dashed lines for total, static and dynamic hold-ups, respectively, agree well with the experimental values (1D model) 10) for both D p 5.4 and 29.8 mm. The present estimated hold-ups for other D p also agree well with the experimental values. Influence of solid/liquid wettability on liquid hold-ups under initially unsoaked bed is shown in Fig. 11 for D p 10.3 mm as a function of V L. The estimated hold-ups are in good agreement with the experimental values for both q 10 and Comparison between Present Estimated Hold-ups and Hot Model Researches Husslage 13) investigated hold-ups of the molten iron and slag in a laboratory experimental setup, which were a packed coke bed (f60 mm 175 mm in height) with the coke sizes of 8 10 mm at high temperature of C. The slags resemble commercial BF slag compositions with CaO, SiO 2, Al 2 O 3 and MgO, but no FeO was added to the slags. The molten iron was saturated with carbon. Husslage reported in the crucible experiments that The static holdup ranges between 1 and 5 % for both molten iron and slag, Fig. 11. in initially unsoaked bed (influence of particle/liquid wettability). and the dynamic hold-up excepting some of the iron experiments was very low. Sasa et al. 14) also experimented in hold-ups of the molten slag (BF slag) without FeO by using a packed coke bed (f60 mm 80 mm in height) with the coke sizes of mm at high temperature of 1500 C. Their results represented that Total, static and dynamic hold-ups were about 3.7, 0.7 and 3.0 %, respectively at CaO/SiO 2 below 1.1. It may be considered that static holdup of 0.7 % and dynamic hold-up of 3.0 % are in inverse, because static hold-up is usually large more than dynamic hold-up. Anyways, hot model experiments for liquid holdups are very difficult and tend to have a large scatter. Present estimated values for molten slag from Eqs. (4), (5) and (6) are 3.6, 3.0 and 0.6 % for total, static and dynamic hold-ups, respectively under the physical conditions 10,13) of D p 10 mm, T C, e 0.4, q 105, m 0.34 Pa s, r kg/m 3 and s 0.42 N/m. Present estimated hold-ups are expected to comparatively agree with those of above hot model experiments. 13,14) ISIJ

7 Influence of Packing Structure on Liquid Hold-ups for Initially Unsoaked Bed The influence of the packing structure on liquid hold-ups was investigated by using two layer bed packed with different particle diameters as shown in Fig. 12 for visualization. Hold-ups measurements for such two layer bed were done with 1D model reported in the latest paper (200 mm in inside diameter 500 mm in packed bed height) 10). One packing structure was that the lower layer was packed up to 250 mm in height with 10.3 mm particle and the upper layer was packed from 250 up to 500 mm with 5.0 mm particle. Another packing structure was the reversed one and their packing structures were named as U5-L10 and U10-L5, respectively. Figure 12 reveals the difference between the liquid flow behavior through two types of bed layers mentioned above under initially unsoaked bed with bad wettability condition of q 65. Within the bed packed with 5.0 mm particle in both cases of U5-L10 and U10-L5, the flow behavior of liquid droplets and/or liquid rivulets is the same and the restricted flow paths 7,10) are formed. On the other hand, within the bed packed with 10.3 mm particle in both cases, the flow behavior completely differs from each other. For the case of U10-L5, liquid droplets and/or liquid rivulets spread out enough in the void between particles and on particle surface, but for the case of U5-L10, only a few liquid paths are formed in the bed packed with 10.3 mm particle. If the liquid paths formed in the upper half of the bed are only a few, then it is the same with the lower half, even when the larger particles are packed there and hence liquid is easy to spread out there. That is, for initially unsoaked bed, channeling factor F c in the lower layer is greatly affected by F c in the upper layer. under initially unsoaked bed with bad wettability condition of 70 is demonstrated in Fig. 13 for the two cases of U5-L10 and U10-L5. The estimated hold-ups for both cases reproduce the experimental ones relatively well. In the case of U5-L10, the estimated hold-ups were simply calculated by using only F c for the upper layer under the assumption that F c for 10.3 mm particle layer is equal to F c for 5.0 mm particle layer. In the case of U10-L5, the estimated hold-ups were calculated by using respective values of F c for the bed packed with single size of 5.0 mm and 10.3 mm particles Influence of Particle Diameter on Liquid Hold-ups for Initially Unsoaked Bed In initially unsoaked bed, total and static hold-ups under bad wettability condition indicate maximum values at about D p 10 mm and decrease abruptly in proportion to a decrease in the particle size in spite of an increase in the specific surface area. 10) The estimated hold-ups for V L 0.2 mm/s under initially unsoaked bed with q 70 are compared to experimental values as shown in Fig. 14 as a function of D p. Estimated hold-ups H t, H S, and H d, which are drawn by a solid, a dotted, and a dashed lines, respectively, agree well with the respective experimental values. Especially, estimated lines for static hold-up H S and total hold-up H t from the present equations perfectly reproduce the inflection phenomena that H S and H t have maximum Fig. 13. Fig. 14. under initially unsoaked bed (influence of packing order of two layer bed packed with different particle diameters). in initially unsoaked bed (influence of particle diameter). values at about D p 10 mm and decrease abruptly for smaller particle size. 5. Conclusions In initially unsoaked bed, correlation equations for liquid hold-ups were experimentally derived by a new approach, in which channeling factor (F c ) was proposed and was measured by using the moving image of liquid paths photographed by a CCD video camera. Empirical equation for F c was obtained by the regression analysis. On the basis of our experimental results, static hold-up H S(I-UB) and dynamic hold-up H d(i-ub) for initially unsoaked bed were assumed to be mainly correlated with both F c and contact angle (q), and their empirical equations were derived by the regression analysis with the author s many hold-up values. The present study leads to the following conclusions: (1) Observation of liquid flow through initially unsoaked bed under good wettability indicated that the liquid dispersed uniformly on the top surface of the packed bed is difficult to spread out within the packed bed, even though 2005 ISIJ 1480

8 liquid spreads out easily on the solid surface under good wettability. (2) The following empirical equation for F c is obtained in initially unsoaked bed. F c 1 exp( Cp 0.75 /Nc 3.5 ) ( ) where, Cp [r L g (d v ) 2 /s L ]: modified capillary number ( ), Nc 1 cos q: dimensionless interfacial force ( ), d v [e/(1 e)] 1/3 D p : mean void diameter (m), g:gravitational acceleration (m/s 2 ), r L : liquid density (kg/m 3 ), q: solid/liquid contact angle (deg), s L : surface tension (N/m), e: void fraction of bed ( ). (3) Static, dynamic and total hold-ups in initially unsoaked bed are derived as follows. H S(I-UB) (%) 0.9 H S(I-SB) F c 0.8 Nc 1 m, H d(i-ub) (%) 0.9 H d(i-sb) F 0.5 c, H t (%) H S H d where, Nc m 1 (cos q) 3, and subscripts I-SB and I-UB designate quantities associated with initially soaked and unsoaked beds, respectively. (4) The estimated hold-ups are in good agreement with the experimental values for any particle diameters used and both contact angles of 10 and 70 under initially unsoaked bed. (5) In the two layer bed packed with different particle diameters, the estimated hold-ups for both packing structures reproduce the experimental ones relatively well under initially unsoaked bed with bad wettability condition of 70. Acknowledgements We wish to express our thanks to Dr. Yoshiyuki Bando of Nagoya University, Dr. Michitaka Sato of JFE Steel Corporation, and Dr. Akihiko Shinotake of Nippon Steel Corporation for their helpful discussion and advice. REFERENCES 1) T. K. Sherwood, G. H. Shipley and F. A. L. Holloway: Ind. Eng. Chem., 30 (1938), ) A. Mersmann: Chem. Inf.-Techn., 37 (1965), ) T. Fukutake and V. Rajakumar: Trans. Iron Steel Inst. Jpn., 22 (1982), ) A. Alidilar, A. Bicer and A. Murathan: Chem. Eng. Commun., 128 (1994), 95. 5) J. Yagi: ISIJ Int., 33 (1993), ) G. S. Gupta and S. Bhattacharyya: ISIJ Int., 43 (2003), ) W. M. Husslage, T. Bakker, A. G. S. Steeghs, R. H. Heerema and M. A. Reuter: 6th World Cong. of Chem. Eng. 2001, AIChE, New York, (2001), 1643 (CD-ROM). 8) T. Usui, H. Kawabata and F. Fujita: CAMP-ISIJ, 16 (2003), ) T. Usui, H. Kawabata, T. Sogo, S. Morii, M. Ichida and Z. Morita: Tetsu-to-Hagané, 82 (1996), ) H. Kawabata, Z. Liu, F. Fujita and T. Usui; ISIJ Int., 45 (2005), ) M. Li, Y. Bando, T. Tsuge, K. Yasuda and M. Nakamura: Chem. Eng. Sci., 56 (2001), ) M. Li, Y. Bando, T. Tsuge, K. Suzuki, K. Yasuda and M. Nakamura: J. Chem. Eng. Jpn., 33 (2000), ) W. M. Husslage: Doctoral Thesis, Delft University of Technology, Netherlands, (2004), ) Y. Sasa, K. Tanaka, M. Kono and T. Fukuda: Tetsu-to-Hagané, 73 (1987), S ISIJ