Numerical Study of the Gas Distribution in an Oxygen BlastFurnace. Part 1: Model Building and Basic Characteristics

ZONGLIANG ZHANG,1 JIALE MENG,1 LEI GUO,1

and ZHANCHENG GUO1,2

1.—State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing,Haidian District, Beijing 100083, People’s Republic of China. 2.—e-mail: zcguo@metall.ustb.edu.cn

Based on multifluid theory, transport phenomena theory, metallurgical reac-tion kinetics, thermodynamics, and computational fluid dynamics, a multifluidmodel for an oxygen blast furnace was established to evaluate the gas distri-bution in a furnace. The uneven distribution of recycling gas in oxygen blastfurnaces was found to be a severe problem. This uneven distribution resultedfrom injecting a large amount of recycling gas into the furnace shaft. Gas dis-tribution substantially affects the energy and heat utilization of an oxygen blastfurnace. Therefore, the basic characteristics of the gas distribution in an oxygenblast furnace are illustrated. The results show that in the top of the oxygen blastfurnace, the concentration differences of the CO and CO2 between the centerand edge reach 7.8% and 11.7%, respectively. The recycling gas from the shafttuyere only penetrates to two thirds the length of the radius.

INTRODUCTION

Approximately two thirds of the global annualsteel production utilizes a long blast furnace pro-cess. Therefore, blast furnaces play a significant rolein the steel industry. However, this process involveshigh energy consumption, heavy environmentalpollution, and high CO2 emission, putting tremen-dous pressure on both the energy sector and theenvironment. Furthermore, the energy-savingpotential of traditional blast furnace technologieshas reached a limit. Fortunately, oxygen blast fur-nace ironmaking1,2 can reduce more than 70% of thecoke consumption, 11.1% of the energy consump-tion, and 59.6% of the CO2 emissions. This processcan significantly improve the energy conservationand reduce environmental pollution by transform-ing a traditional blast furnace. A variety of specificoxygen blast furnace processes have been proposed,among which the gasification furnace–full oxygenblast furnace (GF–FOBF) process3 (Fig. 1) displaysunique advantages because of the reforming andheating effects of the gasification furnace. Thegasification furnace provides safe, adequate, andstable recycling gas.

The ironmaking process involves many complexchemical reactions and flow, phase change, heat

transfer, mass transfer, and momentum transferphenomena. Additionally, the internal processes arenearly unmeasurable because of the high tempera-ture and closed nature of ironmaking. Therefore,the blast furnace is considered to be the most com-plex reactor in the metallurgy field. To study theinternal processes and phenomena of a blast fur-nace, numerous methods have been proposed, suchas a dissection investigation of blast furnaces4 andinstalling sensors in the inner wall of blast fur-naces.5 However, a dissection investigation of blastfurnaces is expensive in terms of time and invest-ment; sensors can only provide limited discretedata, which is not sufficient for studying the com-prehensive internal phenomena. Among the meth-ods, the mathematical models display uniqueadvantages, such as the multifluid model6,7 pro-posed in the 1990s. These models can simulatetemperature, velocities, concentration fields, anddistributions of other parameters through mathe-matical calculations that are based on chemicalreactions, heat and mass transfers, and other com-plex phenomena within the blast furnace. There-fore, the situation inside the blast furnace can bemore visually understood. Moreover, many impor-tant results derived from mathematical models havebeen applied in the production process. Previously,

JOM, Vol. 67, No. 9, 2015

DOI: 10.1007/s11837-015-1529-y� 2015 The Minerals, Metals & Materials Society

1936 (Published online July 8, 2015)

mathematical models have focused on traditionalblast furnaces, and only a few models of oxygenblast furnaces have been reported. Oxygen blastfurnaces such as the top-gas recycling blast furnacein the ultra–low CO2 steelmaking (ULCOS) projectin the European Union8 are currently in experi-mental and pilot-scale test stages. Additionally,limited numerical simulation studies are availableconcerning the internal phenomena of an oxygenblast furnace.9,10 The gas distribution in an oxygenblast furnace seriously affects its smooth operation,energy consumption, and CO2 emissions becausethe recycling gas carries a large amount of heat andreducing gas. The distribution of this gas affects theheat distribution in the blast furnace, which is sig-nificant for energy conservation and environmentalprotection. However, no detailed descriptions areavailable for the gas distribution in an oxygen blastfurnace or for the related influencing factors. InPart 1 of this study, the gas distribution in theoxygen blast furnace was studied with a multifluidmathematical model, and the basic characteristicsof the gas distribution in an oxygen blast furnacewere summarized. Based on the findings of the first

part, the influence of the design and operatingparameters was investigated in Part 2 to furtheroptimize the gas distribution. The multifluid math-ematical model considered three phases: complexchemical reactions, heat and momentum transfer,and other processes. Therefore, this model is con-sidered to be superior to most models that use twophases and limited chemical reactions, ensuring thevalidity of the results.

MODEL DESCRIPTION

Assumptions

To facilitate model building and numerical simu-lation, the following was assumed:

1. Only gas, solid, and liquid phases were consid-ered; the fines in blast furnace were ignored.

2. The coal injected into the blast furnace throughthe hearth tuyere was converted into substancessuch as CO, CO2, and H2O under high temper-atures.

3. Insignificant substances and reactions wereignored.

4. The furnace top pressure was set to1.2 9 105 Pa.

5. The cohesive zone was defined as the region inwhich the solid temperature was 1373 K to1673 K.

6. The blast furnace inner shape, tuyere positions,and inner states were symmetrically dis-tributed.

Phases and Reactions Involved in the Model

The substances in the blast furnace are divided intothree phases in the model.11,12 The phases andsubstances involved in the model are shown inTable I.

Table II shows the 12 chemical reactions andthree phase transitions in the model. In this model,the indirect reduction reaction of iron ore is calcu-lated using the unreacted core model.

Model Framework

The complexity of a blast furnace lies in thechemical reactions and phase interactions, includ-ing the heat and momentum exchanges among gas,solid, and liquid phases. The material behavior inthe blast furnace follows three laws: conservationsof mass, conservation of momentum, and conserva-tion of energy. To facilitate computer programming,

Table I. Phases and substances involved in the model

Phases Substances

Gas CO, CO2, H2, H2O, N2, O2

Solid Fe2O3, Fe3O4, FewO, Fe, C, gangue(CaO, MgO, Al2O3, SiO2)Liquid FewO, Fe, slag(CaO, MgO, Al2O3, SiO2)

Fig. 1. The schematic diagram of the GF–FOBF process.

Numerical Study of the Gas Distribution in an Oxygen Blast Furnace Part 1: Model Buildingand Basic Characteristics

1937

these conservation laws are represented in a unifiedform, as seen in Eq. 1.

@ðeiqiwÞ@t

þ divðeiqiUwÞ ¼ divðeiCwgradwÞ þ Sw (1)

where ei is the volume fraction of phase i in the blastfurnace; qi is the fluid density of phase i, kg m�3; Uis the velocity vector of phase, m s�1; w is the uni-versal variable of the conservation equation; Cw isthe generalized diffusion coefficient; and Sw is thegeneralized source term. Among these variables, wcan represent u, v, w, H, and other solution vari-ables.

Interphase Transfer of Momentum and Heat

Because the phases and materials in the oxygenblast furnace model have been simplified, theinterphase momentum exchanges involved in themodel include interactions among three phases. Thegas–solid, gas–liquid, and solid–liquid interactionforces can be calculated using Eqs. 2, 3, and 4,namely the Ergun equation,13 Richardson–Zakiequation,14 and Kozeny–Carmen equation.15

~Fgs ¼ 150lg 1 � eg

� �2~ug � ~us

� �

e2gd2

s/2s

þ 1:75qg 1 � eg

� �~ug � ~us

� �2

egds/s

(2)

~Fgl ¼ �CDgl3elql

4dl/l

� �~ug � ~ul

�� �� ~ug � ~ul

� �(3)

~Fsl ¼ql

rh~us � ~ulj j 5bþ 0:4b0:1

� �~us � ~ulð Þ (4)

where

b ¼ ll

ql ~us � ~ulj jrh(5)

rh ¼ el/sds

6es(6)

ui is the actual speed of phase i, m s�1; us is theshape factor of the solid particle; CDgl is the gas–liquid interphase drag coefficient; ds is the solidparticle diameter, m; d1 is the droplet diameter, m;and ul is the droplet shape factor.

Similarly, the heat exchanges involved in themodel include interactions among three phases. Thegas–solid, gas–liquid, and solid–liquid heat trans-fers can be calculated using Eqs. 7, 8, and 9, namelythe Ranz–Marshall equation,16 Mackey–Warnerequation,17 and Eckert–Drake equation.18

_Egs ¼ Agshgs Tg � Ts

� �(7)

_Egl ¼ Aglhgl Tg � Tl

� �(8)

_Esl ¼ Aslhsl Tl � Tsð Þ (9)

where

As ¼ fore6eore

dore/ore

þ fcoke6ecoke

dcoke/coke

(10)

Ags ¼ As � Asl (11)

Table II. Chemical reactions and phase transitions involved in the model

n Reactions Description

1 3Fe2O3(s) + CO(g) = 2Fe3O4(s) + CO2(g) CO indirect reduction reactions2 w/(4w � 3)Fe3O4(s) + CO(g) = 3/(4w � 3)FewO(s) + CO2(g)3 FewO(s) + CO(g) = wFe(s) + CO2(g)4 3Fe2O3(s) + H2(g) = 2Fe3O4(s) + H2O(g) H2 indirect reduction reactions5 w/(4w � 3)Fe3O4(s) + H2(g) = 3/(4w � 3)FewO(s) + H2O(g)6 FewO(s) + H2(g) = wFe(s) + H2O(g)7a FewO(l) + C(s) = wFe(l) + CO(absorbed on l) Direct reduction reactions7b CO(absorbed on l) = CO(g)8 C(s) + CO2(g) = 2CO(g) Boudouard reaction9 C(s) + H2O(g) = CO(g) + H2(g) Water gas reaction10 C(s) + 1/2O2(g) = CO(g) Incomplete combustion reaction11 C(s) + O2(g) = CO2(g) Complete combustion reaction12 CO(g) + H2O(g) = CO2(g) + H2(g) Vapor conversion reaction13 Fe(s) = Fe(l) Melting phase change14 FewO(s) = FewO(l)15 Gangue(s) = Slag(l)

Zhang, Meng, L. Guo, and Z. Guo1938

Asl

As¼ 0:400Re0:218

sl We0:0428sl Fr�0:0238

sl ð1 þ cos hslÞ�0:0235

(12)

hgs ¼kg

ds2:0 þ 0:39Re1=2

gs Pr1=3

g

!

(13)

Aglhgl ¼ 4:18 egqg ~ugCpg el ~ulð Þ0:35h i

Re�0:37gl

Scg

Prg

� �2=3

(14)

hl ¼kl

ds

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiResl Prl

p

1:55ffiffiffiffiffiffiffiPrl

pþ 3:09

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:372 � 0:15 Prl

p� �

(15)

hs ¼ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiksCpsqs ~ul � ~usj j

pds

s

(16)

1

hsl¼ 1

hsþ 1

hl(17)

hij is the heat-transfer coefficient between phase iand phase j, W m�2 K�1; Weij is the Weber numberbetween phase i and j; hij is the contact angle be-tween phase i and j, �; Frij is the Froude numberbetween phase i and j; and ks is the thermal con-ductivity of the solid phase, W m�1 K�1.

Boundary Conditions and Solving Strategies

The boundary conditions of the three phases aredifferent, and the specific settings are describedbelow. For the gas phase, the gas composition andtemperature at the tuyere are set as the componentsand temperature after reaction of pulverized coaland oxygen. At the outlet of the top furnace, the gasflow is fully developed. The furnace wall allows thegas phase to slide freely. For the solid phase, thecomposition and temperature of the solid phase atthe burden surface are set according to the actualproduction parameters. The outlet of the solid phasewas set at the bottom of the furnace wall, and thesolid phase flow is fully developed in the outlet. Inaddition, the furnace wall and deadman producesome friction to the solid phase flow. The total heatloss of the furnace wall is allocated to the gas phaseand solid phase. The heat losses of the furnace wallin the gas and solid energy source terms are calcu-lated using Eq. 18. The furnace wall is a freelysliding interface for the liquid phase, and the liquid

Fig. 2. Solution procedures for the multifluid model.

Fig. 3. Geometrical parameters and mesh distribution of the mod-eled blast furnace.

Numerical Study of the Gas Distribution in an Oxygen Blast Furnace Part 1: Model Buildingand Basic Characteristics

1939

phase can pass freely through the slag interface inthe lower portion of the blast furnace.

Qg;wall;Qs;wall ¼ 0:5AwallhwallTg;wall þ Ts;wall

2� Twall

� �

(18)

where Qg,wall and Qs,wall are the gas and solid heatloss of the furnace wall, respectively, W; Awall is thefurnace wall area, m2; and Tg,wall and Ts,wall are thetemperatures of the gas phase and solid phase nearthe furnace wall, respectively, K. The convectiveheat-transfer coefficient hwall and the furnace walltemperature Twall are set to 20 W m�2 K�1 and298 K, respectively.

Because of the strong couplings among the gas,liquid, and solid phases and because each equationsimultaneously requires an iterative solution, aparallel computer cluster is used to solve the modeland reduce the convergence time. When the three-phase continuity equation residuals are less than0.001, the calculation is complete.

NUMERICAL SOLUTION AND OPERATIONPARAMETERS

Solution Procedure

Well-established sequential solution proceduresare employed to calculate the comprehensivemomentum, mass and energy transfers through thesteps shown in Fig. 2. The parameters are calcu-lated through iterations with given operationalconditions.

Blast Furnace Structure and ComputationalGrid

In this model, the study object is a blast furnacewith a hearth diameter of 6.8 m, a height of19.95 m, and an effective volume of 750 m3. A body-fitted coordinates (BFC) grid was generated in thisarea. The geometrical parameters and mesh distri-butions of the blast furnace are shown in Fig. 3. Noshaft tuyeres of a traditional blast furnace wereavailable.

Operating Parameters for the Blast Furnace

The operational results of a traditional blast fur-nace were calculated using the model, and thesimulation results were compared with actual pro-duction data to verify the validity of the model. Themain operating parameters of the actual productionblast furnace are shown in Table III. On the basis ofthe model validation, the boundary conditions andinternal parameters of the model were modified toobtain the oxygen blast furnace mathematicalmodel. In the simulations of the oxygen blast fur-nace, one set of parameters was set as the base case.The operating parameters are shown in Table IV.

Two rows of tuyeres are present in the oxygenblast furnace. The recycling gas volumes, composi-tions, and temperatures of these tuyeres are shownin Table V. To ensure the reasonable setting of theinlet boundary conditions, all conditions were cal-culated by a comprehensive mathematical modelestablished on balancing the chemical reactions andmaintaining the conservation of material and en-ergy under the corresponding operating conditions.

RESULTS AND DISCUSSION

Model Validation

To verify the validity and accuracy of the model,the model was used to calculate the parameters of atraditional blast furnace. Figure 4 shows the tem-perature distribution of the three phases, and the

Table III. The operating parameters for thesimulated traditional blast furnace

PhasesOperatingparameters Values

Gas Blast rate, blasttemperature,

humidity, oxygenenrichment rate,top pressure, and

blast pressure

1700 m3 min�1, 1423 K,1.7%, 1.66%, 1.2 9 105 Pa,

and 2.2 9 105 Pa

Solid Daily output of iron,Fe2O3 content, cokerate, fixed carboncontent of coke,charge tempera-

ture, and coal injec-tion ratio

2100 t day�1, 76.66%,370 kg t�1, 82.28%, 298 K,

and 170 kg t�1

Liquid [C], [Si], [S], [P],and [Mn] content in

hot metal

4.6, 0.5, 0.025, 0.084,and 0.15%

Table IV. The operating parameters of the oxygenblast furnace for the basic case in the GF–FOBFprocess

PhasesOperatingParameters Values

Gas Blast rate, blasttemperature, oxy-gen concentration,and top pressure

536.7 m3 min�1, 29 8 K,90.0%, 1.2 9 105 Pa

Solid Daily output of iron,Fe2O3 content, cokerate, fixed carboncontent of coke,charge tempera-

ture, and coal injec-tion ratio

3150 t day�1, 76.66%,205 kg t�1, 82.28%, 298 K,

200 kg t�1

Liquid [C], [Si], [S], [P],and [Mn] content in

hot metal

4.6%, 0.5%, 0.025%, 0.084%,0.15%

Zhang, Meng, L. Guo, and Z. Guo1940

dashed line represents the cohesive zone. From thisfigure, the calculated temperature fields match wellwith the temperature distribution trends obtainedby anatomical blast furnace or other actual mea-

surements. The cohesive zone displays an invertedV-shape.

The calculated top gas components were com-pared with the values noted during actual produc-

Table V. Recycling gas parameters for the oxygen blast furnace

Region

Recycling Gas composition (vol.%)

Gas volume (m3 t21) Temperature (K)CO CO2 H2 H2O O2 N2

Recycling gas into shaft 80.5 – 8.4 – – 11.1 358.0 1173Recycling gas into hearth 80.5 – 8.4 – – 11.1 400.0 1173

Fig. 4. (a) Gas, (b) solid, and (c) liquid temperature field in a traditional blast furnace (K).

Table VI. Comparisons of the calculated top gas compositions and the measured values for a traditionalblast furnace

Top gas compositions CO CO2 H2 H2O O2 N2

Calculated values (vol.%) 22.5 20.3 1.5 3.1 0.1 52.5Measured values (vol.%) 21.9 20.2 1.9 2.3 0.3 53.4

Numerical Study of the Gas Distribution in an Oxygen Blast Furnace Part 1: Model Buildingand Basic Characteristics

1941

tion (Table VI). Minimal differences were noted be-tween these two sets of values, reflecting the highcredibility of the calculated results of the model.

Basic Characteristics of the Gas Distributionin an Oxygen Blast Furnace

To determine the basic characteristics of the gasdistribution in an oxygen blast furnace, the basecase for an oxygen blast furnace was calculated withthe multifluid model. CO and CO2 replaced N2 asthe main components of the gaseous phase in theoxygen blast furnace, and their distributions areessential to the smooth operation of the blast fur-nace. Therefore, CO and CO2 can be used to char-acterize the distribution of the gas phase in oxygenblast furnaces.

Figure 5 shows the calculated concentration dis-tributions of CO and CO2 in the oxygen blast fur-nace. Below the shaft tuyere in the furnace, thecontours of CO and CO2 are parallel to the hori-zontal plane and their volume fractions decrease orincrease as the height increases, whereas theircontours becomes parallel to the vertical directionabove the shaft tuyere. In the upper and top part ofthe furnace, the CO volume fraction distributionalso presents a gradually decreasing trend from theedge to the center of the furnace, whereas the CO2

volume fraction shows an opposite trend. This phe-nomenon mainly results from the collisions of therecycling gas injected into the blast furnace throughthe shaft tuyere with the charge temperature andthe gas ascending from the hearth. These collisionshamper the horizontal movement of the recyclinggas and promote an upward movement, causing anuneven distribution of the recycling gas.

Figure 6a and b shows the radius distributions ofCO and CO2 at different heights above the shafttuyere in the oxygen blast furnace used in the GF–FOBF process, respectively. From this figure, theCO concentration decreases from the edge to thecenter at the identical height above the shaft tuyere.In addition, as the height increases, the CO con-centration decreases, whereas the CO2 concentra-tion shows an opposite trend. At the top of oxygen

Fig. 5. Volume fraction distributions of (a) CO and (b) CO2 in theoxygen blast furnace.

Fig. 6. Radial distributions of (a) CO and (b) CO2 at different heights in the oxygen blast furnace.

Zhang, Meng, L. Guo, and Z. Guo1942

blast furnace, the concentration differences of theCO and CO2 between center and edge reach amaximum (7.8% and 11.7%, respectively). Thesevalues can be used to represent the uneven distri-bution degree of the reducing gas. However, bothremain stable in the central portion (the inner onethird of the blast furnace). This phenomenon indi-cates that the recycling gas from the shaft tuyerecan only penetrate to two thirds of the radialdirection. Natsui et al.19,20 called the infiltration ofthe recycling gas toward the center the radial eddydiffusion effect; this effect results from the irregulardistribution of the gas in the radial direction causedby turbulent diffusion. Because the even distribu-tion of recycling gas is essential to reducing theburden, distributing the temperature, and utilizingthe reducing gas, the magnitude of the radial eddydiffusion effect plays a significant role in the uti-lization of the recycling gas in an oxygen blast fur-nace.

To further validate the application of the oxygenblast furnace multifluid model in the study of thegas distribution, the simulation results of the gasdistribution in the blast furnace was compared withthe experimental results of the gas distribution inan oxygen blast furnace obtained by Liu et al.21

Figure 7a and b show the typical gas distribution inthe upper furnace and the radial distributions of therecycling gas injected through the shaft tuyere inthe experimental study, respectively. The volumefraction distribution trend is similar to the distri-bution in Fig. 5a. The recycling gas injected throughthe shaft tuyere is concentrated at the edge of theblast furnace. The upper part of the furnace is di-vided into two parts: the hearth gas-affected zoneand the shaft recycling gas-affected zone. For theradial distribution of recycling gas, the experimen-tal data measured at different heights of the furnaceis similar to the radial distribution of CO shown inFig. 6a. Small differences are noted because the

model considers the chemical reactions and hightemperatures that are ignored in this previousexperiment. The similarity between the simulationresults and the experimental results shows that themodel is appropriate for studying the gas distribu-tion in an oxygen blast furnace. Furthermore, themodel is more accurate and comprehensive to con-sider completely the actual conditions.

CONCLUSION

The gas distribution in an oxygen blast furnacewas studied with a recently established multifluidmodel. The main findings of this study are sum-marized as follows:

1. Because of the introduction of the shaft tuyere,the uneven distribution of the recycling gasbecomes a severe problem. Below the shafttuyere, the reducing gas is evenly distributed.However, the recycling gas is unevenly dis-tributed above the shaft tuyere. The distribu-tions of CO and CO2 can be used to demonstratethis problem.

2. The gas distribution in an oxygen blast furnacedisplays concentration differences of CO andCO2 between the center and edge at the top ofthe furnace, reaching 7.8% and 11.7%, respec-tively. The recycling gas from the shaft tuyereonly penetrates two thirds of the radius; i.e., therecycling gas is concentrated at the edge of theblast furnace. Therefore, the recycling gas uti-lization is seriously affected.

ACKNOWLEDGEMENT

This research was supported by the NationalNatural Science Foundation of China (Grant No.51134008) and National Program on Key Basic Re-search Project of China (973 Program) (Grant No.2012CB720401).

Fig. 7. The experimental results from the literature: (a) volume fraction distribution of shaft recycling in the upper furnace and (b) radialdistribution of the shaft recycling gas at different heights of the furnace shaft.

Numerical Study of the Gas Distribution in an Oxygen Blast Furnace Part 1: Model Buildingand Basic Characteristics

1943

REFERENCES

1. M.S. Qin and Y.T. Zhang, Ironmak. Steelmak. 15, 287(1988).

2. R. Murai, M. Sato, and T. Ariyama, ISIJ Int. 44, 2168 (2004).3. J.L. Meng, H.Q. Tang, and Z.C. Guo, Appl. Mech. Mater.

268, 356 (2013).4. T. Inada, A. Kasai, K. Nakano, S. Komatsu, and A. Ogawa,

ISIJ Int. 49, 470 (2009).5. T. Iwamura, H. Sakimura, Y. Maki, T. Kawai, and Y. Asano,

Trans. Iron Steel Inst. Jpn. 22, 764 (1982).6. J. Yagi, ISIJ Int. 33, 619 (1993).7. M.S. Chu, H. Nogami, and J. Yagi, ISIJ Int. 44, 801 (2004).8. K. Meijer, M. Denys, J. Lasar, J.P. Birat, G. Still, and B.

Overmaat, Ironmak. Steelmak. 36, 249 (2009).9. M.S. Chu and J. Yagi, Steel Res. Int. 81, 1043 (2010).

10. M.S. Chu, X.F. Yang, F.M. Shen, J. Yagi, and H. Nogami, J.Iron. Steel Res. Int. 13, 8 (2006).

11. H. Nogami, M.S. Chu, and J. Yagi, Rev. Metall. 102, 189(2005).

12. M.S. Chu, H. Nogami, and J. Yagi, ISIJ Int. 44, 2159 (2004).13. S. Ergun, Chem. Eng. Prog. 48, 89 (1952).14. J.F. Richardson and R.A. Meikle, Trans. Inst. Chem. Eng.

39, 348 (1961).15. P.C. Carman, Chem. Eng. Res. Des. 75, S32 (1997).16. W.E. Ranz and W.R. Marshall, Chem. Eng. Prog. 48, 141

(1952).17. P.J. Mackey and N.A. Warner, Metall. Trans. 3, 1807 (1972).18. E.R.G. Eckert and R.M. Drake, Heat Mass Transfer, 2nd ed.

(New York: McGraw-Hill Book Co., 1976), p. 173.19. S. Natsui, S. Ueda, H. Nogami, J. Kano, R. Inoue, and T.

Ariyama, ISIJ Int. 51, 1410 (2011).20. S. Natsui, S. Ueda, H. Nogami, J. Kano, R. Inoue, and T.

Ariyama, ISIJ Int. 51, 51 (2011).21. J.Z. Liu, Q.G. Xue, X.F. She, and J.S. Wang, Beijing Keji

Daxue Xuebao 36, 817 (2014).

Zhang, Meng, L. Guo, and Z. Guo1944