# Mathematical Modeling of the Prereduction Process of Iron Ore in a Circulating Fluidized Bed.

код для вставкиСкачатьMathematical Modeling of the Prereduction Process of Iron Ore in a Circulating Fluidized Bed Y. B. Hahn,' Y. H. Im, K. J. Kim, D. G. Park,+l. 0. Lee,' 1. S. Nam" and K. S. Chang" Department of Chemical Engineering, Chonbuk National KOREA University, 664-74 Duckjn-dong 1 Gal Chonju 567-756, ~~ A malhematical model has been developed to describe the various subprocesses occurring in a circulating fruidized bed (CFB) used for pre-reduction of iron ore particles in the smelting reductwn iron-making process. The model incorporates hydrodynamics, iron reduction kinetics, and heat and mass transfer. One of the key features is the inclusion of a wall-to-bed heat transfer model to describe the heat transfer phenomena occurring in the CFB. The predicted and measured heat transfer coeficients showed a minima in the lower par1 of the bed due lo the irregular up-and-down movement of ore particles. The model predictions of the reduction degree of iron oxides based on shrinking-unreacted-corechemical reaclwn control mode showed satisfactory overall agreement with measured data. The performance of the CFB reactor has been tested extensively in terms of gas oxidation degree, inlet temperature,particle size and mean particle residence time. It was confirmed that the reduction degree is signifiantly affected by gas oxidation degree, wall temperature and particle size. Introduction CFB reactorshave been u t i l d extensively in both catalytic and noncatalpc gas-solid reactions, such as in the catalytic cracking of crude oil, the combustion of low-grade. fuels to meet strict environmental standards,and the gasification of wood and biomass. However, little work has been done on the behavior of fluidizing iron ore particles in the CFB for the purpose of iron ore reduction. In recent years, various smelting/reductionprocesses have been under development to replace the conventional iron-making process, i.e. the blast furnace process. The smelting- reduction iron-making ~ X O C ~ S Smay be required to satisfy criteria such as the use of different coals, simplified material preparation, hot metal with little impurities, * + Author to whom correspondence should be addressed. Research Institute of Industrial Science and Technology, b h a n g 790-600,KOREA. i-+ Depamnent of Chemical Engineering, Pohang Institute of Science and Technology, Pohang 79@600, KOREA. 23 Y.B. Hahn, et al. independent process steps, dosed energy system, efficient pollution conUoJ and no generation of wastes. The smelting/reduction process that combines a smelting furnace and a CFB pre-reduction reacm has been highlighted as one of promising processes that meet the above requirements [I, 21. For the pre-reduction stage, there is an increasing interest in using a CFB because of its ability for the pre-reduction of iron oxides.The CFB reactor has seveml advantages including no agglomeration of the feed, excellent heat and mass transfer, temperature uniformity through the whole reactor circuit, excellent thermal efficiency. low investment cost, and efficient pollution control. An understanding of the overail phenomena occurring in a CFB is important, but very little work has been done based on first principles. This is mainly due to the complexity of the system. In this work, a mathematical model has been developed to describe the various subprocesses occumng in the CFB used for pre-reduction of iron ores in the smeltinglreductionim-making process. The model incorporates hydrodynamics, iron reduction kinetics, and heat and mass transfer. The model predictions were compared with experimental data and showed good agreement. The performance of the CFE3 reactor has been extensively tested in terms of various operating conditions such as superficial gas velocity, particle size, gas oxidation degree, inlet temperature, and mean parucle residence time. Mathematical Models The circulating fluidized bed consists of a gas inlet, iiser, cyclone, downcomer and solid discharge, as shown in Figure 1. The specified particles are charged into the riser, and the reducing gases are blown in through a perforated bottom plate. The particles are then fluidzed. separated in a recycling cyclone, and circulated through 0 Downcorner(or Circulation tube) 0 Cyclone @ Gas exit 0 Blower 8 0 Aeration tube Electric heater Figure 1. Schematic diagram of a c i r c W g jluidized bed. 24 Mathematical Modeling of Prereduction Process of Iron Ore the downcomer into the bed to maintain the amount of solid in the CFB reactor. The riser in which the pre-reduction reaction of iron ores occurs is important. Fbr efficient operation, stable fluidization of ore panicles has to be maintained in the riser. Model equations basedon first principles may be obtained by considering m a s and momentum balances, gas-solid-wall interactions, and heat and mass transfer for both the gas and solid phases. Hyddynunaic model To describe the fluidizing behavior of solid partides in a CFB,s e v e d hydrodynamic models have been proposed by many research groups. The models can be divided largely into two main groups: entrainment models [3,4] and inviscid models for two fluids [57]. Hahn et al. in 1995 showed that the inviscid model can be adequately used to describe the hydrodynamic behavior of iron ore particles in a CFB [7]. Hence, in this study, the inviscid model in which both phases are considered to be continuous and fully interpenetrating has been used to describe the behavior of fluidizing iron ore in the CFB riser. Detailed descriptions of the hydrodynamic model equations are available elsewhere [ST. Heat transfer model The conservation equation of energy includes conduction, convection and radiation. Based on the assumption of onedmensional steady state, the energy equations for both gas and solid phases can be expressed, respectively, in the following forms : The boundary conditions for solving Equations (1) and (2) are obtained from the inlet values of T8 and T,, The inlet values of ef E,, u8 and usare also used as boundary conditions for solving the hydrodynamic model equations. The gas-solid interphase heat-transfer coefficient (hJ can be obtained from the following equation [8,9]: 6Eh hi =- (3) dP where the gas-solid heat transfer coefficient (h) can be obtained from the following empirical cornlation f9]: 25 Y.B. Hahn, et al, Nu = nd =h( 7 - 1 0 ~ g +%:)[I k8 +0.7R,Q 2 P,1pI a7 Ip +(133 - 2 4 + 12&,+ l.2&i)Re P, (4) where In Equations (1)and (2). the thermal conductivities %and K , represent contributions due to the gas and solid phases, respectively, and they pose some difficulty in solving the energy equations because they are effective transfort properties. Bauer and SchlUnder [ 101 developed an approximate model for the effective thermal conductivity in packed beds. Kuipers et al. [9] and Biyikli et al. [ 111 applied this model to estimate the effective thermal conductivity in fluidized beds. In this work, based on Bauer and Schliinder's model,K,and K, can be obtained from : K,represents the contribution of thermal radiation, and can be expressed as [12J: 26 Mathemaricai Modeling of Prereduction Process of Iron Ore In order to obtain the volumetric wall-to-bed heat transfer coefficients, Hahn et al. in 1994 have developed a wall-to-bed heat transfer model based on core-annulus flow structure [13].where qgand 4, are obtained based on the wall-to-bed heat transfer model : where Reduction Kinetics of Iron Ore Particles The iron ores are reduced by the two major reducing agents, i.e. carbon monoxide and hydrogen. The reduction involves the following steps : Fe30, AH", + co(m = 9.7; H2) 3FeO + W 2 ( m H,O) Hl = 195 (M I md) + FeO+CO(m H2) + F e + W 2 ( u r H 2 0 ) AH",, =-4.4; AM&Hl =5.4(kcallml) The above reactions occur in series depending on reduction degree (RD), that is, reaction (17) when RD e 11%. reaction (18)when 11 5 RD s 308, and reaction (19) when RD > 30%.The overall reduction reaction is written as : 27 Y.B. Hahn, et al. Fe203+3C5(or 3H2) + 2Fe +3C02(a3H20) AI-&, =-6.l; A I $ m H , = 2 3 . 4 ( k C a l I t d ) Iron ore pamcles in the CFB system are much small compared with the conventional blast furnace iron-makmg process in which sintered pellets are reduced. In general, the reducing gases are fed into the reactor in a large excess amount. The CFB system also can be characterized by efficient contact between gas and solid particles, and rapid rate of mass and heat transfer. Hence, it is assumed that mass transfer resistance of gases from the bulk to the surface can be neglected. Based on this assumption, the reduction of nonporous iron ore particles can be described by a chemical reaction control scheme under using the shrinlung unreacted-core model [14]. The conversion is then given by : where the dimensionless time is defined as : The reduction rate is obtained from : Since the reduction of iron oxides is affected by the solids residence time, the residence time distribution of the solids in the bed has to be considered for a continuous fluidized bed reactor. The residence time distribution of soIids at dinlensionless time is given by [Is] : E(f*) = T1e x p [ tR -$] where - kC r',=-T;; PBrP and - iR = W mean residence time = 9 F, 28 Mathematical Modeling of Prereduction Process of Iron Ore By combining Equations (21) and (24),the mean conversion of iron oxides leaving the CFB reactor is : The energy source for the energy equation of the solid phase is : where V,, and G , represent the control cell volume and the solid mass flux in the fluidized bed, respectively. The corresponding equation for the gas-phase energy is : h sp* =-sph In Equation (B),A@ is obtained from : RESULTS A N D DISCUSSION Predictions of Heat Transfer in a CFB In our previous work [13],a wall-tdxd heat transfer model was developed based on the core-annulus flow structure. To verify the heat transfer model, model predictions were compared with measured data obtained by Wu et al. [16] They obtained heat transfer data from two heat transfer surfaces, each 1.53 m long and 148 nvn wide, located on one wall of the rectangular column and beginning 1.22 and 4.27 m above the distributor plate. The profiles for the heat vansfer coefficient as a function of height measured downward along the upper and lower heat transfer surfaces are shown in Figures 2 and 3, respectively, together with the model predictions Ilepresented by the solid lines. From Figure 2 the developed wall-to-bed heat transfer model produces satisfactory prediction of the heat transfer coefficient in the upper part of the bed. The model predictions in the lower part of the bed are less satisfactory (see Figure 3). However, the model predicts almost the same trend as the experimental measurements. The prehcted and measured data show a minima in the heat transfer coefficient in the lower surface region. The particle motion in the lower part of the CFB is likely to be less regular than that in the upper part Particles move sometimes upward and sometimes downward in the lower part of the bed. The upand-down motion of particles may explain the minima in the heat transfer coefficient in the lower part of the bed [16]. Figure 3 also shows sharp increase in the predicted and measured heat transfer coefficient possibly because the suspension density increases 29 Y.B. Hahn, et al. 400 1 350 - I I 0 G,, = 28 kg/m s 250 loo t n 50 I 0.0 W I 1 .o 0.5 Distance along Heat Transfer Surface(m) Figure 2. Effect of solid circurCrrionftux on the Iocai hear trunsfer coefficient along the upper heat transfer surface ( 0 0 measuremenfsby Wu el al. [MI;prediction of this work). 4 tl .r( 0 450 I 400 - 150 - .rl I k rn 0 - 0 0 0 I 4 100 0.0 I 0.5 I 1 .o Distance along the Heat Transfer Surtace(m) Figure 3. EBect of solid circulation flux on the local heat trawfer coeficient along the lower heat transfer surfwe ( 0 measurements by Wu et al. [16];prediction of this work). 30 Mathematical Modeling of Prereduction Process of Iron Ore over the lower part of the heat transfer surface. In spite of the complexityand differences between the upper part (orthe dilute-phase region) and the lower part (or the dense-phase region), the model pmhctions are satisfactory overall. Based on the wall-to-bed heat transfer model, p h c t i o n s were made to explain the heat transfer phenomena occurring in a CFB. The test CFB is 10 rn high and 0.31 rn &meter. Test particles are iron ores with a size distribution of 40% 2ooo pm, 20% 3000 p, 12% 4OOO p and 28% so00 pm. The fluidizing medium is a reducing gas having composition of 54% CO, 5%Ar, 20% CO, and 21% H,. A typical example of the model predrctions in terms of effect of inlet temperature is shown in Figure 4 for the case of an ore inventory of 130 kg, superficial gas velocity of 4 m/s and solid circulation rate of 11.5 kg/rn2.s.For calculations, the wall temperature was fixed at 1073K. The temperature of solid is higher than the gas along the riser height, in spite of feedlng solids at temperatures lower than the gas. This indicates that the solid particles are heated up first,and followed by the gas. This result may be because the heat transfer rate from the wall surface to the solid particles is greater than that to the gas phase. This also may be due to the large heat capacity and conductivity of the iron ores compared to the reducing gas. Reduction of Iron Ores in a CFB Iron ore particles are pre-reduced in the CFB reactor to increase the productivity of the smeltinglreduction furnace, to decrease the consumption of coal as a primary energy source, and to suppress the generation of gas. The gas generated in the smelting/reduction furnace is utilized as a reducing gas in the pre-reduction stage. The reduction rate of iron oxides is significantly affected by the gas oxidation degree (GOD) and the bed temperature. Although the reaction kinetics of iron oxides in the CFB reactor are of importance, very little work has been reported. As described in previous section, the reduction reaction of iron oxides occurs in series dependmg on reduction degree. However, it is v e q difficult to explicitly obtain kinetic data for each reaction step. Hence, apparent experimental kinetic data were used to express the rate constants in Arrhenius form. In a series of experiments with varying temperature and particle size, the reduction of iron oxides with CO was able to be described as chemical reaction control in the shnnlung urueacted-core model as shown in Figure 5. Although not illustrated, similar behavior was obtained for the case of reducing iron oxides with %. The apparent rate constants for reducing iron oxides with CO and % are expressed, respectively, as follows : kco = 1 5 . 4 6 e x p10,412 (-y) It is assumed that the a p p n t kinetic data obtained from Equations (31) and (32) can be used to quantitatively describe the individual reduction steps. This assumption 31 Y.B. Hahn, et al. - 700 700 I Tgo= 573K. TIO= 473K P Tgo= TSo= 473K k4 W Q) s 600 600 f 4 ld k Q) 8 500 500 Q) b Solid temperature 400 400 0 2 4 6 8 1012 1200 n x 1000 0 2 4 6 8 1 0 1 2 11200 T = 773K, Tao= 473K PO 1000 Tgo= 1073K, Tao= 300K W 600 800 600 600 3 4 ld 2 E^ Q) b 400 200 0 Gas temperature 40 0 1 ' 200 - Figure 4. Temperature profile ahng the riser height with varying inlet temperatures (Tw= 1073K). 32 Mathematical Modeling of Prereduction Process of Iron Ore 0.8 I I I I I I 10 20 30 40 50 60 m 0.6 \ d n x I 4 0.4 W I 0.2 4 0.0 0 70 1.0 m 0.6 \ d n x I 0.6 4 W 0.4 I 4 0.2 0.0 0 10 20 30 40 50 Time (min) Figure 5. Reduction degtee versus time with CO reduelion of 1223 K ((a)particle size 0.125-0.25mm; ( b )particle size 0.25-0.5mm I. was verified with Figure 6 in which model predctions based on this assumption showed good agreement with measurements (0)in terms of reduction degree versus time. Prereduction of iron ore particles (size 1-5mm) was carried out in a laboratory-scale circulating fluidized bed (3 m high; 0.08 m diameter). The gas oxidation degree defined as (CO, + H,O)/(CO + CO,+ H, + $0) was maintained at 21% for the first 30 minutes, and at 5% for the next 30 minutes. The prerduction results obtained at a wall temperature 1073K are shown in Figure 6. The sudden increase of reduction degree at 30 minutes is due to switching the gas oxidation degree from 21% to 5%. The solid cuwes (a) and (b) in Figure 6 represent the predicted reduction degree in the riser itself, and in the whole CFB system including cyclone and downcomer, respectively. It is seen that the agreement between the predicted and measured results are satisfactory overall. The effect of wall temperatures on the reduction of iron oxides was predicted and is shown in Figure 7.The reduction rate is greatly affected by the wall temperature. 33 Y.B. Hahn, et al. The reduction of iron ores is also affected by the gas oxidation degree. Predictions were made at a wall temperature 1073K with varying GOD values as given in Table I . Table 1 shows inlet gas compositions for the first 30 minutes of reduction (prereduction)and for the next 30 minutes (final reduction). The predicted results are shown in Figure 8 where the reduction of iron oxides is significantly affected by the gas oxidation degree. The effect of particle size was predicted at the wall temperature of 1073K with switching the GOD from 21 to 5% after 30 minutes reduction time. It is seen from Figure 9 that iron ore parucles smaller than 1 nrm are quickly reduced to 90% reduction degree within 30 minutes. The predicted results may be used to estimate the feed rate of iron ores because the mean residence time is determined depending on the mean reduction degree. Table 1 . Composition of reducing gases. 1.o 0.8 0.8 0.7 0.6 0.5 0 -4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 60 70 Time (min) Figure 6. Comparison of predicted and measured reduction degree versus time [(a) reduction degree in the riser ( ): (b)reduction degree in the whole CFB sysrern f 0 ) I . 34 Mathematical Modeling of Prereduction Process of Iron Ore 1.o 0.9 0.8 - 0.7 - 0.6 (a) 1023 K 0.5 (b) 1073 K 0.4 (c) 1123 K (a) K 0.3 1173 - - 0.2 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 Time (min) Figure 7. Effect of wall temperature on the reduction rate of iron ore (particle size 1-5 m). Time (min) Figure 8. Effect of gas oxidation degree on reduction rate of iron ore: a, b. c and d arefrom Table I (T,= 1073K) 35 Y.B. Hahn. et al. CONCLUSIONS The numerical predictions of the prereduction of iron ores in a circulating fluidized bed show satisfactory overall agreement with experimentaldata in spite of the bmplex nature of the system. This leads to the following conclusions. 1. The developed wall-Wbed heat transfer model produd good prediction of the heat transfer coefficient in the upper part of the bed, and less satisfactory but the same trend in the lower part of the bed. The predicted and measured data showed a minima in the heat transfer coefficient in the lower part of the bed due to the irregular up-anddown movement of parbcles. 2. The reduction of iron oxides in the CFB can be described by chemical reaction control using a shrinking unreacted-core model.The model predictions of reduction degree showed satisfactory overall agreement with measured data 3. The reduction degree is significantly affected by the gas oxidation degree, wall temperature and particle size. 80 I I I I I I I I 1 1 - 80 - Particle Size 70 - (a) 0.25-0.5 'O - mm (b) 0.5-1 m m (c) 1 - 3 mm 50 - (d) 3 40 - ( c )- 30 - - 20 - - - (dl - 5 mm (b) - (4 0.0 0.1 0.2 0.3 0.4 0.6 0.8 0.7 0.8 0.9 1.0 Mean Reduction Degree Figure 9. Mean residence time versus mean reduction degree with varying particle size (Tw= 1073K). 36 Mathematical Modeling of Prereduction Process of Iron Ore NOMENCLATURE C& ‘P8 Bulk concentration of reducing gas [mOUm?. Heat capacity of gas [JlkgeKJ. Heat capacity of solid [Jlkg-KJ. Particle drameter [ m]. Solid feed rate [kglh]. Fs h Gas-solid heat transfer coefficient [ Jlm’sK 1. Volumetric heat transfer coefficient [ J/m2.sK ] . h, hwg,h, Wall-&bed heat hansfer coefficientsof gas and solid [ J/m2.sK 1. Thermal conductivity of gas [ J l m s K 1. kg Thermal conductivity of solid [JlmsK 1. 4 Defined in Equation (6) [JlmAsK I. K/ Radiation contribution to heat conductivity, Equation (12) [Jlrn.s.K]. KR Defined in Equation (7) [Jlm-sK 1. KS P Pressure [N/m2] P Radius of parhcle. Rates of enthalpy change due to the reaction of iron ore. Muation (28). t Dimensionless time, Equation (22). c&= dP tPg, s”, - 1; Ts TS T*. % US X X X Dimensionlessmean residence time of particles, Equation (25). Gas temperature [ 4. Solid temperature Wall temperature [a. Gas velocity [mls]. Solid velocity [ d s ] . Average falling velocity of emulsion [ d s ] . Mole fraction. Conversion Mean conversion, Equation (27). Bed weight [kg]. [a. W, Greek Symbols awg, am Volumetricwall-@bed heat transfer coefficientsof gas and solid, respectively [J/m2.sK 1. B Gas-solid friction coefficient. ax Thcbess of emulsion layer [m]. Voidage. 5 Volume fraction of solid. 5 PB Molar density of iron oxide [mUmq. Gas density [kg/m3]. ’8 Solid density [kglm’ 1. P* 0 Stephan-Boltzmannconstant. @S Sphericity of solid particle. ACKNOWLEDGEMENTS Parttal financial support from Korea Science and Engineering Foundation through the 37 Y.B. Hahn, er al. Automation Research Center at POSTECH is gratefully acknowledged. REFERENCES 1. Capel, F.and Hirsch, M 1991. "Reduction of Fine Ore in the Circulating Fluid Bed as !he Initial Stage in Smelting Reduction." Metallurgical Plant and Technology International. 3.28-32. 1. 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