Solids Circulation and Attrition Rates and Gas Bypassing in an

Ray et al.14 proposed a mechanical model to assess the effects of various mechanical factors on the attrition rate for a bubbling fluidized bed. This ...
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Ind. Eng. Chem. Res. 2003, 42, 5915-5923

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GENERAL RESEARCH Solids Circulation and Attrition Rates and Gas Bypassing in an Internally Circulating Fluidized Bed Hsin Hong Shih, Chen Yeon Chu, and Shyh Jye Hwang* Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China

Solids circulation and attrition rates and gas bypassing in an internally circulating fluidized bed (ICFB) were studied. The bed materials used were mixtures of silica sand and calcium particles. The effects of the superficial gas velocities in the annulus and the draft tube, average diameter of the calcium particles, and geometry of the draft tube on the solids circulation and attrition rates and gas-bypassing fractions were investigated. It was found that the solids circulation rate first increased with increasing superficial gas velocity in the annulus and then leveled off. It also increased with increasing superficial gas velocity in the draft tube and the orifice diameter. However, it decreased with increasing average diameter of the calcium particles. When the draft tube height increased from 25 to 35 cm, a minimum solids circulation rate occurred at 30 cm. Moreover, when the inner diameter of the draft tube increased from 3 to 5 cm, a maximum solids circulation rate occurred at 4 cm. Gas-bypassing fractions depended primarily on the solids circulation rate, superficial gas velocity in the draft tube, and state of solids packing and bed height in the annulus. The attrition rate initially depended on the solids circulation rate and the extent of collisions among the particles, and it would then reach a steady state. Therefore, the characteristics of the calcium particles were the most important factors affecting the attrition rate in ICFB. Finally, an empirical correlation equation for the steadystate solids circulation rate proposed in this study could match the experimental results. Introduction An internally circulating fluidized bed (ICFB) is a fluidized bed with a draft tube. The draft tube was fixed directly to the distributor of the riser section, and a number of orifices were positioned on the wall of the draft tube near its base.1,2 ICFB was an improvement over the spout-fluid bed with a draft tube in alleviating the problem of gas bypassing.1 In addition, the separate aeration of gas for the draft tube and the annulus could provide more flexible operation. The solids circulation rate can be controlled by adjusting the relative magnitude of the spouting and aerating velocities.1-4 Several investigators studied the solids circulation rate in ICFB.1,2,5 Milne et al.1 found that the solids circulation rate based on the annulus cross-sectional area was a nearly linear function of the superficial gas velocity in the annulus and the effect of the superficial gas velocity in the draft tube was slight. The results of Ahn et al.2 showed that the enhancement effect of the superficial gas velocity in the annulus section on the solids circulation rate in ICFB was greater than that of the superficial gas velocity in the draft tube section. Milne et al.1 and Ahn et al.2 used the equation derived by De Jong and Hoelen6 to fit the experimental data of the solids circulation rate per orifice and obtained the * To whom correspondence should be addressed. Tel.: +88635723221. Fax: +886-35715408. E-mail: sjhwang@ che.nthu.edu.tw.

values of the discharge coefficient. Three kinds of gas distributors were used to study the solids circulation rate and gas bypassing in an ICFB by Song et al.5 They indicated that the solids circulation rate could be correlated with the pressure drop across the gap opening and opening ratio using the orifice equation. They also found that the conical plate distributor was the most suitable configuration for the solids circulation in ICFB. La Nauze7 presented a model of solids circulation based on the density difference between the two beds and the shear stress at the wall. Kuramoto et al.8 used a twodimensional bed and found that the solids circulation was controlled by the superficial gas velocity in the draft tube and the ratio of the opening area to the crosssectional area of the downcomer. They developed an equation using the pressure drop across an opening and the opening ratio to correlate the solids circulation. Choi and Kim9 used an optical probe to study the bubble characteristics in an ICFB. The effect of sulfation on solids circulation and attrition has been discussed by Chu and Hwang.10 Reports on attrition in the fluidized bed were numerous.11-15 Merrick and Highley11 found that the total rate of fines by abrasion in a fluidized bed was proportional to the bed weight and excess velocity. They used the particle size and overall bed size distribution to predict the resulting size reduction of the particles in a bed of wide size distributions. Lin et al.12 found that the attrition rate of production of fines of char particles

10.1021/ie0302490 CCC: $25.00 © 2003 American Chemical Society Published on Web 10/03/2003

5916 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003

in a char/sand fluidized bed increased exponentially with the excess velocity. Shamlou et al.13 reported that the breakage of the bed material could occur by purely hydrodynamic effects in the fluidized bed. In addition, the breakage process was predominantly the removal of single particles or small groups of particles from the surface of the parent material by attrition. Lin et al.12 and Shamlou et al.13 also employed a first-order attrition rate model to evaluate the weight changes of the bed material in the fluidized bed. Ray et al.14 proposed a mechanical model to assess the effects of various mechanical factors on the attrition rate for a bubbling fluidized bed. This model predicted that larger coal and smaller limestone were more desirable for reducing attrition in a coal combustor. Lee et al.15 observed that the weight of the solid in a fluidized bed would approach a constant value, so they introduced a minimum weight of the bed material into the first-order attrition rate model. Cook et al.16 further proposed a modified secondorder model using a minimum weight and excess velocities for lime sorbent in a circulating fluidized-bed absorber and expressed the attrition rate in an Arrhenius form. Mathur and Epstein17 indicated that a smaller diameter of the air inlet orifice, a higher air flow rate, and a deeper bed resulted in a larger attrition in the spouted bed. However, studies of attrition in ICFB were limited. Previous works on gas bypassing in ICFB were conducted by Milne et al.,1 Ahn et al.,2 and Song et al.5 Milne et al.1 observed that the gas flow rate from the annulus to the draft tube was approximately 85% of the auxiliary gas flow rate, and the inlet gas to the draft tube was confined to the riser. Ahn et al.2 found that the gas bypassing from the annulus to the draft tube increased but that from the draft tube to the annulus decreased with increasing superficial gas velocity in the draft tube at a constant superficial gas velocity in the annulus. Similar results were also reported by Song et al.5 Ahn et al.2 also found that the orifice diameter greatly affected the gas-bypassing fraction from the annulus to the draft tube. Moreover, Song et al.5 observed that the gas-bypassing fraction from the annulus to the draft tube had a minimum value at 0.6 < Ua/Umf < 0.8. Detailed information on the solids circulation and attrition rates and gas bypassing are required when designing an ICFB reactor. However, studies of these properties in ICFB with mixtures of solids as the bed materials were limited. In this study, the effects of the geometry of the draft tube, average diameter of the calcium particles, and superficial gas velocities in the draft tube and annulus sections on these properties were investigated. In addition, a correlation for the solids circulation rate in ICFB was developed. Experimental Section Experimental Setup and Procedure. A schematic diagram of the ICFB used in this study is shown in Figure 1. The bed was made of acrylic, and its inner diameter and height (included in the conical section) were 9 cm and 2.5 m, respectively. A coaxial draft tube with four orifices was used in the ICFB, and it was fixed to the gas distributor. The heights of the draft tube used were 25, 30, 35, and 40 cm. The inner diameters of the draft tubes used were 3, 4, and 5 cm. In addition, the location of the orifices was 5 cm above the conical gas distributor, and the diameters of the orifices near the

Figure 1. Schematic diagram of the experimental apparatus. (1) Compressor, (2) CO2 cylinder, (3) valve, (4) gas mixing tank, (5) rotameter, (6) windbox of riser section, (7) windbox of annulus section, (8) draft tube, (9) annulus, (10) sampling tube, (11) feed, (12) freeboard, (13) three-way valve, (14) bag filter. Table 1. Chemical Properties of the Calcium Particles chemical composition

weight (%)

CaO Ca(OH)2 CaCO3

62.46 27.00 4.56

chemical composition

weight (%)

MgO others

3.42 2.56

base of the draft tube used were 1.0, 1.4, 1.9, and 2.2 cm. The conical gas distributor at the bottom of the bed was a stainless steel perforated plate with 0.2 cm holes on an equilateral triangle pitch, and the distance between the holes was 0.3 cm. A sheet of steel screen (mesh 400) covered the distributor to prevent the bed materials from falling into the windbox. There were two windboxes under the gas distributor, one for the draft tube section and the other for the annulus section. The air from an air compressor was separated into two streams. One stream passed through the draft tube section, while the other mixed with CO2 gas from an CO2 cylinder and flowed into the annulus section. Rotameters were used to measure the gas flow rate in the draft tube and the annulus sections. It should be noted that under the operating conditions used in this study the draft tube section was always in a bubbling fluidized-bed mode. Also note that in this study all experiments were conducted at room temperature. Bed Materials. The bed materials were mixtures of calcium particles and silica sand. The chemical properties of the calcium particles measured by an atomic absorption spectrometer (AAS; Varian, SpectrAA-30) and a thermogravimetric analyzer (TGA; Dupont 2100, General V4.1 c) are shown in Table 1. The physical characteristics of the bed materials are shown in Table 2. The average diameter of the silica sand was 460 µm, while those of the calcium particles were 254, 324, 385, and 460 µm. The densities of the calcium particles and silica sand were 2300 and 2630 kg/m3, respectively. The weights of the calcium particles and silica sand in the

Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5917 Table 2. Physical Characteristics of the Bed Materials calcium silica sand

bed materials

particle size range average particle size (dpc) particle size range average particle size (dps) average particle size (dp) initial steady state

500-420 µm 460 µm 500-420 µm 460 µm

420-350 µm 385 µm

350-297 µm 324 µm

297-210 µm 254 µm

460 µm 448 µm

438 µm 421-426 µm

416 µm 396 µm

382 µm 350 µm

bed were 500 and 1500 g, respectively. The minimum fluidization velocities of the silica sand and calcium particles with dpc of 254, 324, 385, and 460 µm obtained by the pressure drop versus superficial gas velocity diagram in a bubbling fluidized bed were 19.3, 5.6, 8.9, 12.4, and 17.0 cm/s. The minimum fluidization velocities of various bed materials were then calculated by the method of Rincon et al.18 They were 11.8, 15.0, 16.7, and 18.2 cm/s respectively for the mixtures of the silica sand and calcium particles with dpc of 254, 324, 385, and 460 µm. Measurements. a. Solids Circulation Rate. The solids circulation rate was calculated by

Ws ) Fs(1 - a)AaVa

(1)

where Fs was the average density of the bed materials, a was the bed voidage in the annulus, Aa was the crosssectional area in the annulus, and Va was the bulk velocity of the solids in the annulus. Because the particles in the annulus were always close to the minimum fluidization state for all experimental runs, a was assumed to be equal to mf.1,2 The value of mf obtained from the experiments in this study was 0.5. He et al.19 used a fiber-optic probe system to measure the particle velocity profiles in the annulus of spouted beds. Their system was complicated, and the method was intrusive. Thus, a simpler method used by Yang and Kearns3 was also used in this study. This method was shown to be suitable for the situation of packed bed flow in the annulus.20 Some black silica sand particles taken from the bed materials were used as the tracer particles. Because the flow of the bed materials in the annulus was similar to that in a moving bed, the velocities of the silica sand and calcium particles would be the same. Hence, the velocity of the tracer particles could represent the bulk velocity of the bed materials in the annulus. A stopwatch was used to measure the time (t) of one of the tracer particles traveling a fixed distance (L ) 15 cm) in the annulus. Va was then calculated by

Va ) L/t

(2)

Note that under each operating condition, more than five measurements of t were made. The average value of t was then used in eq 2 to obtain Va. b. Gas-Bypassing Fractions. Gas-bypassing fractions were obtained by the methods of Song et al.5 and Muir et al.20 Tracer gas (CO2) was injected continuously into the annulus, and gas samples were taken at the inlet and outlet of the annulus and the outlet of the draft tube at 30, 90, 150, and 210 min. The concentrations of CO2 in the samples were obtained by a gas chromatograph (GC-TCD; Shimadzu, GC-8A). The gas-bypassing fractions were then calculated by using mass balance

Figure 2. Effect of Ua on the solids circulation rate (Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm).

equations for the draft tube and the annulus sections

fAD )

QAD × 100 QAi

(3)

fDA )

QDA × 100 QDi

(4)

where fAD was the gas-bypassing fraction from the annulus to the draft tube, fDA was the gas-bypassing fraction from the draft tube to the annulus, QAD was the flow rate of the bypassed gas from the annulus to the draft tube, QDA was the flow rate of the bypassed gas from the draft tube to the annulus, QAi was the gas flow rate at the annulus inlet, and QDi was the gas flow rate at the draft tube inlet. All of the values of the gasbypassing fractions were the average value of the data obtained at 90, 150, and 210 min. The data at 30 min was unstable; therefore, it was not taken into account in the evaluation of the gas-bypassing fractions. c. Attrition Rate. Two bag filters were used alternatively by switching the three-way valve periodically to collect all of the fines elutriated. Plots of the cumulative weight of the solids elutriated (We) versus time (t) were then made. The slope of the tangent line at any given time represented the attrition rate at that time. Note that we assumed that the elutriation rate was the same as the attrition rate because the superficial gas velocity used in the experiments was always less than the terminal velocity of the bed materials. This method was similar to that used by Cook et al.16 and Scala et al.21 Results and Discussion Effect of the Superficial Gas Velocity in the Annulus (Ua). The effect of the superficial gas velocity in the annulus (Ua) on the solids circulation rate (Ws) is shown in Figure 2. Ws increased with increasing Ua when Ua was increased from 8.3 to 16.7 cm/s as a result of a higher pressure drop across the orifices.2,7

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Figure 3. Effect of Ua on Wss and gas-bypassing fractions (Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm).

Ws then leveled off when Ua was greater than 16.7 cm/s (Ua/Umf ) 1) because the difference in density between the draft tube and the annulus was reduced with bubble formation in the annulus section.5,7 Also shown in Figure 2 is that, at a given Ua, the solids circulation rate decreased initially and then reached a constant value. Initially, the calcium particles were irregular in shape, which made the solids packing loose. The solids packing became denser when the surface of the calcium particles became smoother because of attrition. As a result, the interaction among particles became stronger, which would hinder the movement of the particles. Therefore, the solids circulation rate decreased with time and then reached a constant value. Normally, chemical or physical processes are operated at steadystate conditions. Therefore, the effects of the experimental parameters on the steady-state solids circulation rate (Wss) were discussed as follows. The effect of Ua on the gas-bypassing fractions is shown in Figure 3. The gas-bypassing fraction from the annulus to the draft tube (fAD) increased with increasing Ua and then leveled off. This was similar to the relationship between the steady-state solids circulation rate and Ua (also shown in Figure 3). Because the entering solids from the annulus to the draft tube would carry some of the annulus gas to the draft tube, a higher solids circulation rate resulted in a higher fAD. Similar results were reported by Song et al.5 Moreover, the effect of Ua on the gas-bypassing fraction from the draft tube to the annulus (fDA) was negligible. Note that the values of fDA were always less than 5%. The effect of Ua on the cumulative weight of the elutriated fines (We) and attrition rate (Rt) is shown in Figure 4. We and the initial attrition rate increased significantly with Ua when Ua was increased from 8.3 to 11.7 cm/s, and they then increased slightly when Ua was increased from 11.7 to 20.0 cm/s. This is due to the fact that most of the attrition occurs in the draft tube section. A higher gas flow rate in the draft tube could result in more violent collisions among the particles in the draft tube, which gave rise to a higher attrition rate. As shown in Figure 4, the superficial gas velocity in the draft tube was fixed at 66.6 cm/s. However, fAD increased significantly with Ua when Ua was less than 11.7 cm/s, and it then increased only slightly with Ua when Ua was greater than 11.7 cm/s (Figure 3). Consequently, the total gas flow rate in the draft tube initially increased significantly with Ua and then leveled off. Therefore, We and Rt first increased and then leveled off as Ua

Figure 4. Effect of Ua on We and Rt (Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, Dd ) 4 cm, and dor ) 22 mm). Table 3. Typical Particle Size Distribution of the Reduced Particlesa calcium particle size distribution (average) 297-210 µm 210-178 µm 178-104 µm 104-90 µm (254 µm) (194 µm) (141 µm) (97 µm) t ) 0 min t ) 30 min t ) 60 min t ) 120 min t ) 240 min

100% 80.3% 71.4% 67.6% 63.7%

0% 12.0% 18.3% 16.2% 18.6%

0% 6.5% 8.7% 11.4% 13.2%

0% 1.2% 1.6% 4.8% 4.5%

a Experimental conditions: U ) 16.7 cm/s, U ) 66.6 cm/s, d ) a d pc 254 µm, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm.

Figure 5. Effect of Ud on the solids circulation rate (Ua ) 16.7 cm/s, dpc ) 385 µm, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm).

increased. Also shown in Figure 4 is that the attrition rate decreased with time initially and then reached a steady state. This is due to the fact that the irregular surface of the particles in the bed at the beginning of each experiment abrades easily, but the particles become harder to abrade when the attrition is closer to the inner surface of the particles. Eventually, Rt reached a stable value. A typical particle size distribution of the reduced particles is shown in Table 3. Effect of the Superficial Gas Velocity in the Draft Tube (Ud). The effect of the superficial gas velocity in the draft tube (Ud) on Ws is shown in Figure 5. As shown in this figure, Ws increased with increasing Ud because of the fact that the pressure drop across the orifices increased with increasing Ud when Ua was fixed.2,20 In addition, Ws decreased with time initially and then reached a constant value. Moreover, the decrease was more rapid at a higher Ud. This was due to a higher attrition on the surface of the calcium

Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5919

Figure 6. Effect of Ud on Wss and gas-bypassing fractions (Ua ) 16.7 cm/s, dpc ) 385 µm, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm).

Figure 8. Effect of dpc on Wss and gas-bypassing fractions (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm).

Figure 7. Effect of Ud on We and Rt (Ua ) 16.7 cm/s, dpc ) 385 µm, Hd ) 30 cm, Dd ) 4 cm, and dor ) 22 mm).

Figure 9. Effect of dpc on We and Rt (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, Hd ) 30 cm, Dd ) 4 cm, and dor ) 22 mm).

particles at a higher Ud. As a result, the bed in the annulus became denser more rapidly. Therefore, Ws decreased more rapidly with time at a higher Ud. The effect of Ud on Wss and the gas-bypassing fractions is shown in Figure 6. fAD increased significantly with increasing Ud, but fDA decreased with increasing Ud. This was due to the solids circulation rate, and the pressure drop across the orifices increased with increasing Ud. Note that similar results were reported by Ahn et al.2 and Song et al.5 In addition, Wss increased with increasing Ud, which was similar to the relationship between fAD and Ud. The effect of Ud on We and Rt is shown in Figure 7. We and Rt increased with increasing Ud at low values of Ud. Attrition depended on the energy transformation and the nature of the surface of the particles.14 A higher Ud could result in a higher impact effect on the calcium particles in the draft tube. However, the effect of Ud on We and Rt was negligible when Ud was higher than 100 cm/s. Under these operating conditions, the irregular surface of the calcium particles in the bed originally was rounded off very quickly. The newly exposed surface of the particles was difficult to abrade. As a result, the effect of Ud on We and Rt was negligible at high values of Ud. A similar trend was also observed by Chu and Hwang.10 Effect of Average Diameter of the Calcium Particles (dpc). The effect of the average diameter of the calcium particles (dpc) on Wss and the gas-bypassing fractions is shown in Figure 8. Wss decreased with

increasing dpc due to decreasing relative velocity between the gas and the particles. A similar trend has been reported in the literature. Milne et al.1 observed that doubling the particle size resulted in a decrease in the solids flux by approximately half. Beverloo et al.22 found that the solids flow decreased with increasing particle size due to an increase in the size of the useless zone of the orifice. fAD decreased with increasing dpc due to decreasing Ws. A lower Wss would carry less gas from the annulus to the draft tube. This resulted in a decrease in fAD with increasing dpc. Moreover, fDA increased slightly with increasing dpc. The effect of dpc on We and Rt is shown in Figure 9. The attrition was strongly influenced by the total external particle surface of the calcium particles. Thus, We and the initial attrition rate decreased with increasing dpc due to decreasing total external particle surface exposed to abrasion. However, because the rounding off of the calcium particles caused the particles to be difficult to abrade, the steady-state attrition rate did not change significantly with dpc. Effect of the Height of the Draft Tube (Hd). The effect of the height of the draft tube (Hd) on Wss and the gas-bypassing fractions is shown in Figure 10. Note that, with the weight of the bed materials used in this study, the bed height in the annulus was higher than Hd when Hd ranged from 25 to 30 cm, while the bed height was lower than Hd when Hd ranged from 35 to 40 cm. It should also be noted that the circulating solids generally consisted of two parts. The first part was

5920 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003

Figure 10. Effect of Hd on Wss and gas-bypassing fractions (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc ) 385 µm, Dd ) 4.0 cm, and dor ) 22 mm).

overflow of particles from the draft tube section to the annulus section. The second part was particles ejected into the freeboard due to bubble breakage at the bed surface of the draft tube section (this section was in a bubbling/slugging fluidized-bed mode in this study). Most of the ejected particles would then flow into the annulus section. However, when the bed surface in the draft tube section was lower than Hd (e.g., Hd ) 40 cm), the solids circulation was due to ejection of particles alone. It is seen in Figure 10 that Wss decreased with Hd when Hd was varied from 25 to 30 cm. This was due to the friction between the particles, and the wall of the draft tube increased with Hd, which resulted in a decrease in Wss with Hd. Wss then increased with Hd when Hd was increased from 30 to 35 cm. It was observed during the experiments that the bed surface of the annulus was a little higher than the height of draft tube at 30 cm. Some of the solids circulated from the draft tube to the annulus would flow back to the draft tube, which reduced Wss. However, when Hd was increased to 35 cm, the draft tube was higher than the bed surface of the annulus. Thus, the particles in the draft tube overflowed into the annulus section more easily, and the solids would not flow back to the draft tube. Therefore, a minimum solids circulation rate occurred at 30 cm when Hd was increased from 25 to 35 cm. Furthermore, the height of the draft tube at 40 cm was much higher than the bed height in the annulus; thus, it needed much more energy to eject the solids from the draft tube into the freeboard. As a result, Wss decreased significantly. fAD first increased and then decreased with increasing Hd. When Hd was increased, the bed voidage in the added section of the draft tube (with a higher gas velocity, i.e., QD/Ad) would be larger than that at the same section before the increase (with a lower gas velocity, i.e., Q/A, A . Ad). As a result, more particles were in the annulus; thus, the bed height in the annulus increased. Note that this was confirmed by experimental observations. Thus, the resistance to the gas flow in the annulus would increase with increasing bed height in the annulus. Therefore, the gas bypassing from the annulus to the draft tube increased when Hd was increased from 25 to 30 cm even though Wss decreased with Hd in this range. Furthermore, as expected, when Hd was varied from 30 to 40 cm, the effect of Hd on fAD was similar to that of Hd on Wss. Figure 10 also shows that fDA was always less than 5%. We and Rt were affected by both the solids circulation

Figure 11. Effect of Hd on We and Rt (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc ) 385 µm, Dd ) 4 cm, and dor ) 22 mm).

Figure 12. Effect of Dd on Wss and gas-bypassing fractions (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, and dor ) 22 mm).

rate and Hd. A higher Hd had a larger amount of particles in the draft tube, which could result in a higher attrition because the gas velocity in the draft tube was higher than that in the annulus. As shown in Figure 11, We and Rt changed slightly when Hd was increased from 25 to 30 cm due to counteracting effects of decreasing Wss (particles attrition decreased) and increasing Hd (particles attrition increased). Similar results were observed when Hd was increased from 35 to 40 cm. Moreover, as shown in Figure 10, Wss increased with Hd when Hd was varied from 30 to 35 cm; thus, We and Rt increased significantly in this range. Effect of the Inner Diameter of the Draft Tube (Dd). The effect of the inner diameter of the draft tube (Dd) on Wss and the gas-bypassing fractions is shown in Figure 12. The resistance to the solids circulation between the annulus and the draft tube became large when Dd was too small or too large. A small Dd resulted in an increase in the resistance to the solids flow due to a decrease in the draft tube cross section, while a large Dd resulted in an increase in the resistance due to a decrease in the annulus cross section. In this study, the highest Wss occurred at Dd ) 4.0 cm when Dd was increased from 3 to 5 cm. fAD increased with Dd when Dd was increased from 3.0 to 4.0 cm due to increasing Wss. fAD also increased with Dd when Dd was increased from 4.0 to 5.0 cm even though Wss decreased. This was due to the bed in the annulus becoming denser at Dd ) 5.0 cm as a result of the reduction of the annulus cross section area by almost 20%. As a result, the gas flow to the annulus decreased, while the gas flow to the draft

Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5921

Figure 13. Effect of Dd on We and Rt (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, and dor ) 22 mm).

Figure 15. Effect of dor on We and Rt (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, and Dd ) 4 cm). Table 4. Values of the Constant k and Coefficients a, b, and c in Equation 5 geometry of draft tube

k (kg/s)

a

b

c

25 cm e Hd e 30 cm, 3 cm e Dd e 4 cm 30 cm < Hd e 35 cm, 4 cm < Dd e 5 cm

0.00735

0.655

-0.267

0.756

0.00026

0.655

1.347

0.756

Figure 14. Effect of dor on Wss and gas-bypassing fractions (Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc ) 385 µm, Hd ) 30 cm, and Dd ) 4.0 cm).

tube increased. Therefore, fAD increased dramatically but fDA reduced to a negligible value when Dd was increased from 4.0 to 5.0 cm. Figure 13 illustrates the effect of Dd on We and Rt. A larger Dd resulted in a larger amount of solids in the draft tube, which was under a much higher gas velocity than the annulus. Consequently, more vigorous collisions occurred among the particles in the draft tube. Hence, We and Rt increased as Dd was increased. Effect of the Diameter of the Orifice (dor). Figure 14 shows the effect of the orifice diameter (dor) on Wss and the gas-bypassing fractions. Wss increased with increasing dor due to reducing solids flow resistance. These results were similar to those reported by Milne et al.1 and Ahn et al.2 When dor was small, solids clustered in the annulus near the orifices and resisted the gas flow into the annulus. Hence, fAD changed only slightly even though Wss increased significantly when dor was increased from 10 to 14 mm. However, when dor was increased from 14 to 19 mm, the phenomenon of solids cluster in the annulus near the orifices became less severe. As a result, fDA increased and fAD decreased significantly. Moreover, the solids cluster no longer existed when dor was increased from 19 to 22 mm, and fAD changed only slightly with dor as a result of a small increase in Wss. Figure 15 illustrates the effect of dor on We and Rt. The attrition rate increased with increasing solids circulation rate and velocity of the particles passing through the orifices. As shown in Figure 14, the solids

Figure 16. Predicted Wss versus experimental data.

circulation rate increased as dor was increased. However, the velocity of the particles passing through the orifices decreased with increasing dor. As a result, the effect of dor on We and Rt was negligible because of the counteracting effects of the solids circulation rate and the velocity of the particles passing through the orifices. Correlations. On the basis of the experimental results obtained in this study, a correlation equation for Wss was proposed:

( )( )( )

Wss ) k

dor dp

a

Hd Dd

b

UaUd Umf2

c

(5)

The values of the constant k and the coefficients a, b, and c in eq 5 were illustrated in Table 4. Comparisons of Wss predicted by eq 5 and the experimental values are shown in Figure 16. It is seen in these figures that eq 5 could predict the solids circulation rate satisfactorily. Another method of calculating the solids circulation rate was described and discussed as follows. Milne et al.1 and Ahn et al.2 used the following equation derived

5922 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 Table 5. Values of the Orifice Discharge Coefficients Cda Ua (cm/s)

Cd

Ud (cm/s)

Cd

dp (µm)

Cd

Hd (cm)

Cd

Dd (cm)

Cd

dor (mm)

Cd

8.3 11.7 16.7 20.0

0.18 0.18 0.18 0.18

43.2 66.6 100.0 116.7

0.18 0.18 0.18 0.18

350 396 421-426 448

0.18 0.18 0.18 0.18

25 30 35 40

0.18 0.18 0.18 0.10

3.0 4.0 5.0

0.18 0.18 0.08

10 14 19 22

0.10 0.15 0.18 0.18

a

Base case: Ua ) 16.7 cm/s, Ud ) 66.6 cm/s, dpc) 385 µm, Hd ) 30 cm, Dd ) 4.0 cm, and dor ) 22 mm.

by De Jong and Hoelen6 to predict the solids flow rate per orifice (Wso):

Wso ) [-Fs(1 - mf)Cd2(b + 2aFor/mf) + FsCd(4aFor2/mf2 + 4bFor/mf + Cd2b2)0.5]/ 2(1 - aCd2) (6) where

a ) 1.75Fgdor(1 - kdp/dor)4/12Fsφsdpmf

(7)

b ) 150Fµdor3(1 - mf)(1 - kdp/dor)4/8Fs(φsdpmf)2 (8) The orifice correction factor (k) in eqs 7 and 8 was taken to be 2.9, as suggested by Beverloo et al.,22 and the particle sphericity (φs) was assumed to be 0.89 for round sand.1,2 The gas flow rate in the orifice (For) was obtained by the following equation:

For ) (fADQAi - fDAQDi)/4 = fADQAi/4

(9)

Because there were four orifices in each of the draft tubes used in this study, the steady-state solids circulation rate was then calculated by

Wss ) 4Wso

(10)

The values of the orifice discharge coefficient (Cd) evaluated for each operating condition by nonlinear regression were listed in Table 5. It was found that Cd ranged from 0.08 to 0.18, and it was independent of Ua and Ud. In addition, Cd ) 0.1 when Hd ) 40 cm because Hd was much higher than the bed height in the annulus as mentioned previously, and Cd ) 0.08 when Dd ) 5 cm because a large Dd resulted in a dramatic increase in the resistance to the solids flow. Moreover, Cd increased with increasing dor and then leveled off when dor was greater than 19 mm because of the fact that the solids cluster no longer existed. However, the effect of the average particle size of the bed materials on Cd was negligible. Milne et al.1 found that Cd values for dp ) 610 and 1310 µm were 0.45 and 0.65, respectively. Ahn et al.2 correlated Cd with dor and dp as follows:

Cd ) 0.23(dor0.73/dp0.44)

(11)

Equation 11 showed that Cd increased with dor but decreased with dp. Comparisons of Wss predicted by eq 6 and the experimental values are shown in Figure 17. It is seen in this figure that, using the values of Cd shown in Table 5, eq 6 could predict the solids circulation rate satisfactorily. However, Milne et al.1 and Ahn et al.2 overestimated Wss. This might be due to the different solid particles used. They used sand particles, whereas mixtures of sand and calcium particles were used in this study. Note that, in the case of Milne et al.,1 the values of Cd used for dp of 350, 396, 423, and

Figure 17. Predicted Wss versus experimental data.

448 µm found by extrapolating their data were 0.25, 0.28, 0.30, and 0.33, respectively. Conclusions The solids circulation and attrition rates and gas bypassing in an ICFB with mixtures of silica sand and calcium particles were studied. It was found that the solids circulation rate initially increased with increasing superficial gas velocity in the annulus (Ua) and then leveled off at around Ua/Umf ) 1. It also increased with increasing superficial gas velocity in the draft tube (Ud) and the orifice diameter (dor). However, it decreased with an increase in the average particle diameter of the calcium particles (dpc). A minimum Wss occurred at 30 cm when the height of the draft tube (Hd) was varied from 25 to 35 cm. In addition, a maximum value of Wss occurred at 4 cm when the inner diameter of the draft tube (Dd) was varied from 3 to 5 cm. The correlation equation proposed in this study could predict Wss with good accuracy. The gas-bypassing fractions (fAD and fDA) depended primarily on the solids circulation rate, superficial gas velocity in the draft tube, and state of solids packing and bed height in the annulus. fAD first increased with increasing Ua and then leveled off. fAD also increased with increasing Ud and Dd but decreased with increasing dpc. fAD had a maximum value with respect to Hd. Moreover, fAD changed slightly when dor was increased from 10 to 14 mm, decreased significantly when dor was increased to 19 mm, and changed slightly when dor was increased from 19 to 22 mm. Note that the values of fDA were always less than 5%. The attrition rate depended on the solids circulation rate, gas-bypassing fraction from the annulus to the draft tube, height of the draft tube, and extent of collisions among particles. It increased with an increase in the superficial gas velocity in the draft tube and solids velocity through the orifices. The attrition rate first increased and then leveled off as Ua and Ud increased, but it decreased with increasing dpc. The attrition rate

Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5923

changed slightly when Hd was increased from 25 to 30 cm and from 35 to 40 cm due to counteracting effects of decreasing Wss and increasing Hd. In addition, the attrition rate increased as Dd increased. Furthermore, the attrition rate changed negligibly with dor due to counteracting effects of the solids circulation rate and the velocity of the particles passing through the orifices. Finally, the attrition rate would reach a steady-state value at the end of each experiment. Nomenclature A ) cross-sectional area of the bed, m2 Aa ) cross-sectional area of the annulus, m2 Ad ) cross-sectional area of the draft tube, m2 Cd ) orifice discharge coefficient dp ) average particle diameter, 1/(Xc/dpc + Xs/dps), µm dpc ) average particle diameter of the calcium particles, µm dps ) particle diameter of the silica sand, µm dor ) orifice diameter at the base of the draft tube, mm Dd ) inner diameter of the draft tube, cm fAD ) gas-bypassing fraction from the annulus to the draft tube, % fDA ) gas-bypassing fraction from the draft tube to the annulus, % For ) gas flow rate in the orifice, m3/s Hd ) height of the draft tube, cm k ) orifice correction factor L ) distance the tracer particles traveled in the annulus, cm Q ) total gas flow rate in the bed, m3/s QAD ) flow rate of bypassed gas from the annulus to the draft tube, m3/s QAi ) gas flow rate at the annulus inlet, m3/s QDA ) flow rate of bypassed gas from the draft tube to the annulus, m3/s QD ) total gas flow rate in the draft tube, m3/s QDi ) gas flow rate at the draft tube inlet, m3/s Rt ) attrition rate, g/s t ) time, min Ua ) superficial gas velocity in the annulus, cm/s Ud ) superficial gas velocity in the draft tube, cm/s Umf ) superficial gas velocity at minimum fluidizing conditions, cm/s Va ) bulk velocity of the solids in the annulus, cm/s We ) cumulative weight of the elutriated fines, g Ws ) solids circulation rate defined by eq 1, kg/s Wso ) solids flow rate per orifice, kg/s Wss ) steady-state solids circulation rate, kg/s Xc ) weight fraction of the calcium particles in the bed Xs ) weight fraction of the silica sand in the bed Greek Letters a ) bed voidage in the annulus mf ) bed voidage at the minimum fluidization condition φs ) particle sphericity Fg ) gas density, kg/m3 Fs ) average density of the bed materials, kg/m3 µ ) gas viscosity, kg/m‚s Subscripts a ) annulus AD ) gas bypassing from the annulus to the draft tube d ) draft tube DA ) gas bypassing from the draft tube to the annulus mf ) minimum fluidization or ) orifice

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Received for review March 20, 2003 Revised manuscript received July 25, 2003 Accepted August 18, 2003 IE0302490