Flow Characteristics of Coal Ash in a Circulating Fluidized Bed

Flow Characteristics of Coal Ash in a Circulating Fluidized Bed ... in the lower dense region, significant particle segregation, and more uniform annu...
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Ind. Eng. Chem. Res. 1998, 37, 1499-1509

1499

Flow Characteristics of Coal Ash in a Circulating Fluidized Bed Jianping Zhang, Peijun Jiang, and Liang-Shih Fan* Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210

Solids flow characteristics of coal ash are investigated with the measurement of the local solids flux, local solids concentration, and spatial distribution of particle size. Two sets of the solids sampling probe are used to quantify the local solids flux at different radial and axial locations. The macroscopic flow structure is presented by analyzing the radial profiles of solids flux and the local particle size distributions, while the mesoscale flow structure is illustrated on the basis of probability density function of instantaneous solids concentration, the intermittency index, and the cluster frequency. It is found that both macroscopic and mesoscopic structures of gassolid flow of coal ash are different from those of commonly studied fluid catalytic cracking and sand particles. The differences include higher upward and downward solids fluxes in the lower dense region, significant particle segregation, and more uniform annular flow. Furthermore, a semiempirical model taking into consideration the higher slip velocity between gas and solids is developed to account for the radial profiles of the solids flux in the upper dilute region of the riser. Introduction Circulating fluidized bed (CFB) combustion systems are widely recognized as one of the advanced technologies for power generation. They offer the flexibility of types of fuel used and the ability of efficient control of sulfur and nitrogen oxides emission. The solid materials in a CFB combustor consist of coal, ash, and sorbent. The coal particles in the feed usually have a wide range of size distribution, and the sizes of solid materials in the combustor vary due to attrition in the combustion processes. Under a given operating condition, the hydrodynamic behavior of a CFB combustor primarily depends on the physical properties of bed materials such as the size distribution, density, and surface properties of particles. Combustion efficiency, sorbent utilization, and heat transfer are significantly influenced by solids concentration profiles, local solids flux, and the extent of particle segregation. Therefore, the successful design and operation of a CFB combustor requires an understanding of the underlying hydrodynamics. The hydrodynamics of CFB systems with fluid catalytic cracking (FCC) particles has been the subject of many prior studies as demonstrated by numerous review articles (e.g., Werther, 1993; Berruti et al., 1995). There is a relative paucity of studies concerning the behavior of a CFB combustor with coal ash particles. Hartge et al. (1988) revealed the core-annular structure for FCC, sand, and coal ash particles. A series of studies were performed to investigate the characteristics of bed materials at the bottom and boundary layer region of the CFB boilers (e.g., Zhang et al., 1995; Svensson et al., 1996). Compared with FCC and sand particles, coal ash particles possess the unique features of a wide size distribution and complicated shape and surface structures. It has been recognized that the particle properties have significant effects on the hydrodynamic behavior of gas-solid flow in the CFB systems. Weinstein et al. (1981) examined the hydrodynamics of a circulating fluidized bed with particles of different densities and found the axial variation of solids holdups to be much * To whom correspondence should be addressed.

smaller for light particles than for heavy particles. A similar trend was also reported by Li et al.(1990) in the study of low-density aerogel powders in a small-scale circulating fluidized bed. It was also reported that the hydrodynamic behavior for a bed with mixed particles of a wide size distribution is different from that with particles of a narrow size distribution. For example, particle segregation occurs in a pneumatic transport system (Nakamura and Capes, 1976) and a circulating fluidized bed (Ijichi et al., 1990) with nonuniform particle properties. Recently, Liu et al. (1996) reported a lateral particle segregation in a CFB riser with a square cross section. Under dilute conditions, a maximum mean particle size was observed to be located between the center and wall for the upward flow, while large particles were detected in the wall region for the downward flow. Note that a mixture of fine sand particles (Fs ) 2484 kg/m3 and d ) 30.8∼710 µm) and coarse resin particles (Fs ) 1152 kg/m3 and d ) 224∼1000 µm) was used in their study. Therefore, it is not clear whether particle segregation is caused by the differences in particle densities or sizes, and/or their combination. In a binary particle system, it was observed that the solids holdup of fine particles in a riser can be enhanced by the addition of coarse particles (Liu et al., 1979; Kitano et al., 1988; and Bi et al., 1992). The terminal velocity and minimum fluidization velocity of coarse particles are smaller in systems with fine particles (Satija and Fan, 1985; Na et al., 1996). Geldart and Pope (1983) observed an increase in the carry-over of coarse particles in the freeboard of a fluidized bed with fine particles. They suggested that the increase was due to the momentum gain of coarse particles through frequent interactions between fastmoving fine particles and slow-moving coarse particles. An axial particle segregation was observed by Jiang et al. (1992a) under low gas velocities and/or low solids circulation rates in a binary particle system. Win et al. (1996) investigated the solids mass flux and particle size distribution in a multisolid fluidized bed (MSFB) combustor, which is a type of CFB reactor. Their results showed a strong radial particle segregation with a high

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1500 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998

Figure 1. Schematic diagram of the experimental apparatus.

mass fraction of large coal particles in the wall region. The radial particle segregation is enhanced in the upper dilute region. Ma et al. (1996) studied the behavior of circulating fine particles in a powder-particle fluidized bed and found that the elutriation rate of group C powder decreases with decreasing particle diameter due to the agglomeration of fine particles and the adhesion of fine particles to coarse particles. Furthermore, Bagster and Roberts (1985) and Li et al. (1990) reported that the mobility or fluidization quality of fine powders was affected by adding or removing large particles from a high-velocity fluidized bed. The surface structure was also found to affect the flowability of particles. Using particles with different surface friction coefficients, Chang and Louge (1992) found that particles with smaller surface friction coefficients yielded a smaller pressure drop. Coal ash particles are characterized by a wide range of size distribution and complex surface structures. The differences in particles size distribution and surface structure may lead to changes in solids concentration profiles, solids flux, and particle segregation. These changes will significantly affect the hydrodynamic behavior of circulating fluidized beds. Therefore, experimental data for CFB combustors with the coal ash particles are required to provide reliable predictive tools for such systems. The objective of this study is to examine the flow behavior of coal ash particles in the riser of a CFB system. Detailed solids flow characteristics are quantified with measurement of local solids flux, solids concentration, and the particle size distribution. The experiments are conducted under ambient conditions; the temperature effect on the flow behavior is beyond the scope of this study. Experimental Section The schematic diagram of the experimental apparatus is shown in Figure 1. The circulating fluidized bed consists of a riser of 10.2 cm in diameter and 6.32 m in height, a separator and secondary cyclone system, an L-valve, and a large volume particle storage hopper. The whole system is made of Plexiglas except the particle separator which is made of steel. A stainless steel plain

Figure 2. Geometry of the probe bend and schematic diagram of the solids sampling system.

square weave with an opening width of 104 µm and 37.4% open area is used as the gas distributor. Particles are carried upward through the riser and exit at the top through a right-angle bend into a 10.2-cm horizontal tube connected to the separator. The particles are separated from the gas through the separator and the secondary cyclone and then fed back to the riser at the bottom through the L-valve. The solids circulating rate is controlled by adjusting the air aeration rate at the injection points of the L-valve. The solids circulation rate is measured by timing the descent distance of identifiable particles in the standpipe. The compressed air is fed to the riser through a filter and a pressure regulator. The relative humidity of the air, which is monitored by a psychrometer, is maintained at about 14%. Twenty-four pressure taps are flush-mounted along the inner wall of the riser. The pressure drops along the riser are measured using manometers and differential pressure transducers with high sensitivity and high-frequency response (100 Hz). The cross-sectional averaged voidage (or solids holdup) is calculated from the axial pressure profiles. An optical fiber probe developed earlier (Jiang et al., 1992b) is used to measure the local solids concentration. The distance between the transmitting and receiving probes is 5 mm. Analogue outputs of the pressure transducers and the optic probe are connected to a PC data acquisition system for data collection, with a sampling rate of 50 Hz. Two sets of the solids sampling probe are mounted at 1.6 and 4.5 m from the bottom of the riser. The geometry of the probe bend and schematic diagram of the probe system are shown in Figure 2. The sampling probe is made of copper tube with a 7-mm i.d. and 1.3mm thickness. A static pressure probe is also placed at the same level as the solids sampling probe. The hole on the static pressure probe is situated at the same radial position as the opening of the solids sampling probe. Initially, the solids sampling probe is purged to keep the sampling path clear. The isokinetic condition is obtained by adjusting the opening of the exhaust valve to maintain a zero-pressure difference between the static pressure probe and the solids sampling probe. The collection vessel is replaced with an empty one

Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1501 Table 1. Physical Properties of Coal Ash average particle diameter 172 µm

particle density

bulk density

packed density

1647 kg/m3 833.8 kg/m3 990.8 kg/m3

angle angle of of repose fall 35°

19°

Figure 3. Particle size distribution of coal ash.

when the isokinetic condition is reached, and the system is switched into the sampling mode at the same time. The sampling time ranges from 30 s to 2 min with the solids weight ranging from 20 to 200 g, depending on the radial and axial locations and local solids flux. The flux of upward flow is measured with the sampling tube facing downward, while the flux of downward flow is measured with the sampling tube facing upward. The flux of the net flow is defined as the difference between the fluxes of upward and downward flows. The radial profiles of solids fluxes are obtained by changing the radial locations of the solids sample probe and the static pressure probe. The cross-sectional averaged solids flux is calculated by integrating the local solids fluxes obtained at four radial positions, that is,

Gs )

2 R2

∫0R Gs,r r dr

(1)

It should be noted that the isokinetic condition can only be obtained under the dilute operating conditions. The difference between the cross-sectional averaged solids flux measured under isokinetic conditions and that obtained by the solids circulation rate measurement is in the range of -20% to -4% of the solids circulation rate. Under the dense operating conditions, no isokinetic condition can be achieved due to the higher static pressure and strong flow fluctuations. Measurements are conducted under the conditions of the minimum static pressure difference between the static pressure hole and the opening of the solids sampling probe. Moreover, frequent chokings in the sampling tube are encountered under dense operating conditions, and the readings are based on a cumulative measurement at a nonchoking condition. The size distributions of sampled solids particles are obtained using particle sieves. The coal ash used in the experiments is the bottom ash of Ohio coal with the maximum sieve cutoff of 1500 µm. About 40 wt % of the particles is less than 120 µm, and 20 wt % of the particles is larger than 590 µm. The ash particles are composed of group A and B particles. The physical properties of ash particles are given in

Figure 4. Axial profiles of the cross-sectional averaged solids concentration: (a) Ug ) 2.55 m/s and (b) Gs ) 26.1 kg/m2 s.

Table 1. The bulk density, packed density, angle of repose, and angle of fall are measured using the Hosakawa powder-testing instrument. The particle density is measured by the immersing method. The particle size distribution obtained from sieving analysis is given in Figure 3. The particle size is monitored during the experiments, and fresh particles are added periodically to compensate for the loss of fine particles. Results and Discussion Time-Averaged Solids Flow Characteristics. Axial Profile of Solids Concentration. The axial variation of the cross-sectional averaged solids concentration is shown in Figure 4 for various operating conditions. The solids concentration here is obtained based on the pressure measurement, that is,

s )

∆P Fs g∆Z

(2)

As can be seen from the figure, the axial concentration distributions are of a sigmoidal shape at higher solids circulation rates of 26.1 and 34.9 kg/m2 s and of an exponential shape at a lower solids circulation rate of 17.4 kg/m2 s and a gas velocity of 2.55 m/s. For a given solids circulation rate, the axial solids concentration decreases from that of the sigmoidal profile to the exponential profile when the gas velocity increases from 2.55 to 4.4 m/s as shown in Figure 4b. This trend is

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Figure 6. Effects of gas velocity on the radial profiles of reduced solids flux in the lower region of the riser (Gs ) 26.1 kg/m2s).

Figure 5. Radial profiles of the reduced solids flux in the lower region of the riser (Ug ) 2.55 m/s): (a) netflow, (b) upflow, and (c) downflow.

similar to that for FCC particles (Kwauk et al., 1986; Bai et al., 1992). Radial Profile of Solids Flux in the Lower Dense Region. The radial profiles of fluxes for upward, downward, and net solids flows are obtained for various operating conditions. Figure 5 shows the radial distributions of reduced solids fluxes in the lower dense region of the riser (z ) 1.6 m) at various solids circulation rates and a gas velocity of 2.55 m/s. The reduced solids flux is defined as a ratio of the local solids flux to the cross-sectional averaged solids flux. It can be seen from Figures 5a-c that the solids fluxes of the upward, downward, and net flows are rather uniform in the core region, while significant downward flow is observed in the wall region. The reduced solids flux distributions are similar for the higher solids circulation rates of 26.1 and 34.9 kg/m2 s. At a lower solids circulation rate of 17.4 kg/m2 s, the reduced solids fluxes in both the core and the annular regions are higher than those at higher solids circulation rates. This indicates a higher degree of segregation in the lower region at a lower solids flow rate. At a given gas velocity, the relatively lower reduced solids fluxes in both upward and downward flows indicate a higher degree of mixing at a higher solids circulation rate. On the other hand, at a given solids circulation rate, increasing gas velocity decreases the solids concentration, thereby enhancing the flow segregation, which is similar to the effect of reducing the solids circulation rate at a given gas velocity. As shown in Figure 6, the radial profiles of the solids fluxes at Ug ) 4.4 are sharper than that at the gas velocity of 2.55 m/s. An opposite trend was observed for FCC particles (Rhodes et al., 1992; Herb et al., 1992) which

Figure 7. Comparison of the radial profiles of reduced solids flux for coal ash and FCC particles. Operation conditions. Coal ash: D ) 0.10 m, Ug ) 2.55 m/s, Gs ) 17.4 kg/m2 s, Z ) 1.6 m, d ) 172 µm. FCC: D ) 0.15 m, Ug ) 2.4 m/s, Gs ) 20 kg/m2 s, Z ) 1.5 m, d ) 87 µm. (FCC data from Herb et al., 1992.)

showed a flatter profile at a lower solids circulation rate. Figure 7 shows the comparison of the radial profiles of the reduced solids fluxes for coal ash and FCC particles under similar operating conditions. It can be seen from the figure that the reduced solids fluxes of both the upward and downward flows for coal ash are much higher than those for FCC particles. The sharper distribution of the reduced solids flux indicates a higher degree of particle segregation: a higher flux of the fine particles flowing upward in the core region and a higher flux of the coarse particles flowing downward in the annular region. The present results indicate that the size distribution of the particles has a significant effect

Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1503

Figure 9. Effects of gas velocity on the radial profiles of reduced solids flux in the upper region of the riser (Gs ) 26.1 kg/m2 s).

Figure 8. Radial profiles of the reduced solids flux in the upper region of the riser (Ug ) 2.55 m/s).

on the particle segregation as reflected by the higher degree of segregation of coal ash compared to that of FCC particles. It should be noted that in the above comparison, the diameters of the riser are different, that is, 0.10 m in the present study and 0.15 m in the study of Herb et al. The effect of the riser diameter on particle segregation needs to be further examined. Radial Profile of Solids Flux in the Upper Dilute Region. The radial distributions of the reduced solids flux in the upper dilute region (z ) 4.5 m) are shown in Figure 8. There are several distinctive differences in the radial profiles of the solids fluxes compared to that in the bottom dense region. First, as shown in Figure 8a, fluxes of the net flow in the annular region are positive, indicating a net upward solids flow in this region, although a substantial downward flow is observed in the annular as shown in Figure 8c. Similar behavior can also be seen in Bodelin et al. (1993) in which they observed a net upward flow in the wall region for sand particles at the gas velocity of 5.4 m/s and solids circulation rates ranging from 2.6 to 24.8 kg/ m2 s. Second, as can be seen in Figure 8b, at a solids circulation rate of 17.4 kg/m2 s, the solids flux of the upward flow is uniformly distributed over the cross section. This is totally different from the solids flow in the lower dense region where the highest extent of segregation is observed at a lowest solids circulation rate (see Figure 5b). The significant difference in the radial profiles of the reduced solids fluxes for the upward flow is closely associated with the local particle size distributions. At a low gas velocity and a low solids circulation rate, a large fraction of coarse particles are retained in the lower dense region. The fraction of coarse particles decreases along the riser, yielding a more uniform radial

distribution of the solids flux in the upper dilute region. Little effect of the gas velocity is observed on the radial distribution of the solids flux as shown in Figure 9. Particle Segregation. The particle size distributions are analyzed at different locations for all operating conditions. Figure 10 shows the size distributions of upward flow (UF) and downward flow (DF) in the core and the annular regions at different operating conditions for two axial locations. The Sauter mean diameter is used to describe the averaged particle size. As expected, the averaged particle size of downward flow is always larger than that of the upward flow in the annular region. In the core region, no significant difference is observed for the averaged particle sizes of the upward and downward flows. The variations in particle size distribution reflect the extent of particle segregation. As shown in Figures 10a,b, at a low solids circulation rate of 17.4 kg/m2 s, significant differences of the particle size distributions are observed in both upper dilute and lower dense regions. In the lower dense region, a large fraction of coarse particles is presented in the downward flow of the annular region, which indicates a significant recirculation of coarse particles in the dense region. However, a certain amount of fine particles are also present in this recirculation flow, implying the occurrence, to certain extent, of the turbulent mixing in the lower dense region. The average particle size decreases along the vertical direction of the riser. In the upper dilute region, the averaged particle sizes are smaller than that in the lower dense region in both the core and annular regions (Figure 10b). Another noticeable feature in Figure 10b is that the particles in the annular downward flow are larger than those of downward flow in the core region, while the particles of the annular upward flow are smaller than those of upward flow in the core region. This result can be related to the gas velocity distribution, because the gas velocity in the wall region is lower than that in the core region. Since the upward solids flux profile is rather uniform, it can be projected that a substantial amount of fine particles are flowing upward in the annular region. At a higher solids circulation rate of 34.9 kg/m2 s (Figure 10c,d), the particle size segregation is not significant in the lower dense region. However, the particle segregation is still observed in the upper dilute region. Note the difference of the flow behavior and the solids holdups at the different locations. The present results indicate that the particle segregation in the riser

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Figure 10. Local size distributions at different operation conditions. (a) Lower region: Gs ) 17.4 kg/m2 s, Ug ) 2.55 m/s, and Z ) 1.6 m. (b) Upper region: Gs ) 17.4 kg/m2 s, Ug ) 2.55 m/s, and Z ) 4.5 m. (c) Lower region: Gs ) 34.9 kg/m2 s, Ug ) 2.55 m/s, and Z ) 1.6 m. (d) Upper region: Gs ) 34.9 kg/m2 s, Ug ) 2.55 m/s, and Z ) 4.5 m. (e) Lower region: Gs ) 26.1 kg/m2 s, Ug ) 4.4 m/s, and Z ) 1.6 m. (f) Upper region: Gs ) 26.1 kg/m2 s, Ug ) 4.4 m/s, and Z ) 4.5 m.

is affected by the solids concentration, size distribution, and the flow behavior. This can be further confirmed by the experimental results shown in Figure 10e,f. The extent of particle size segregation at Ug ) 4.4 m/s and Gs ) 26.1 kg/m2 s is similar to that observed under Ug ) 2.55 m/s and Gs ) 17.4 kg/m2 s. As shown in Figure 4a,b, increasing the solids circulation rate from 17.4 to 26.1 kg/m2 s and the gas velocity from 2.55 to 4.4 m/s results in similar solids concentration profiles along the riser. Transient Flow Structure. As discussed above, the flow behavior of coal ash particles is qualitatively dissimilar in many aspects to that of FCC particles in a macroscale. There also is a significant difference in the flow structures at a mesoscale between FCC and ash particles. The transient flow structure of coal ash is analyzed by using a statistical analysis of the instantaneous pressure drop and solids concentration measured by the optic fiber probe. Figure 11 shows the probability density functions (PDF) of the instantaneous

solids concentration in the upper dilute region under different operating conditions. For the instantaneous solids concentration in the center region, the PDF profiles exhibit a unimodal distribution with a sharp peak near the mean value. As shown in Figure 11a,b, the peak values increase with the solids circulation rate. This indicates that the relative fluctuation range of the solids concentration decreases with increasing mean solids concentration. In the wall region, a broad profile of the PDF for the local solids concentration is observed. Two peaks, one at the low solids concentration and the other at the high solids concentration, can be identified from the PDF profiles of solids concentration in the wall region. The bimodal PDF curves, which represent the coexistence of particle clusters and dilute dispersed particles in the local solids concentration, have been reported for common group A particles (Hartge et al., 1988) and group B particles in a square cross-sectional riser (Zhou et al., 1994). Similar to the fluctuations at the center region, the peaks of the PDF curves increase

Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1505

Figure 11. Probability density functions of the instantaneous solids concentration in the upper region: (a) Gs ) 17.4 kg/m2 s and Ug ) 2.55 m/s; (b) Gs ) 34.9 kg/m2 s and Ug ) 2.55 m/s; (c) Gs ) 26.1 kg/m2 s and Ug ) 4.4 m/s.

Figure 13. Radial profiles of intermittency index and the corresponding solids concentration profiles in the upper dilute region: (a) radial profiles of intermittency index and (b) radial solids concentration profiles.

Figure 14. Radial profiles of intermittency index and the corresponding solids concentration profiles in the lower dense region: (a) radial profiles of intermittency index and (b) radial solids concentration profiles.

Figure 12. Probability density functions of the instantaneous solids concentration in the lower region: (a) Gs ) 17.4 kg/m2 s and Ug ) 2.55 m/s; (b) Gs ) 34.9 kg/m2 s and Ug ) 2.55 m/s; (c) Gs ) 26.1 kg/m2 s and Ug ) 4.4 m/s.

with the increasing solids circulation rate, which implies a narrower fluctuation range at a higher solids circulation rate. Figure 12 shows the probability density functions (PDF) of the instantaneous solids concentration in the lower dense region. It can be seen from the figure that the PDF curves are more diverse and have wider spans than those in the upper dilute region. This indicates a stronger mixing in the lower dense region. The span

of the PDF curve increases with an increase in the solids circulation rate and hence, an increase in the solids holdup (see Figure 12a,b). However, unlike those of the common group A particles, the PDF curves of coal ash in the lower dense region show the unimodal shapes. That is, there is no distinctive boundary between the dense cluster phase and the dilute dispersed phase. While the PDF curves of the instantaneous solids concentration give the quantitative description of the fluctuations, the intermittency index defined by Brereton and Grace (1993) can be used to quantify the nonuniformity of the segregated flow. The intermittency index has the value of zero for the perfect coreannular flow and uniform suspension and 1 for the

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Figure 15. An example of the instantaneous solids concentration signals. Operation condition: Gs ) 34.9 kg/m2 s, Ug ) 2.55 m/s, r/R ) 0, and Z ) 4.5 m.

perfect cluster flow. Figure 13a shows the intermittency index profiles obtained in the upper dilute region of the riser. The corresponding profiles of solids concentration are shown in Figure 13b. As can be seen from Figure 13a, the intermittency indices for all the operating conditions shown in the plot are between 0.1 and 0.2 in the core region and range from 0.15 to 0.3 in the wall region. This indicates that the local flow structure is close to a perfect core-annular flow with a dominant dense layer in the annular region. The probability of clusters being present in the core is also very low. The intermittency indices in the center region have the values close to that of sand particles as reported by Brereton and Grace (1993). However, the intermittency indices at the wall region are lower than that of sand particles. This indicates a more uniform/less cluster flow in the annular region for the coal ash than for the sand particles. It is very likely that the more uniform/ less cluster flow for the coal ash is caused by the wide range of particle size distribution. The presence of the coarse particles increases the interactions of fine and coarse particles, thereby suppressing the formation of particle clusters. The intermittency index profiles of the solids concentration in the lower dense region are shown in Figure 14a, and the corresponding solids concentration profiles are shown in Figure 14b. As can be seen from Figure 14a, the intermittency indices at the lower dense region have the values between 0.1 and 0.25, which are similar to those in the upper dilute region but much lower than the intermittency indices for the sand particles (Brereton and Grace, 1993). This result indicates a less cluster flow for the coal ash than for the sand particles in the lower dense region. In the radial direction, as shown in Figure 14a, the intermittency indices in the wall region are lower than those in the center region, which suggests a less cluster flow in the wall region. This tendency is also different from the result obtained for the sand particles in the lower region of the riser which has a higher value of the intermittency index in the wall region. Because of the distinctive difference in the solids concentrations between the cluster and dispersed dilute suspensions, the particle clusters can be distinguished on the basis of variations in the instantaneous solids concentration signals. Figure 15 gives an example of the instantaneous solids concentration measured at r/R ) 0 in the upper dilute region. If clusters are defined to be present when the local instantaneous solids

Figure 16. The cluster frequency at different locations and operation conditions: (a) upper region and (b) lower region.

volume fraction exceeds the time-averaged solids fraction by 3 times the standard deviation of the local solids concentration (Soong et al., 1993), the cluster frequencies ranging from 0 to 1.25 Hz obtained at different locations and operating conditions can be shown in Figure 16. The result indicates a similar range of cluster frequencies for sand particles in the core region (Johnsson et al., 1996) but much lower than the cluster frequencies (4-5 Hz) for sand particles in the wall region. Similar to that obtained from the intermittency index analysis, the result from the cluster frequency again indicates that a wide range of size distribution leads to a less heterogeneous flow in the annulus of the riser. However, it should be noted that because the criterion used in identifying the cluster is based on the standard deviation of the local instantaneous solids concentration, the solids concentration of clusters in the center dilute region may be lower than that of noncluster flow in the annular dense region and the local flow with a larger standard deviation may be identified as a less clustering flow. Thus, it is understandable why the cluster frequencies are higher in the core region than

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those in the annulus as shown in Figure 16. As can be seen from the results of the PDF and intermittency index analyses, the fluctuations of solids concentration in the center region are smaller than those in the wall region under most of the operating conditions. Model of Radial Solids Flux Profile in the Upper Dilute Region. For FCC particles, Monceaux et al. (1986) showed that at a given gas velocity, the radial profiles of the reduced solids mass flux were insensitive to the changes in the total solids flux. They suggested a similarity in radial profiles based on the reduced solids mass flux. However, Bodelin et al. (1993) and Letizia et al. (1996) recently found that the similarity in profiles of the reduced mass flux was only valid in a limited range of operating conditions. For the reduced solids flux similarity, Rhodes et al. (1992) developed a semiempirical model to link solids flux to the local solids concentration, solids velocity, and gas velocity. They assumed a two-parameter curve for the radial solids flux distribution. Combining the parabolic profile of solids concentration with the solids and gas mass conservation, the parameters can be determined from the best fit of experiment data. However, in their model, the gas-solid slip velocity was assumed to be the particle terminal velocity which is in contradiction with many experimental observations in which the gas-solid slip velocity is much larger than the terminal velocity in the riser (e.g., Yerushalmi and Cankurt, 1979). When using Rhodes et al.’s model, Pugsley et al. (1993) indicated that the determination of the constant β is very difficult. This may be caused by the oversimplified assumption of the slip velocity. On the other hand, for coal ash particles, the slip factors are greater than 1 due to the nonuniform distribution of solids. Clearly, a more realistic term of slip velocity needs to be incorporated into the solids flux model. A model for radial profiles of the solids flux, taking into account the effects of slip velocity, is developed as follows. Assume that the gas-solid flow in the upper dilute region is well-developed, and thus, variables are only a function of the radial location. Also assume that the slip velocity is proportional to the particle terminal velocity:

Usl,r )

Ug,r r

r - Us,r ) R Ug,Gs, Ut,r R

(

)

(3)

where, Ut,r is the local particle terminal velocity determined by the mean local particle diameter. The slip factor, R, is assumed to be a function of superficial gas velocity, Ug, overall solids flux, Gs, and radial distance, r/R. The local gas velocity has the following form:

(

Ug,r ) Uc 1 -

r 1/n R

)

(4)

and the index n can be calculated by (Yang et al., 1994)

( ) ()

Gs,r 1 1 ) + 0.8231 n n0 Gs

1.413

Z D

-1.879

-0.262

Re

(5)

where n0 equals 7 as obtained for the turbulent flow of a single fluid. The cross-sectional mass balance of gas gives

Ug )

2 R2

∫0R Ug,r r dr

(6)

Table 2. Best Fit Values of the Slip Factor (r) at Varying Operation Conditions Ug

Gs

r/R ) 0

r/R ) 0.33

r/R ) 0.67

r/R ) 0.99

2.55 2.55 2.55 4.4

17.4 26.1 34.9 26.1

2.93 3.4 3.1 7.5

2.35 2.97 2.6 5.56

2.3 3.75 3.61 6.57

1.44 2.15 1.72 3.32

Figure 17. The comparison of correlation with experimental data.

Combining eqs 4 and 6 the maximum gas velocity Uc can be obtained as

Uc )

2n2 + 3n + 1 Ug 2n2

(7)

Therefore, the local solids velocity has the form of

Us,r )

[

( )

(2n2 + 3n + 1) Ug r 12  R 2n r

1/n

]

- RUt,r

(8)

The local solids flux is

Gs,r ) FsUs,r(1 - r)

(9)

and the cross-sectional mass balance for the solids phase is given by eq 1. The slip factor, R, can be obtained by solving simultaneously eqs 1, 5, 8, and 9 using the experimental values for the solids flux. For coal ash, the calculated results at different locations and operation conditions are given in Table 2. As can be seen from the table, the slip factors for coal ash particles are much greater than 1. King (1989) has shown that the average slip velocity of FCC particles is 2 m/s, which gives the slip factor 2-4 for the terminal velocity of particles ranged from 1 to 0.5 m/s. The overall averaged slip factor of the current study is 3.45 which is within the range of King’s result for the FCC particles. Assuming the dependence of the slip factor R on the gas superficial velocity, overall solids flux and the dimensionless radial distance has the form of

R ) aUgbGscf

(Rr )

(10)

and the dimensionless slip factor can be written as

r R )f R0 R

()

(11)

where R0 is the slip factor at the center of the riser. A multivariable regression based on the data of Table 2 gives

1508 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998

R r r 2 r 3 ) 1 - 2.08 + 6.09 - 4.51 R0 R R R

()

()

()

(12)

with a standard deviation of 0.11 and

R0 ) 0.514Ug1.59Gs0.1

(13)

with a standard deviation of 0.18. Comparisons of the correlation eq 12 with the experimental data are shown in Figure 17. As shown in the figure, the radial profile of the slip factor fits a third-order polynomial curve. Conclusions The solids flow characteristics of coal ash are investigated with the measurement of the local solids flux, local solids concentration, and particle size distribution. It is found that both the macroscopic and mesoscopic structures of gas-solid flow of coal ash are different from that of commonly studied FCC and sand particles due to the wide range of size distribution and complex surface properties. In the lower dense region of the riser, a typical core-annular flow is observed with a higher solids flux at both the core and annular regions than that for FCC particles. Although a significant downward flow is present, an upward net flow is observed in the annular of the upper dilute region. A significant particle segregation is observed at a lower solids circulation rate and at different altitudes of the riser with the largest particles being found in the annular downward flow. At a higher solids circulation rate, the particle segregation is not significant in the lower region of the riser. The particles in the annular downward flow in the upper dilute region are found to have a larger mean particle diameter than those at other locations. The particle segregation is affected by the solids concentration, the particle size distribution, and the flow structure. The analyses of the transient flow structure by PDF of solids concentration signals, the intermittency index, and cluster frequency indicate that in both the lower dense and the upper dilute regions of the riser, the flow is more uniform/less cluster in the annular region compared to situations with particles of a narrow size distribution. In the core region, a uniform and less fluctuating flow is observed which is similar to the flow of particles of a narrow size distribution. On the basis of a semiempirical model for the radial solids flux, the correlation coefficients are obtained which can be used to quantify the slip factor for the calculation of radial solids flux. Nomenclature a ) constant in eq 10 b ) constant in eq 10 c ) constant in eq 10 d ) average particle diameter D ) diameter of the riser g ) gravitational acceleration Gs ) overall solids flux Gs,r ) local solids flux at radial r n ) index in eq 4 n0 ) index in eq 5 r ) radial distance from the center of the riser R ) radial of the riser Re ) Reynolds number based on the diameter of the riser Uc ) gas velocity at the center of the riser Ug ) superficial gas velocity

Ug,r ) local gas velocity Us,r ) local solids velocity Usl,r ) local slip velocity Ut,r ) local terminal velocity determined on the local mean diameter of particles Z ) axial distance from the bottom of riser Greek Letters R ) slip factor defined by eq 3 R0 ) slip factor at the center of the riser r ) local gas holdup (voidage) s ) mean solids holdup Fs ) solids density

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Received for review June 16, 1997 Revised manuscript received December 14, 1997 Accepted January 10, 1998 IE970436W