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Circulating fluidised bed hydrodynamics
Powder Technology 113 Ž2000. 249–260 www.elsevier.comrlocaterpowtec
Circulating fluidised bed hydrodynamics J.F. Davidson ) Department of Chemical Engineering, UniÕersity of Cambridge, Pembroke Street, Cambridge, CB2 3RA UK Received 4 March 1999; received in revised form 6 October 1999; accepted 28 April 2000
Abstract Analysis is given for flow regimes in the riser of a circulating fluidised bed ŽCFB. in the range of gas velocities Ž2–8 mrs. and particulate solids fluxes Ž15–90 kgrm2 s. appropriate for a CFB combustor. It is shown that the simplest version of the core-annulus model gives the correct magnitudes of slip velocity and average solids hold-up. The anomaly in the core-annulus model, whereby diffusion of particles is towards the region of high solids concentration, is ascribed to the presence of clusters, diffusion towards the wall occurring in the dilute regions between clusters. The clusters are conjectured to be fragments of the relatively dense particle film falling near the wall: this film is shown to have features in common with a film of ordinary liquid flowing down a vertical surface. Implications for scale-up are discussed, using published data showing that very large CFBs exhibit core-annulus flow. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Fluidisation; Circulating fluidised beds; Two-phase flow
1. Introduction This paper describes conjectures about flow regimes in the riser of a circulating fluidised bed. The discussion is mostly about the core-annulus regime, which is observed when the average upward gas velocity in the riser is 2–8 mrs and the average upward flux of granular material is 15–90 kgrm2 s. In these circumstances, most of the riser cross-section is occupied by an upward flow of gas and solids, the volume fraction of the solids being of order 1%. Adjacent to the duct walls is a region of solids downflow, where the solids concentration may be quite high so that the instantaneous voidage can Adrop to that of a loosely packed bedB w1x. A simple characteristic is the slip Õelocity, Õs , the difference between the mean interstitial gas velocity and the mean upward particle velocity. Values of Õs are much above the terminal free-falling velocity, Ut , of a single particle and reasons why Õs 4 Ut are sought. It is shown that two regimes give Õs 4 Ut , namely: Ži. the churn-turbulent regime, and Žii. the core-annulus regime.
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A simple analysis for the core-annulus regime demonstrates why Õs 4 Ut and also shows why the solids inventory usually diminishes with vertical distance above the distributor. This model of the core-annulus regime is based on the idea of radial diffusion of particles towards the falling particle film adjacent to the wall. The particles diffusing towards the wall are captured by the falling wall film, which appears to be relatively stable, though subject to periodic detachment of particle clusters, which move inwards towards the centre of the duct. These clusters may be carried up in the core, disintegrating to form part of the dilute core phase. These conjectures are shown to be consistent with measurements of particle flux: there is upflux over the whole cross-section and downflux near the wall; the downflux, believed to be due to the falling wall film and to clusters, diminishes with increased radial distance from the wall. This flow regime is consistent with Ža. the observation that overall mean solids concentration increases almost monotonically towards the wall and, yet, Žb. there is radial diffusion of particles towards the wall; this radial diffusion is believed to be due to the concentration gradients in the dilute phase, excluding the cluster phase. Thus, there is a rational explanation as to why radial diffusion takes place against what appears to be an adverse concentration gradient of solids concentration.
0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 3 0 8 - 9
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
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A final speculation concerns the falling velocity of clusters, observed to be in the range 0.1–3 mrs, usually 1–2 mrs. Such velocities are predicted by assuming that the wall film of particles behaves like a viscous liquid film falling down a vertical surface: such a falling film always generates waves, which have much the same appearance as the clusters observed near the wall of a circulating fluidised bed.
2. Slip velocity Considering the cocurrent upward flow of gas and solids in the riser, an important quantity is the slip velocity, Õs , between gas and particles. The superficial velocity of the gas is U s Žvolume flow rate.rŽriser cross-sectional area.. The voidage fraction is ´ s Žinterstitial volume.rŽtotal volume. and so the solids volume fraction is Ž1 y ´ . s Žsolids volume.rŽtotal volume.. Then the upward interstitial velocity of the gas is: u G s Ure .
Ž 1.
The physical meaning of u G can be understood by imagining the solids to be evenly dispersed so that ´ s Žcross-section for gas flow.rŽtotal cross-section.. Thus, assuming the gas velocity between the particles is vertically upwards, u G is simply the upward gas velocity between particles, higher than U because the particles occupy part of the cross-sectional area. A similar argument applies for the solids: they occupy a fraction Ž1 y ´ . of the riser cross-sectional area, A, so the actual solids velocity, u s is given by: us s
m
rs A Ž 1 y e .
,
Ž 2.
where m s mass feed rate of solids to the riser; rs is the density of the material of the particles. Then the slip velocity, Õs , is simply given by: Õs s u G y u s s
U
e
m y
rs A Ž 1 y e .
.
Ž 3.
Ref. w2x gives a now familiar diagram showing slip velocity plotted against bed expansion for a variety of fluidised beds. Note that the slip velocity for CFBs is a maximum as compared with other bed types, i.e., bubbling beds and transport reactors. Numerical values of the slip velocity are not given in Ref. w2x, but can readily be calculated from Eq. Ž3., using published data, for example, that of Hartge et al. w3x, shown in Fig. 1. The diagrams in Fig. 1 show how solids volume fraction varies with height in risers of small and medium diameters. Assuming the circulating material was quartz sand of solid density 2600 kgrm3 , values of u G , u s and Õs can be calculated from Eq. Ž3. and are given in Table 1.
Fig. 1. Volume fraction of solids in CFB riser, plotted against height in riser w3x.
The values of slip velocity in Table 1 for a circulating fluidised bed, 2.4 and 4.8 mrs, are higher than would be expected for: Ža. a bubbling bed for which Õs might be 0.5–1.0 mrs, the rising velocity of a bubble, or Žb. a transport reactor for which the slip velocity would be of the same order as the terminal free-falling velocity of a single particle, Ut ; for the 58 mm sand used in the experiments, the free-falling velocitys 0.3 mrs w4x. The high slip velocities reported in Table 1 arise from the following flow regimes in the CFB. 2.1. Churn-turbulent flow at the bottom The bottom of the riser contains a dense bed, about 20% vol. solids. The high slip velocity, Õs s 4.8 mrs ŽTable 1., is consistent with slug flow, for which the absolute slug velocity is w5x:
'
Õs s U y Umf q 0.35 gD , Umf being the incipient fluidizing velocity. For D s 0.4 m ŽTable 1., the single bubble rise velocitys 0.35 gD s 0.35'9.81 = 0.4 s 0.69 mrs, g being the acceleration of gravity. Now Umf is much less than U and so from the above equation, Õs s 4.69 mrs, close to the estimated Õs s 4.8 mrs in Table 1.
'
2.2. Core r annulusr cluster flow in the main riser The churn-turbulent regime at the bottom is unstable: particles get carried up in dilute phase to give the lower solids volume fractions seen in Fig. 1, reaching about 2.5% solids at the top. However, the slip velocity, Õs s 2.4 mrs ŽTable 1., is much greater than the terminal free-falling velocity Ut s 0.3 mrs mentioned above. Why should Õs be so much greater than Ut for the disperse-phase motion? The answer is that the particles form aggregates, which can
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260 Table 1 CFB values of u G , u s and slip velocity, Õs s u G y u s , from data of Ref. w3x with riser diameter Ds 0.4 m, Us 4 mrs, m r As90 kgrm2 s Position
Gas velocity, u G wmrsx
Solids velocity, u s wmrsx
Slip velocity, Õs s Ž u G y u s . wmrsx
Bottom Top
5.0 4.1
0.17 1.7
4.8 2.4
fall through the gas at velocities much higher than the free-falling velocity of one particle. These aggregates are of two forms as follows. 2.2.1. Clusters Many authors have reported seeing AclustersB of particles, whose form has been described in a qualitative manner, though not in full detail, by a variety of authors, e.g, Refs. w6–8x; cluster sizes have been measured by Horio et al. w9x and data on cluster velocities are summarised by Glicksmann w10x. The conclusion is that clusters appear to be in the form of particle groups whose widthrheight ratio is small: thus, they are vertical sheets, which retain coherence over a considerable distance of fall. Particle clusters are familiar: a handful of sand dropped from a cliff top disperses gradually as it falls; the sportsperson with a shot gun uses the cluster principle, the charge of lead shot retaining its coherence over a considerable distance of flight. 2.2.2. Falling film near the wall: core r annulus flow Observation of a CFB riser with a transparent wall suggests that the particles are moving down, even though particles are supplied at the base and withdrawn at the top. This deceptive appearance of downflow is because of falling films adjacent to the wall, although the motion is decidedly irregular: the falling film appears to move in waves, which leave the wall in a random way, so that the wall is occasionally exposed to the upward moving dilute phase region in the main part of the riser. This suggests the concept of core-annulus flow: particles are elutriated from the churn turbulent region by bursting bubbles and slugs. These elutriated particles are carried upwards in the central region of the riser. In this central region, the motion is turbulent, so particles are thrown towards the wall where they form the falling film, which makes it look as if the particles are going down, not up. Particles impinging on the falling film are readily captured by the falling film but not readily re-entrained into the upflowing gas. Evidence that a close packed AsheetB or AclusterB of particles is coherent, and that particles are not readily re-entrained, is from studies on jets of close-packed particles w11x. Such jets, a few millimetres diameter, are stable over a flight of several metres with little entrainment of particles into the surrounding air. This suggests that in
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core-annulus flow, the falling wall film of particles would readily accept particles from the core, but return them reluctantly. Thus, the upward flow of entrained particles in the core should diminish with vertical distance above the churn-turbulent region. Likewise, it would be expected that the down flow in the falling film should, from a material balance, diminish with vertical distance above the churnturbulent region. Experimental evidence for this core-annulus model is given below.
3. Particle flux measurements: experimental Bolton and Davidson w12x describe an experimental CFB with means of measuring the downflow of particles near the wall of the Afast bedB. They describe a AscoopB for collecting particles falling near the wall. The scoop simply received downward flowing particles within about 2-mm distance from the wall. The particles were collected in a bottle from which some leakage of air to atmosphere was permitted. The measured particle flow rate received by the scoop was multiplied by p Dr5, the 5 representing the scoop width Žmm. and D being the riser diameter in millimetres. This gives the total downflow w as measured by the scoop. Typical results are shown in Fig. 2, together with a fitted exponential relating downflow w to height x above the distributor. w s w` q DweyK x ,
Ž 4.
where Dw and w` are shown in Fig. 2; K is a decay constant whose reciprocal, about 1.3 m, is also shown in Fig. 2. The existence of an asymptotic downflow, w` , implied by fitting Eq. Ž4. to the data, suggests that there is some re-entrainment from the wall film into the upward
Fig. 2. Variation of wall downflow with height for a fast fluidized riser w12x.
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252
flowing gasrsolid mixture: if there was no re-entrainment, w would tend to zero for large values of x.
4. Deposition coefficient, core to falling film A number of core-annulus models have been published, e.g., that of Horio w13x. The version given below is highly simplified and is believed to represent the major features of core-annulus flow. The form of Eq. Ž4. can be shown, as follows, to be consistent with the existence of a deposition coefficient, k d , giving the rate of particle transfer from the gas core to the surface of the falling particle film: k d is analogous to a mass transfer coefficient. Assuming that in the core, the particles are carried up with velocity ŽU y Ut ., then a particle balance on height d z of riser gives:
pD 4
2
Ž U y Ut .
dc dz
s yk dp D Ž c y c` . .
Ž 5.
Here, c` is the equilibrium concentration, the core concentration at which deposition and entrainment take place at the same rate, z is vertical distance and z s x y h ) , where h ) is the height of the churn-turbulent region at the bottom of the riser. Eq. Ž5. may be integrated to give: c s c` q Ž c 0 y c` . eyK z ,
Ž 6.
where: Ks
4 kd D Ž U y Ut .
.
Ž 7.
Assuming that the wall film is thin, i.e., its thickness is much less than the riser diameter D, then the upward flow rate of particles, the elutriation rate, is E s Ž1r4.p D 2 ŽU y Ut . c, so from Eq. Ž6.: E s E` q Ž E0 y E` . eyK z .
Ž 8.
Here, E0 is the elutriation rate at the top of the churnturbulent region and E` is the upward transport rate of particles in the upper reaches of a very tall riser. The external circulation rate of particles, being m, follows from a material balance, so that: m s E y w s E` y w` s E0 y w 0 .
Ž 9.
Eqs. Ž8. and Ž9. may be combined to get the relation between w and x. This relation is identical with Eq. Ž4. provided: )
Fig. 3. Deposition coefficient, k d , as a function of gas velocity w12x.
)
Dw s Ž E0 y E` . e K h s Ž w 0 y w` . e K h . Thus, Eq. Ž8., derived from the deposition model, is consistent with Eq. Ž4., which simply summarises experi-
mental measurements of downwards particle film flow. Hence, the data for particle down flow may be summarised in terms of the deposition coefficient, k d : results are given in Fig. 3. Qualitative profiles of E and of w, the up and down particle flows, are shown in Fig. 4. Following Ref. w12x, it is to be expected that k d is proportional to uX the fluctuating component of velocity, due to turbulence; assuming uX s 0.1 U gives the relation shown in Fig. 4, which fits the data and can be used for scale-up, see below. Fig. 3 also shows that the values of k d , deduced from the experimental measurements, are roughly consistent with published results for diffusion of liquid droplets in turbulent flow.
5. Particle inventory: contributions from core and film It is instructive to calculate the contributions to particle inventory from Ža. the core flow and Žb. the film flow. For each phase the volume fraction of particles, if the particles were evenly distributed across the riser, would be ŽParticle volume fraction. s ŽMass flowrrs A = Phase velocity.. Thus, the total volume fraction of particles is: 1yes
E
w q
rs A Ž U y Ut .
rs A Uf
.
Ž 10 .
Here, Uf s falling film velocity. Bolton and Davidson w12x observed that Uf was about 0.5 mrs. Glicksman w10x summarises results from ten papers see Table 2 below: he gives values of Uf ranging from 0.2 to 3 mrs for wall cluster falling velocity, presumably the same as Uf . It is instructive to calculate the numerical values of the terms in Eq. Ž10., using representative values from ex-
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Fig. 4. Core-annulus model: use of the deposition coefficient, k d , to predict fluxes.
periments w12x as follows Žsee also Fig. 5.: D s 0.15 m, rs s 384 kgrm3, U s 2.21 mrs, Ut s 0.32 mrs, m s 0.061 kgrs, w s 0.2 kgrs, Uf s 0.5 mrs. These data relate to experiments with vermiculite Žhence, the low solids density. with mean particle diameter 0.2 mm. Inserting these numbers in the terms on the right-hand side of Eq. Ž10. gives: volume fraction solids due to core s ErŽ rs AŽU y Ut .. s 0.02, volume fraction solids due to falling film of
particless wrrs AUf s 0.06. Total volume fraction of particles s 0.08. Mean volume fraction of gas, ´ s 0.92.
6. Slip velocity, zs It is instructive to calculate the slip velocity from Eq. Ž3. for the above data. The result is Õs s 2.21r0.92 y
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
254 Table 2 Published data on cluster falling velocity w10x Particles
Superficial gas velocity Žmrs.
Column diameter Žcm.
Velocity measurement technique
Cluster velocity at wall Žmrs.
FCC, 76 mm Glass, 520 mm Sand, 80 mm Aluminum, 600 mm Silica sand, 260 mm
3.7 5 0–6.5
30.5 7.6 10
Pitot tube External visual Visual
0.3 1.1 1.2
3.5–6.5
Cross-correlation of double thermocouple Intrusive light reflection probe Intrusive light reflection probe Intrusive light reflection probe External visual External visual
FCC, 85 mm CFB ash, 120 mm FCC, 60 mm
2.9–3.7
170 = 170 membrane wall 40
1.17–1.29
5.0
FCC, 46 mm
4.0
20.5
Alumina, 70 mm Phosphorescent ZnS, 50 mm Sand, 171 mm Sand, 171 mm
3–4 0.6–1.9
30.5 16.8
7 7
15.2 15.2
0.061r384 = 0.018 = 0.08 s 2.4 y 0.11 s 2.3 mrs, i.e., much higher than the terminal free-falling velocity of one particle, Ut s 0.32 mrs. The explanation is obvious: much of the particle inventory is the film, which is falling and giving rise to the high slip velocity. The results are summarised in Fig. 5.
7. Scale-up: tentative calculations for large unit Fig. 6 shows highly tentative calculations for a 3-m-diameter unit. The important effect of scale is on the decay constant, K, from Eq. Ž7.. The deposition coefficient, k d , is proportional to uX , the fluctuating component of velocity due to turbulence and assuming uX s 0.1 U, a typical value for turbulent flow in a pipe gives, approximately, K s 0.07rD, i.e., the decay coefficient diminishes as D increases. This is simply a statement of the fact that as the diameter increases, the particles must diffuse further, to reach the walls. Fig. 6 shows results for a 3-m-diameter bed, assuming an external particle circulation rate equivalent to an upward flux of 75 kgrm2 s. The results include estimates of solids hold-up at the top and bottom of the riser using the plausible value of Uf s 2 mrs, consistent with the data of Glicksman w10x and of Zhou et al. w14x.
8. Concentration profiles Fig. 7 shows data given by Werther as to voidage profiles in CFB risers w15x. These results imply that the
External visual Cross-correlation of double thermocouple
™ 0.9 ™2 1.4 ™ 2.2 0.2 ™ 2.8 0.45 ™ 0.65 0.6 ™ 1.0 0.1 ™ 2.2 1.0 ™ 3.0 0.64 ™ 2.77 1.62
solids volume fraction increases progressively towards the wall. Taken at their face value, these results are not consistent with the above theory of particle diffusion within the core towards the falling film at the wall. The radial diffusion model implies that the solids concentration should decrease as radius increases and then increase sharply on entering the wall film as the radius r approaches R, the radius of the tube. However, it is known that the falling film is regularly stripped off the wall, to give the falling AclustersB or AsheetsB of relatively densely packed particles that fall through the gas. These clusters, originating from the wall, are likely to diminish in frequency and size as r decreases. So it can be argued that the whole riser contains a mixture of three gas–solid phases as follows. Ž1. The wall film phase, containing up to 50% volume of solids, is dominant in a thin layer near the wall. Ž2. The cluster phase is important near the wall; the cluster phase decreases its volume fraction as r decreases. Ž3. The dilute phase, containing about 1–2% volume of solids, has a solids concentration, which decreases as r increases, thus, causing radial diffusion and eventually deposition onto the falling film at the wall. It is to this dilute phase that the transfer coefficient k d relates. Fig. 8 depicts the flow regime envisaged by this hypothesis, together with the concentration profiles in the wall film and cluster phase and in the dilute phase. The filmrcluster phase is assumed to be dominant near the walls, the clusters arising from periodic break-up of the dense falling film on the walls. The clusters themselves are expected to be unstable, their break-up contributing particles to the dilute phase. It is conceivable that small clusters get carried up in the core before finally breaking up. This
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Fig. 5. Contributions to solids volume fraction: calculation of voidage and slip velocity.
picture is consistent with the measurements of Horio et al. w9x, see also Ref. w13x, who give data on cluster size in a 50-mm-diameter CFB riser: cluster length was about 5 mm for 0 F r - 20 mm; the cluster size increased abruptly near the wall, lengths of up to 30 mm being reported. Fig. 8 shows speculative concentration profiles for the two phases: the dilute phase concentration is assumed to fall monotonically towards the walls, consistent with the radial diffusion in the core-annulus model described in Section 4 above. Devices to measure solids concentration,
e.g., using X-ray attenuation or fibre optic probes w1x, give a time-averaged value of solids concentration, the averaging arising from the combined concentrations of the dilute and wall-filmrcluster phases. The result, admittedly conjectural, is shown in Fig. 8. The wall-filmrcluster phase concentration is assumed to fall sharply with radial distance from the wall, but clusters may contribute a little to the solids concentration near the centre of the riser. The total solids concentration, dilute plus wall-filmr cluster phase, might give profiles like those shown in
256
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
Fig. 6. Scale-up. Tentative calculations for a large unit, D s 3 m, based on core-annulus model.
Fig. 7, the total concentration rising monotonically towards the walls. Alternatively, the concentration could fall slightly
as r increased from zero, reaching a weak minimum at r f Ž0.5–0.7. R: this type of profile was reported by Zhou
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
Fig. 7. Measured voidage fraction, ´ , in riser as a function of radius r w15x.
et al. w1x, who observed a maximum in the relation between time-mean voidage and distance from the axis.
9. Flux measurements Evidence in favour of the flow regime depicted in Fig. 8 is from measurements of solids flux, using a suction probe w16–18x. The method is to use a small sample tube like a pilot tube, the end of the tube facing upwards or downwards in the vertical duct. The particles impinging on the end of the tube are conveyed through the tube to a sampling system where their flow rate is measured. It appears that the inertia of the particles is enough to render the sampling rate almost independent of the gas suction rate through the probe; thus, isokinetic sampling is not required. It is found that there is upward particle flux over the whole of the riser cross-section and downward particle
Fig. 8. Conjecture as to core-annulus flow regime showing: Ž1. Disperse phase, Ž2. Cluster phase, Ž3. Wall film. Cluster lengths are approximately to scale for a 50-mm-diameter riser, from measurements w9,13x.
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flux near the walls. It appears that the downward particle flux is due to the falling film and the clusters. The upward flux must be mainly the dilute phase, approximately homogeneous, but perhaps also including clusters small enough to be carried up by the gas stream. Fig. 9 shows data of Werdermann w17x and of Harris w16x replotted. The conditions used by both workers were similar with regard to solids flux Ž50 and 52 kgrm2 s. and gas velocity Ž4.2 and 5 mrs.; but the riser diameters were rather different Ž0.4 and 0.14 m.. Nevertheless, the solids flux profiles, observed independently by the two workers, Refs. w16,17x, are remarkably similar: there is an upward solids flux profile of roughly parabolic form, with a maximum flux, at the centre-line, of about three times the mean. The downward flux rises from zero at r ( 0.7R to a maximum downward value of about five times the mean. The scale-up effect is shown in Fig. 10, which gives data for a large square riser w17x replotted as dimensionless flux, G ) , against dimensionless radius, j , in the same way as the data of Fig. 9. Fig. 10 shows the curves derived
Fig. 9. CFB risers. Dimensionless solids flux, G ) , plotted against dimensionless radius j , from suction probe measurements. Ž1. Data of Werdermann w17x for 0.4 m riser. The open points ŽI e `. give upflux for three angular positions, f . The corresponding downflux is shown by solid points ŽB l v .. Gas velocity 4.2 mrs. Net solids flux 50 kgrm2 s. Height above distributor, z s 4.9 m. Ž2. Data of Harris w16x for 0.14-mdiameter riser: the curves fit his data points ŽUpflux - - -. ŽDownflux . . . .. Gas velocity 5 mrs. Net solids flux 52 kgrm2 s. z s 4 m.
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J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
Fig. 10. Scale up effects in CFB risers. Ž1. Data of Werdermann w17x for 5.1-m square duct. Data from suction probe traverses giving dimensionless particle flux, G ) , along two traverse lines shown. Upflux I `. Downflux B v. Gas velocity 6.3 mrs, solids flux 15 kgrm2 s. Height above distributor 17.3 m. Ž2. Data of Harris w16x for 0.14 m diameter riser. Curves for upflux - - - and downflux . . . from Fig. 9.
from Harris’s data w16x from the 0.14-m-diameter unit, for comparison. It is clear from Fig. 10 that the large unit exhibits core-annulus flow, but there are major differences between the large unit and the two small units Ž0.14-m diameter w16x and 0.4-m diameter w17x. as follows: 1. For the large unit, the annulus region, the region of solids downflow, occupies only about 5% of the halfwidth of the square duct, instead of about 10% of the radius for the small circular section units. 2. For the large unit, the maximum solids upflux — towards the middle of the duct — is about 1.5 times the mean flux, compared with about three times the mean upflux for the small units. 3. The peak downflux, for the large unit, is about ten times the mean solids flux, as compared with about five times the mean solids flux for the small units. For the large unit, therefore, the picture is of a very dense falling-filmrcluster regime near the wall, with solids volume fraction of order 0.2, but this dense falling film is thin in relation to the lateral dimension of the cross-section.
the layer . . . becomes thicker than the tail part and the shape of the layer looks like a waveB . Analysis given by Wallis w20x predicts the velocity, V, of a continuity wave on a liquid film of density r , thickness h, and viscosity m , falling down a vertical surface, giving: Vs
r g h2 m
.
Ž 11 .
Plausible values for r , h and m can be estimated as follows. 10.1. Film density, r Zhou et al. w1x measured voidage profiles, reporting voidages of 0.8– 0.9 near the wall. Hatano et al. w21x measured solids build-ups Ain particle swarmsB of Aat least 0.25 and possibly reaching that in a loosely packed conditionB. Hence, it is reasonable to assume that the bulk density of the falling film is 20% of the solid particle density, so r s 500 kgrm3 will be assumed. 10.2. Film thickness, h
10. Cluster velocity: waves on a falling film Table 2 shows data collected by Glicksman w10x on measured values of the cluster velocity. These are likely to relate to the wall film: observation of the falling particle film suggests it exhibits waves like those seen on a wetted column with liquid supplied continuously at the top. Indeed, Jiang et al. w19x report that: AThe frontal face . . . of
The data in Table 2 are for laboratory units so h can be estimated from Fig. 9, which relates to units of radius R s 0.07 and 0.2 m. From Fig. 9, it can be inferred that the wall film occupies the region 0.95 - j - 1: in this region, it is clear that there is predominantly downflow, with downward flux of three to five times the mean flux, as would be expected for a wall film. Using the two values of R, it follows that h is either 0.07 = 0.05, i.e., 3.5 mm or
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
0.2 = 0.05, i.e., 10 mm. The mean of these values is h s 6.75 mm. 10.3. Film Õiscosity, m Clift and Grace w22x report values of viscosity, for dense fluidised beds, of 0.4–1.4 N srm2 . Bearing in mind that the falling film appears to be a loosely packed bed, w1,19x, a value of m s 0.1 N srm2 will be assumed. 10.4. Predicted waÕe Õelocity Using these deduced values, namely r s 500 kgrm3 , m s 0.1 N srm2 and h ranging from 3.5 to 10 mm, with a mean value h s 6.75 mm, the wave velocity V can be estimated from Eq. Ž11.. This gives: Ži. with h s 6.75 mm, V s 2.2 mrs; Žii. with h s 3.5 mm, V s 0.6 mrs; Žiii. with h s 10 mm, V s 4.9 mrs. This wide range of predicted wave velocities, from 0.6 to 4.9 mrs, is reasonably consistent with the data in Table 2, which shows V ranging from 0.1 to 3.0 mrs. The above predictions are also consistent with the values of Athe descending velocity of wavy solid layerB reported by Jiang et al. w19x: their Fig. 8 gives data for wave velocity in the range 1.6–1.7 mrs, not far from the prediction V s 2.2 mrs for h s 6.75 mm. It is obvious that the use of laminar liquid film theory to predict the wave velocity of falling particle wall films, Eq. Ž11., is highly speculative; but other analogies between gas–particle flow and gas–liquid flow have been helpful. The above calculations do at least give the right order of magnitude for the very scattered data on cluster falling velocity. Lim et al. w23x give theory to predict the falling velocities of clusters, using a balance between gravity and drag. This is not inconsistent with the above theory leading to Eq. Ž11., which is for incipient clusters Žwaves., whereas Lim et al.’s w23x theory is to predict the velocities of fully established clusters.
11. Conclusions Ž1. The core-annulus model explains why the slip velocity between gas and solids in a CFB riser is much higher than the terminal free-falling velocity of a single isolated particle. Ž2. The core-annulus model gives the right order of magnitude for mean solids hold-up in the riser. The model also explains why solids hold-up usually decreases in the riser with distance above the distributor: this is because particles diffuse from the core region towards the walls, where the particles are readily captured by the falling particle film on the walls and are not readily re-entrained. Ž3. There is some evidence for the hypothesis that the CFB riser contains three phases, as follows.
259
Ži. A dilute phase, containing a small volume fraction of particles moving up with the gas, occupies most of the riser cross-section. Žii. Against the wall is a falling film of particles with a solids volume fraction about the same as in a loosely packed bed. Žiii. The falling film is unstable, so clusters of particles detach from the film, to enter the dilute phase Ži. above. The clusters decompose in the dilute phase, so clusters are larger near the wall and diminish in size towards the middle of the riser. The decomposition of clusters contributes particles to the dilute phase. Ž4. Calculations of wave velocity, for the falling wall film of particles, using theory for a viscous liquid falling down a vertical surface, give a wave velocity of the same order as observed cluster falling velocities, supporting the proposition that clusters arise from detaching waves on the liquid film. Ž5. There is firm evidence that a large CFB riser Ž5.1-m square. exhibits core-annulus flow. In proportion to the riser width, the falling film near the wall of the large unit appears to be thinner than for laboratory CFB risers. Ž6. Tentative scale-up calculations, using the core-annulus model, show that for a large unit the decay of solids inventory with height is slower on a large unit as compared with a small unit.
List of A c co c` CFB D E E0 E` G G) g H h h) K kd m R r U Uf Umf Ut uX uG us
symbols Riser cross-sectional area s p D 2r4 Particle concentration in dilute phase Value of c at z s 0 Žkgrm3 . Value of c far above bed surface Žkgrm3 . Circulating fluidised bed Riser diameter Žm. Upwards particle flow rate in core Žkgrs. Value of E at z s 0 Žkgrs. Value of E far above bed surface Local solids flux Žkgrm2 s. Dimensionless solids flux s GArm Ž – . Acceleration of gravity Žmrs 2 . Total height of riser Žm. Thickness of liquid film, or height Žm. Depth of bubbling or churnrturbulent bed Žm. Decay constants 4 k drDŽU y Ut . Žmy1 . Deposition coefficient Žmrs. Solids feed rate to riser Žkgrs. Radius of circular riser Žm. Radius within circular riser Žm. Superficial gas velocity Žmrs. Falling velocity of wall film Žmrs. Incipient fluidising velocity Free-falling velocity of one particle Žmrs. Fluctuating velocity due to turbulence Žmrs. Absolute gas velocity Žmrs. Solids velocity Žmrs.
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V Õs w wo w` Dw x z
Wave velocity Žmrs. Slip velocity between phases Žmrs. Solids flow rate down wall Žkgrs or grs. Value of w at top of churn-turbulent bed Žkgrs or grs. Value of w at large bed height Žkgrs or grs. Fitting parameter, Eq. Ž4. Žkgrs or grs. Height above distributor Žm. Height above churn-turbulent bed s x y h ) Žm.
Greek letters ´ Mean voidage fraction Ž – . m Viscosity of liquid ŽPa s. j Dimensionless radius s rrR Ž – . r Density of liquid Žkgrm3 . rs Density of particle Žkgrm3 . f Angular position in riser Ž8.
Acknowledgements The first draft of this paper was written during a visit to Monash University in 1997, whose support at that time is gratefully acknowledged. Further support from Nisshin Engineering, to complete the work, 1998, is equally appreciated.
References w1x J. Zhou, J.R. Grace, S. Qin, C.M.H. Brereton, C.J. Lim, J. Zhu, Chem. Eng. Sci. 49 Ž1994. 3217. w2x L. Reh, The circulating fluid bed reactor — a key to efficient gas–solid processing,Circulating Fluidized Bed Technology, Pergamon, 1986, p. 105. w3x E-W. Hartge, Y. Li, J. Werther, Fluidization V, Engineering Foundation, 1986, p. 345, New York.
w4x R. Clift, J.R Grace, M.E. Weber, Bubbles Drops and Particles, 1978, p. 116. w5x J.F. Davidson, D. Harrison ŽEds.., Fluidization, Academic Press, 1971, p. 201. w6x H. Takeuchi, T. Hirama, Circulating Fluidized Bed Technology II, Pergamon, 1991, p. 177. w7x M. Horio, Proc. Second Int. Conf. on Multiphase Flow, Kyoto, Japan, 1995, FBI-1. w8x H. Kuroki, M. Horio, Circulating Fluidized Bed Technology IV, AIChE Ž1994. 77. w9x M. Horio, K. Morishta, O. Tachibana, N. Murata, in: P. Basu, J.F. Large ŽEds.., Circulating Fluidized Bed Technology II, Pergamon, 1988, p. 147. w10x L.R. Glicksman, in: J.R. Grace, A. Avidan, T.M. Knowlton ŽEds.., Circulating Fluidized Beds, Blackie, 1997, p. 261. w11x P.D. Martin, J.F. Davidson, Chem. Eng. Res. Des. 61 Ž1983. 162. w12x L.W. Bolton, J.F. Davidson, Recirculation of particles in fast fluidised risers,Proc. Second Conf. on Circulating Fluidized Beds, Pergamon, 1988, p. 139. w13x M. Horio, in: J.R. Grace, A. Avidan, T.M. Knowlton ŽEds.., Circulating Fluidized Beds, Blackie, 1997, p. 21. w14x J. Zhou, J.R. Grace, C.J. Lim, C.M.H. Brereton, Chem. Eng. Sci. 50 Ž1995. 237. w15x J. Werther, Circulating Fluidized Bed Technology IV, Fluid mechanics of large scale CFB units, AIChE 1994, p. 1. w16x B.J. Harris, The hydrodynamics of circulating fluidized beds, PhD dissertation, Cambridge, 1992. w17x C.C. Werderman, Feststoffbewgung und Warmeubergang in zirkulierenden Wirbelschichten von Kohlekraftwerken, PhD thesis, Technischen Universitat, Hamburg-Harburg, Hamburg, 1992, pp. 79, 93, 94. w18x E.H. Van der Meer, Riser exists and scaling of circulating fluidized beds, PhD dissertation, Cambridge, 1997. w19x P. Jiang, P. Cai, L-S. Fan, Circulating fluidized bed technology IV, AIChE Ž1994. p. 111. w20x G.B. Wallis, One-dimensional two-phase flow, McGraw-Hill, 1969, p. 125. w21x H. Hatano, H. Takeuchi, S. Sakurai, T. Masuyama, K. Tsuchiya, AIChE Symp. Ser. No. 318 94 Ž1998. 31. w22x R. Clift, J.R. Grace, in: J.F. Davidson, R. Clift, D. Harrison ŽEds.., Fluidization, Academic Press, 1985, p. 77. w23x K.S. Lim, J. Zhou, C. Finley, J.R. Grace, C.J. Lim, C.M.H. Brereton, in: Mooson Kwauk, Jinghai Li ŽEds.., Circulating Fluidized Bed Technology V, Science Press, Beijing, 1997, p. 218.
Circulating fluidised bed hydrodynamics J.F. Davidson ) Department of Chemical Engineering, UniÕersity of Cambridge, Pembroke Street, Cambridge, CB2 3RA UK Received 4 March 1999; received in revised form 6 October 1999; accepted 28 April 2000
Abstract Analysis is given for flow regimes in the riser of a circulating fluidised bed ŽCFB. in the range of gas velocities Ž2–8 mrs. and particulate solids fluxes Ž15–90 kgrm2 s. appropriate for a CFB combustor. It is shown that the simplest version of the core-annulus model gives the correct magnitudes of slip velocity and average solids hold-up. The anomaly in the core-annulus model, whereby diffusion of particles is towards the region of high solids concentration, is ascribed to the presence of clusters, diffusion towards the wall occurring in the dilute regions between clusters. The clusters are conjectured to be fragments of the relatively dense particle film falling near the wall: this film is shown to have features in common with a film of ordinary liquid flowing down a vertical surface. Implications for scale-up are discussed, using published data showing that very large CFBs exhibit core-annulus flow. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Fluidisation; Circulating fluidised beds; Two-phase flow
1. Introduction This paper describes conjectures about flow regimes in the riser of a circulating fluidised bed. The discussion is mostly about the core-annulus regime, which is observed when the average upward gas velocity in the riser is 2–8 mrs and the average upward flux of granular material is 15–90 kgrm2 s. In these circumstances, most of the riser cross-section is occupied by an upward flow of gas and solids, the volume fraction of the solids being of order 1%. Adjacent to the duct walls is a region of solids downflow, where the solids concentration may be quite high so that the instantaneous voidage can Adrop to that of a loosely packed bedB w1x. A simple characteristic is the slip Õelocity, Õs , the difference between the mean interstitial gas velocity and the mean upward particle velocity. Values of Õs are much above the terminal free-falling velocity, Ut , of a single particle and reasons why Õs 4 Ut are sought. It is shown that two regimes give Õs 4 Ut , namely: Ži. the churn-turbulent regime, and Žii. the core-annulus regime.
)
Tel.: q44-1223-334799; fax: q44-1223-334796.
A simple analysis for the core-annulus regime demonstrates why Õs 4 Ut and also shows why the solids inventory usually diminishes with vertical distance above the distributor. This model of the core-annulus regime is based on the idea of radial diffusion of particles towards the falling particle film adjacent to the wall. The particles diffusing towards the wall are captured by the falling wall film, which appears to be relatively stable, though subject to periodic detachment of particle clusters, which move inwards towards the centre of the duct. These clusters may be carried up in the core, disintegrating to form part of the dilute core phase. These conjectures are shown to be consistent with measurements of particle flux: there is upflux over the whole cross-section and downflux near the wall; the downflux, believed to be due to the falling wall film and to clusters, diminishes with increased radial distance from the wall. This flow regime is consistent with Ža. the observation that overall mean solids concentration increases almost monotonically towards the wall and, yet, Žb. there is radial diffusion of particles towards the wall; this radial diffusion is believed to be due to the concentration gradients in the dilute phase, excluding the cluster phase. Thus, there is a rational explanation as to why radial diffusion takes place against what appears to be an adverse concentration gradient of solids concentration.
0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 3 0 8 - 9
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250
A final speculation concerns the falling velocity of clusters, observed to be in the range 0.1–3 mrs, usually 1–2 mrs. Such velocities are predicted by assuming that the wall film of particles behaves like a viscous liquid film falling down a vertical surface: such a falling film always generates waves, which have much the same appearance as the clusters observed near the wall of a circulating fluidised bed.
2. Slip velocity Considering the cocurrent upward flow of gas and solids in the riser, an important quantity is the slip velocity, Õs , between gas and particles. The superficial velocity of the gas is U s Žvolume flow rate.rŽriser cross-sectional area.. The voidage fraction is ´ s Žinterstitial volume.rŽtotal volume. and so the solids volume fraction is Ž1 y ´ . s Žsolids volume.rŽtotal volume.. Then the upward interstitial velocity of the gas is: u G s Ure .
Ž 1.
The physical meaning of u G can be understood by imagining the solids to be evenly dispersed so that ´ s Žcross-section for gas flow.rŽtotal cross-section.. Thus, assuming the gas velocity between the particles is vertically upwards, u G is simply the upward gas velocity between particles, higher than U because the particles occupy part of the cross-sectional area. A similar argument applies for the solids: they occupy a fraction Ž1 y ´ . of the riser cross-sectional area, A, so the actual solids velocity, u s is given by: us s
m
rs A Ž 1 y e .
,
Ž 2.
where m s mass feed rate of solids to the riser; rs is the density of the material of the particles. Then the slip velocity, Õs , is simply given by: Õs s u G y u s s
U
e
m y
rs A Ž 1 y e .
.
Ž 3.
Ref. w2x gives a now familiar diagram showing slip velocity plotted against bed expansion for a variety of fluidised beds. Note that the slip velocity for CFBs is a maximum as compared with other bed types, i.e., bubbling beds and transport reactors. Numerical values of the slip velocity are not given in Ref. w2x, but can readily be calculated from Eq. Ž3., using published data, for example, that of Hartge et al. w3x, shown in Fig. 1. The diagrams in Fig. 1 show how solids volume fraction varies with height in risers of small and medium diameters. Assuming the circulating material was quartz sand of solid density 2600 kgrm3 , values of u G , u s and Õs can be calculated from Eq. Ž3. and are given in Table 1.
Fig. 1. Volume fraction of solids in CFB riser, plotted against height in riser w3x.
The values of slip velocity in Table 1 for a circulating fluidised bed, 2.4 and 4.8 mrs, are higher than would be expected for: Ža. a bubbling bed for which Õs might be 0.5–1.0 mrs, the rising velocity of a bubble, or Žb. a transport reactor for which the slip velocity would be of the same order as the terminal free-falling velocity of a single particle, Ut ; for the 58 mm sand used in the experiments, the free-falling velocitys 0.3 mrs w4x. The high slip velocities reported in Table 1 arise from the following flow regimes in the CFB. 2.1. Churn-turbulent flow at the bottom The bottom of the riser contains a dense bed, about 20% vol. solids. The high slip velocity, Õs s 4.8 mrs ŽTable 1., is consistent with slug flow, for which the absolute slug velocity is w5x:
'
Õs s U y Umf q 0.35 gD , Umf being the incipient fluidizing velocity. For D s 0.4 m ŽTable 1., the single bubble rise velocitys 0.35 gD s 0.35'9.81 = 0.4 s 0.69 mrs, g being the acceleration of gravity. Now Umf is much less than U and so from the above equation, Õs s 4.69 mrs, close to the estimated Õs s 4.8 mrs in Table 1.
'
2.2. Core r annulusr cluster flow in the main riser The churn-turbulent regime at the bottom is unstable: particles get carried up in dilute phase to give the lower solids volume fractions seen in Fig. 1, reaching about 2.5% solids at the top. However, the slip velocity, Õs s 2.4 mrs ŽTable 1., is much greater than the terminal free-falling velocity Ut s 0.3 mrs mentioned above. Why should Õs be so much greater than Ut for the disperse-phase motion? The answer is that the particles form aggregates, which can
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260 Table 1 CFB values of u G , u s and slip velocity, Õs s u G y u s , from data of Ref. w3x with riser diameter Ds 0.4 m, Us 4 mrs, m r As90 kgrm2 s Position
Gas velocity, u G wmrsx
Solids velocity, u s wmrsx
Slip velocity, Õs s Ž u G y u s . wmrsx
Bottom Top
5.0 4.1
0.17 1.7
4.8 2.4
fall through the gas at velocities much higher than the free-falling velocity of one particle. These aggregates are of two forms as follows. 2.2.1. Clusters Many authors have reported seeing AclustersB of particles, whose form has been described in a qualitative manner, though not in full detail, by a variety of authors, e.g, Refs. w6–8x; cluster sizes have been measured by Horio et al. w9x and data on cluster velocities are summarised by Glicksmann w10x. The conclusion is that clusters appear to be in the form of particle groups whose widthrheight ratio is small: thus, they are vertical sheets, which retain coherence over a considerable distance of fall. Particle clusters are familiar: a handful of sand dropped from a cliff top disperses gradually as it falls; the sportsperson with a shot gun uses the cluster principle, the charge of lead shot retaining its coherence over a considerable distance of flight. 2.2.2. Falling film near the wall: core r annulus flow Observation of a CFB riser with a transparent wall suggests that the particles are moving down, even though particles are supplied at the base and withdrawn at the top. This deceptive appearance of downflow is because of falling films adjacent to the wall, although the motion is decidedly irregular: the falling film appears to move in waves, which leave the wall in a random way, so that the wall is occasionally exposed to the upward moving dilute phase region in the main part of the riser. This suggests the concept of core-annulus flow: particles are elutriated from the churn turbulent region by bursting bubbles and slugs. These elutriated particles are carried upwards in the central region of the riser. In this central region, the motion is turbulent, so particles are thrown towards the wall where they form the falling film, which makes it look as if the particles are going down, not up. Particles impinging on the falling film are readily captured by the falling film but not readily re-entrained into the upflowing gas. Evidence that a close packed AsheetB or AclusterB of particles is coherent, and that particles are not readily re-entrained, is from studies on jets of close-packed particles w11x. Such jets, a few millimetres diameter, are stable over a flight of several metres with little entrainment of particles into the surrounding air. This suggests that in
251
core-annulus flow, the falling wall film of particles would readily accept particles from the core, but return them reluctantly. Thus, the upward flow of entrained particles in the core should diminish with vertical distance above the churn-turbulent region. Likewise, it would be expected that the down flow in the falling film should, from a material balance, diminish with vertical distance above the churnturbulent region. Experimental evidence for this core-annulus model is given below.
3. Particle flux measurements: experimental Bolton and Davidson w12x describe an experimental CFB with means of measuring the downflow of particles near the wall of the Afast bedB. They describe a AscoopB for collecting particles falling near the wall. The scoop simply received downward flowing particles within about 2-mm distance from the wall. The particles were collected in a bottle from which some leakage of air to atmosphere was permitted. The measured particle flow rate received by the scoop was multiplied by p Dr5, the 5 representing the scoop width Žmm. and D being the riser diameter in millimetres. This gives the total downflow w as measured by the scoop. Typical results are shown in Fig. 2, together with a fitted exponential relating downflow w to height x above the distributor. w s w` q DweyK x ,
Ž 4.
where Dw and w` are shown in Fig. 2; K is a decay constant whose reciprocal, about 1.3 m, is also shown in Fig. 2. The existence of an asymptotic downflow, w` , implied by fitting Eq. Ž4. to the data, suggests that there is some re-entrainment from the wall film into the upward
Fig. 2. Variation of wall downflow with height for a fast fluidized riser w12x.
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252
flowing gasrsolid mixture: if there was no re-entrainment, w would tend to zero for large values of x.
4. Deposition coefficient, core to falling film A number of core-annulus models have been published, e.g., that of Horio w13x. The version given below is highly simplified and is believed to represent the major features of core-annulus flow. The form of Eq. Ž4. can be shown, as follows, to be consistent with the existence of a deposition coefficient, k d , giving the rate of particle transfer from the gas core to the surface of the falling particle film: k d is analogous to a mass transfer coefficient. Assuming that in the core, the particles are carried up with velocity ŽU y Ut ., then a particle balance on height d z of riser gives:
pD 4
2
Ž U y Ut .
dc dz
s yk dp D Ž c y c` . .
Ž 5.
Here, c` is the equilibrium concentration, the core concentration at which deposition and entrainment take place at the same rate, z is vertical distance and z s x y h ) , where h ) is the height of the churn-turbulent region at the bottom of the riser. Eq. Ž5. may be integrated to give: c s c` q Ž c 0 y c` . eyK z ,
Ž 6.
where: Ks
4 kd D Ž U y Ut .
.
Ž 7.
Assuming that the wall film is thin, i.e., its thickness is much less than the riser diameter D, then the upward flow rate of particles, the elutriation rate, is E s Ž1r4.p D 2 ŽU y Ut . c, so from Eq. Ž6.: E s E` q Ž E0 y E` . eyK z .
Ž 8.
Here, E0 is the elutriation rate at the top of the churnturbulent region and E` is the upward transport rate of particles in the upper reaches of a very tall riser. The external circulation rate of particles, being m, follows from a material balance, so that: m s E y w s E` y w` s E0 y w 0 .
Ž 9.
Eqs. Ž8. and Ž9. may be combined to get the relation between w and x. This relation is identical with Eq. Ž4. provided: )
Fig. 3. Deposition coefficient, k d , as a function of gas velocity w12x.
)
Dw s Ž E0 y E` . e K h s Ž w 0 y w` . e K h . Thus, Eq. Ž8., derived from the deposition model, is consistent with Eq. Ž4., which simply summarises experi-
mental measurements of downwards particle film flow. Hence, the data for particle down flow may be summarised in terms of the deposition coefficient, k d : results are given in Fig. 3. Qualitative profiles of E and of w, the up and down particle flows, are shown in Fig. 4. Following Ref. w12x, it is to be expected that k d is proportional to uX the fluctuating component of velocity, due to turbulence; assuming uX s 0.1 U gives the relation shown in Fig. 4, which fits the data and can be used for scale-up, see below. Fig. 3 also shows that the values of k d , deduced from the experimental measurements, are roughly consistent with published results for diffusion of liquid droplets in turbulent flow.
5. Particle inventory: contributions from core and film It is instructive to calculate the contributions to particle inventory from Ža. the core flow and Žb. the film flow. For each phase the volume fraction of particles, if the particles were evenly distributed across the riser, would be ŽParticle volume fraction. s ŽMass flowrrs A = Phase velocity.. Thus, the total volume fraction of particles is: 1yes
E
w q
rs A Ž U y Ut .
rs A Uf
.
Ž 10 .
Here, Uf s falling film velocity. Bolton and Davidson w12x observed that Uf was about 0.5 mrs. Glicksman w10x summarises results from ten papers see Table 2 below: he gives values of Uf ranging from 0.2 to 3 mrs for wall cluster falling velocity, presumably the same as Uf . It is instructive to calculate the numerical values of the terms in Eq. Ž10., using representative values from ex-
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Fig. 4. Core-annulus model: use of the deposition coefficient, k d , to predict fluxes.
periments w12x as follows Žsee also Fig. 5.: D s 0.15 m, rs s 384 kgrm3, U s 2.21 mrs, Ut s 0.32 mrs, m s 0.061 kgrs, w s 0.2 kgrs, Uf s 0.5 mrs. These data relate to experiments with vermiculite Žhence, the low solids density. with mean particle diameter 0.2 mm. Inserting these numbers in the terms on the right-hand side of Eq. Ž10. gives: volume fraction solids due to core s ErŽ rs AŽU y Ut .. s 0.02, volume fraction solids due to falling film of
particless wrrs AUf s 0.06. Total volume fraction of particles s 0.08. Mean volume fraction of gas, ´ s 0.92.
6. Slip velocity, zs It is instructive to calculate the slip velocity from Eq. Ž3. for the above data. The result is Õs s 2.21r0.92 y
J.F. DaÕidsonr Powder Technology 113 (2000) 249–260
254 Table 2 Published data on cluster falling velocity w10x Particles
Superficial gas velocity Žmrs.
Column diameter Žcm.
Velocity measurement technique
Cluster velocity at wall Žmrs.
FCC, 76 mm Glass, 520 mm Sand, 80 mm Aluminum, 600 mm Silica sand, 260 mm
3.7 5 0–6.5
30.5 7.6 10
Pitot tube External visual Visual
0.3 1.1 1.2
3.5–6.5
Cross-correlation of double thermocouple Intrusive light reflection probe Intrusive light reflection probe Intrusive light reflection probe External visual External visual
FCC, 85 mm CFB ash, 120 mm FCC, 60 mm
2.9–3.7
170 = 170 membrane wall 40
1.17–1.29
5.0
FCC, 46 mm
4.0
20.5
Alumina, 70 mm Phosphorescent ZnS, 50 mm Sand, 171 mm Sand, 171 mm
3–4 0.6–1.9
30.5 16.8
7 7
15.2 15.2
0.061r384 = 0.018 = 0.08 s 2.4 y 0.11 s 2.3 mrs, i.e., much higher than the terminal free-falling velocity of one particle, Ut s 0.32 mrs. The explanation is obvious: much of the particle inventory is the film, which is falling and giving rise to the high slip velocity. The results are summarised in Fig. 5.
7. Scale-up: tentative calculations for large unit Fig. 6 shows highly tentative calculations for a 3-m-diameter unit. The important effect of scale is on the decay constant, K, from Eq. Ž7.. The deposition coefficient, k d , is proportional to uX , the fluctuating component of velocity due to turbulence and assuming uX s 0.1 U, a typical value for turbulent flow in a pipe gives, approximately, K s 0.07rD, i.e., the decay coefficient diminishes as D increases. This is simply a statement of the fact that as the diameter increases, the particles must diffuse further, to reach the walls. Fig. 6 shows results for a 3-m-diameter bed, assuming an external particle circulation rate equivalent to an upward flux of 75 kgrm2 s. The results include estimates of solids hold-up at the top and bottom of the riser using the plausible value of Uf s 2 mrs, consistent with the data of Glicksman w10x and of Zhou et al. w14x.
8. Concentration profiles Fig. 7 shows data given by Werther as to voidage profiles in CFB risers w15x. These results imply that the
External visual Cross-correlation of double thermocouple
™ 0.9 ™2 1.4 ™ 2.2 0.2 ™ 2.8 0.45 ™ 0.65 0.6 ™ 1.0 0.1 ™ 2.2 1.0 ™ 3.0 0.64 ™ 2.77 1.62
solids volume fraction increases progressively towards the wall. Taken at their face value, these results are not consistent with the above theory of particle diffusion within the core towards the falling film at the wall. The radial diffusion model implies that the solids concentration should decrease as radius increases and then increase sharply on entering the wall film as the radius r approaches R, the radius of the tube. However, it is known that the falling film is regularly stripped off the wall, to give the falling AclustersB or AsheetsB of relatively densely packed particles that fall through the gas. These clusters, originating from the wall, are likely to diminish in frequency and size as r decreases. So it can be argued that the whole riser contains a mixture of three gas–solid phases as follows. Ž1. The wall film phase, containing up to 50% volume of solids, is dominant in a thin layer near the wall. Ž2. The cluster phase is important near the wall; the cluster phase decreases its volume fraction as r decreases. Ž3. The dilute phase, containing about 1–2% volume of solids, has a solids concentration, which decreases as r increases, thus, causing radial diffusion and eventually deposition onto the falling film at the wall. It is to this dilute phase that the transfer coefficient k d relates. Fig. 8 depicts the flow regime envisaged by this hypothesis, together with the concentration profiles in the wall film and cluster phase and in the dilute phase. The filmrcluster phase is assumed to be dominant near the walls, the clusters arising from periodic break-up of the dense falling film on the walls. The clusters themselves are expected to be unstable, their break-up contributing particles to the dilute phase. It is conceivable that small clusters get carried up in the core before finally breaking up. This
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Fig. 5. Contributions to solids volume fraction: calculation of voidage and slip velocity.
picture is consistent with the measurements of Horio et al. w9x, see also Ref. w13x, who give data on cluster size in a 50-mm-diameter CFB riser: cluster length was about 5 mm for 0 F r - 20 mm; the cluster size increased abruptly near the wall, lengths of up to 30 mm being reported. Fig. 8 shows speculative concentration profiles for the two phases: the dilute phase concentration is assumed to fall monotonically towards the walls, consistent with the radial diffusion in the core-annulus model described in Section 4 above. Devices to measure solids concentration,
e.g., using X-ray attenuation or fibre optic probes w1x, give a time-averaged value of solids concentration, the averaging arising from the combined concentrations of the dilute and wall-filmrcluster phases. The result, admittedly conjectural, is shown in Fig. 8. The wall-filmrcluster phase concentration is assumed to fall sharply with radial distance from the wall, but clusters may contribute a little to the solids concentration near the centre of the riser. The total solids concentration, dilute plus wall-filmr cluster phase, might give profiles like those shown in
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Fig. 6. Scale-up. Tentative calculations for a large unit, D s 3 m, based on core-annulus model.
Fig. 7, the total concentration rising monotonically towards the walls. Alternatively, the concentration could fall slightly
as r increased from zero, reaching a weak minimum at r f Ž0.5–0.7. R: this type of profile was reported by Zhou
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Fig. 7. Measured voidage fraction, ´ , in riser as a function of radius r w15x.
et al. w1x, who observed a maximum in the relation between time-mean voidage and distance from the axis.
9. Flux measurements Evidence in favour of the flow regime depicted in Fig. 8 is from measurements of solids flux, using a suction probe w16–18x. The method is to use a small sample tube like a pilot tube, the end of the tube facing upwards or downwards in the vertical duct. The particles impinging on the end of the tube are conveyed through the tube to a sampling system where their flow rate is measured. It appears that the inertia of the particles is enough to render the sampling rate almost independent of the gas suction rate through the probe; thus, isokinetic sampling is not required. It is found that there is upward particle flux over the whole of the riser cross-section and downward particle
Fig. 8. Conjecture as to core-annulus flow regime showing: Ž1. Disperse phase, Ž2. Cluster phase, Ž3. Wall film. Cluster lengths are approximately to scale for a 50-mm-diameter riser, from measurements w9,13x.
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flux near the walls. It appears that the downward particle flux is due to the falling film and the clusters. The upward flux must be mainly the dilute phase, approximately homogeneous, but perhaps also including clusters small enough to be carried up by the gas stream. Fig. 9 shows data of Werdermann w17x and of Harris w16x replotted. The conditions used by both workers were similar with regard to solids flux Ž50 and 52 kgrm2 s. and gas velocity Ž4.2 and 5 mrs.; but the riser diameters were rather different Ž0.4 and 0.14 m.. Nevertheless, the solids flux profiles, observed independently by the two workers, Refs. w16,17x, are remarkably similar: there is an upward solids flux profile of roughly parabolic form, with a maximum flux, at the centre-line, of about three times the mean. The downward flux rises from zero at r ( 0.7R to a maximum downward value of about five times the mean. The scale-up effect is shown in Fig. 10, which gives data for a large square riser w17x replotted as dimensionless flux, G ) , against dimensionless radius, j , in the same way as the data of Fig. 9. Fig. 10 shows the curves derived
Fig. 9. CFB risers. Dimensionless solids flux, G ) , plotted against dimensionless radius j , from suction probe measurements. Ž1. Data of Werdermann w17x for 0.4 m riser. The open points ŽI e `. give upflux for three angular positions, f . The corresponding downflux is shown by solid points ŽB l v .. Gas velocity 4.2 mrs. Net solids flux 50 kgrm2 s. Height above distributor, z s 4.9 m. Ž2. Data of Harris w16x for 0.14-mdiameter riser: the curves fit his data points ŽUpflux - - -. ŽDownflux . . . .. Gas velocity 5 mrs. Net solids flux 52 kgrm2 s. z s 4 m.
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Fig. 10. Scale up effects in CFB risers. Ž1. Data of Werdermann w17x for 5.1-m square duct. Data from suction probe traverses giving dimensionless particle flux, G ) , along two traverse lines shown. Upflux I `. Downflux B v. Gas velocity 6.3 mrs, solids flux 15 kgrm2 s. Height above distributor 17.3 m. Ž2. Data of Harris w16x for 0.14 m diameter riser. Curves for upflux - - - and downflux . . . from Fig. 9.
from Harris’s data w16x from the 0.14-m-diameter unit, for comparison. It is clear from Fig. 10 that the large unit exhibits core-annulus flow, but there are major differences between the large unit and the two small units Ž0.14-m diameter w16x and 0.4-m diameter w17x. as follows: 1. For the large unit, the annulus region, the region of solids downflow, occupies only about 5% of the halfwidth of the square duct, instead of about 10% of the radius for the small circular section units. 2. For the large unit, the maximum solids upflux — towards the middle of the duct — is about 1.5 times the mean flux, compared with about three times the mean upflux for the small units. 3. The peak downflux, for the large unit, is about ten times the mean solids flux, as compared with about five times the mean solids flux for the small units. For the large unit, therefore, the picture is of a very dense falling-filmrcluster regime near the wall, with solids volume fraction of order 0.2, but this dense falling film is thin in relation to the lateral dimension of the cross-section.
the layer . . . becomes thicker than the tail part and the shape of the layer looks like a waveB . Analysis given by Wallis w20x predicts the velocity, V, of a continuity wave on a liquid film of density r , thickness h, and viscosity m , falling down a vertical surface, giving: Vs
r g h2 m
.
Ž 11 .
Plausible values for r , h and m can be estimated as follows. 10.1. Film density, r Zhou et al. w1x measured voidage profiles, reporting voidages of 0.8– 0.9 near the wall. Hatano et al. w21x measured solids build-ups Ain particle swarmsB of Aat least 0.25 and possibly reaching that in a loosely packed conditionB. Hence, it is reasonable to assume that the bulk density of the falling film is 20% of the solid particle density, so r s 500 kgrm3 will be assumed. 10.2. Film thickness, h
10. Cluster velocity: waves on a falling film Table 2 shows data collected by Glicksman w10x on measured values of the cluster velocity. These are likely to relate to the wall film: observation of the falling particle film suggests it exhibits waves like those seen on a wetted column with liquid supplied continuously at the top. Indeed, Jiang et al. w19x report that: AThe frontal face . . . of
The data in Table 2 are for laboratory units so h can be estimated from Fig. 9, which relates to units of radius R s 0.07 and 0.2 m. From Fig. 9, it can be inferred that the wall film occupies the region 0.95 - j - 1: in this region, it is clear that there is predominantly downflow, with downward flux of three to five times the mean flux, as would be expected for a wall film. Using the two values of R, it follows that h is either 0.07 = 0.05, i.e., 3.5 mm or
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0.2 = 0.05, i.e., 10 mm. The mean of these values is h s 6.75 mm. 10.3. Film Õiscosity, m Clift and Grace w22x report values of viscosity, for dense fluidised beds, of 0.4–1.4 N srm2 . Bearing in mind that the falling film appears to be a loosely packed bed, w1,19x, a value of m s 0.1 N srm2 will be assumed. 10.4. Predicted waÕe Õelocity Using these deduced values, namely r s 500 kgrm3 , m s 0.1 N srm2 and h ranging from 3.5 to 10 mm, with a mean value h s 6.75 mm, the wave velocity V can be estimated from Eq. Ž11.. This gives: Ži. with h s 6.75 mm, V s 2.2 mrs; Žii. with h s 3.5 mm, V s 0.6 mrs; Žiii. with h s 10 mm, V s 4.9 mrs. This wide range of predicted wave velocities, from 0.6 to 4.9 mrs, is reasonably consistent with the data in Table 2, which shows V ranging from 0.1 to 3.0 mrs. The above predictions are also consistent with the values of Athe descending velocity of wavy solid layerB reported by Jiang et al. w19x: their Fig. 8 gives data for wave velocity in the range 1.6–1.7 mrs, not far from the prediction V s 2.2 mrs for h s 6.75 mm. It is obvious that the use of laminar liquid film theory to predict the wave velocity of falling particle wall films, Eq. Ž11., is highly speculative; but other analogies between gas–particle flow and gas–liquid flow have been helpful. The above calculations do at least give the right order of magnitude for the very scattered data on cluster falling velocity. Lim et al. w23x give theory to predict the falling velocities of clusters, using a balance between gravity and drag. This is not inconsistent with the above theory leading to Eq. Ž11., which is for incipient clusters Žwaves., whereas Lim et al.’s w23x theory is to predict the velocities of fully established clusters.
11. Conclusions Ž1. The core-annulus model explains why the slip velocity between gas and solids in a CFB riser is much higher than the terminal free-falling velocity of a single isolated particle. Ž2. The core-annulus model gives the right order of magnitude for mean solids hold-up in the riser. The model also explains why solids hold-up usually decreases in the riser with distance above the distributor: this is because particles diffuse from the core region towards the walls, where the particles are readily captured by the falling particle film on the walls and are not readily re-entrained. Ž3. There is some evidence for the hypothesis that the CFB riser contains three phases, as follows.
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Ži. A dilute phase, containing a small volume fraction of particles moving up with the gas, occupies most of the riser cross-section. Žii. Against the wall is a falling film of particles with a solids volume fraction about the same as in a loosely packed bed. Žiii. The falling film is unstable, so clusters of particles detach from the film, to enter the dilute phase Ži. above. The clusters decompose in the dilute phase, so clusters are larger near the wall and diminish in size towards the middle of the riser. The decomposition of clusters contributes particles to the dilute phase. Ž4. Calculations of wave velocity, for the falling wall film of particles, using theory for a viscous liquid falling down a vertical surface, give a wave velocity of the same order as observed cluster falling velocities, supporting the proposition that clusters arise from detaching waves on the liquid film. Ž5. There is firm evidence that a large CFB riser Ž5.1-m square. exhibits core-annulus flow. In proportion to the riser width, the falling film near the wall of the large unit appears to be thinner than for laboratory CFB risers. Ž6. Tentative scale-up calculations, using the core-annulus model, show that for a large unit the decay of solids inventory with height is slower on a large unit as compared with a small unit.
List of A c co c` CFB D E E0 E` G G) g H h h) K kd m R r U Uf Umf Ut uX uG us
symbols Riser cross-sectional area s p D 2r4 Particle concentration in dilute phase Value of c at z s 0 Žkgrm3 . Value of c far above bed surface Žkgrm3 . Circulating fluidised bed Riser diameter Žm. Upwards particle flow rate in core Žkgrs. Value of E at z s 0 Žkgrs. Value of E far above bed surface Local solids flux Žkgrm2 s. Dimensionless solids flux s GArm Ž – . Acceleration of gravity Žmrs 2 . Total height of riser Žm. Thickness of liquid film, or height Žm. Depth of bubbling or churnrturbulent bed Žm. Decay constants 4 k drDŽU y Ut . Žmy1 . Deposition coefficient Žmrs. Solids feed rate to riser Žkgrs. Radius of circular riser Žm. Radius within circular riser Žm. Superficial gas velocity Žmrs. Falling velocity of wall film Žmrs. Incipient fluidising velocity Free-falling velocity of one particle Žmrs. Fluctuating velocity due to turbulence Žmrs. Absolute gas velocity Žmrs. Solids velocity Žmrs.
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V Õs w wo w` Dw x z
Wave velocity Žmrs. Slip velocity between phases Žmrs. Solids flow rate down wall Žkgrs or grs. Value of w at top of churn-turbulent bed Žkgrs or grs. Value of w at large bed height Žkgrs or grs. Fitting parameter, Eq. Ž4. Žkgrs or grs. Height above distributor Žm. Height above churn-turbulent bed s x y h ) Žm.
Greek letters ´ Mean voidage fraction Ž – . m Viscosity of liquid ŽPa s. j Dimensionless radius s rrR Ž – . r Density of liquid Žkgrm3 . rs Density of particle Žkgrm3 . f Angular position in riser Ž8.
Acknowledgements The first draft of this paper was written during a visit to Monash University in 1997, whose support at that time is gratefully acknowledged. Further support from Nisshin Engineering, to complete the work, 1998, is equally appreciated.
References w1x J. Zhou, J.R. Grace, S. Qin, C.M.H. Brereton, C.J. Lim, J. Zhu, Chem. Eng. Sci. 49 Ž1994. 3217. w2x L. Reh, The circulating fluid bed reactor — a key to efficient gas–solid processing,Circulating Fluidized Bed Technology, Pergamon, 1986, p. 105. w3x E-W. Hartge, Y. Li, J. Werther, Fluidization V, Engineering Foundation, 1986, p. 345, New York.
w4x R. Clift, J.R Grace, M.E. Weber, Bubbles Drops and Particles, 1978, p. 116. w5x J.F. Davidson, D. Harrison ŽEds.., Fluidization, Academic Press, 1971, p. 201. w6x H. Takeuchi, T. Hirama, Circulating Fluidized Bed Technology II, Pergamon, 1991, p. 177. w7x M. Horio, Proc. Second Int. Conf. on Multiphase Flow, Kyoto, Japan, 1995, FBI-1. w8x H. Kuroki, M. Horio, Circulating Fluidized Bed Technology IV, AIChE Ž1994. 77. w9x M. Horio, K. Morishta, O. Tachibana, N. Murata, in: P. Basu, J.F. Large ŽEds.., Circulating Fluidized Bed Technology II, Pergamon, 1988, p. 147. w10x L.R. Glicksman, in: J.R. Grace, A. Avidan, T.M. Knowlton ŽEds.., Circulating Fluidized Beds, Blackie, 1997, p. 261. w11x P.D. Martin, J.F. Davidson, Chem. Eng. Res. Des. 61 Ž1983. 162. w12x L.W. Bolton, J.F. Davidson, Recirculation of particles in fast fluidised risers,Proc. Second Conf. on Circulating Fluidized Beds, Pergamon, 1988, p. 139. w13x M. Horio, in: J.R. Grace, A. Avidan, T.M. Knowlton ŽEds.., Circulating Fluidized Beds, Blackie, 1997, p. 21. w14x J. Zhou, J.R. Grace, C.J. Lim, C.M.H. Brereton, Chem. Eng. Sci. 50 Ž1995. 237. w15x J. Werther, Circulating Fluidized Bed Technology IV, Fluid mechanics of large scale CFB units, AIChE 1994, p. 1. w16x B.J. Harris, The hydrodynamics of circulating fluidized beds, PhD dissertation, Cambridge, 1992. w17x C.C. Werderman, Feststoffbewgung und Warmeubergang in zirkulierenden Wirbelschichten von Kohlekraftwerken, PhD thesis, Technischen Universitat, Hamburg-Harburg, Hamburg, 1992, pp. 79, 93, 94. w18x E.H. Van der Meer, Riser exists and scaling of circulating fluidized beds, PhD dissertation, Cambridge, 1997. w19x P. Jiang, P. Cai, L-S. Fan, Circulating fluidized bed technology IV, AIChE Ž1994. p. 111. w20x G.B. Wallis, One-dimensional two-phase flow, McGraw-Hill, 1969, p. 125. w21x H. Hatano, H. Takeuchi, S. Sakurai, T. Masuyama, K. Tsuchiya, AIChE Symp. Ser. No. 318 94 Ž1998. 31. w22x R. Clift, J.R. Grace, in: J.F. Davidson, R. Clift, D. Harrison ŽEds.., Fluidization, Academic Press, 1985, p. 77. w23x K.S. Lim, J. Zhou, C. Finley, J.R. Grace, C.J. Lim, C.M.H. Brereton, in: Mooson Kwauk, Jinghai Li ŽEds.., Circulating Fluidized Bed Technology V, Science Press, Beijing, 1997, p. 218.