Epstein N., Grace J.R. Spouted and Spout-Fluid Beds: Fundamentals and Applications

Подождите немного. Документ загружается.

Particle mixing and segregation 147

300

250

200

150

100

04812

measured

predicted

injection

= 150 mm

time (s)

(mm)

Figure 8.6. Axial mixing time for three different heights of release. Measured versus simulated

mixing curves.

ﬂuctuations, whereas radial mixing requires less than a single cycle time, and circumfer-

ential uniformity is achieved in about two cycles. An idealized spouted bed model was

proposed with a descriptive parameter-free four-region (cylindrical and conical annulus,

spout, and fountain) two-dimensional axisymmetric stochastic model to simulate the

tracer trajectories. This model can be used predictively after deﬁning the jump probabil-

ities at the spout/annulus interface and within the annulus, the fountain height, relative

maximum residence time of particles, and the ﬂow reversal radius. Model validation was

carried out by comparing the controlling mixing components with experimental results

from γ -ray par ticle tracking. Figure 8.6 demonstrates this method.

Original cor relations have been proposed

for calculating the average cycle time in

a 0.152-m unit from the geometric factors, θ and D

, and experimental conditions, H

, and U. The distrib ution of cycle times was determined experimentally by monitoring

a colored particle trajectory with an image analysis system. Particle trajectories in the

annulus and spout were calculated by dividing each zone into streamtubes having the

same particle mass ﬂow, and their Stokes stream functions were solved in cylindrical

coordinates based on the experimental values of v

; v

was derived by solving local mass

balances. Particle ﬂow patterns were indicated by local velocity vectors. By comparing

these maps for different geometries and operating conditions, the effect of each parameter

was clariﬁed. Cycle times and frequencies were then calculated and compared with

the experimental results. I n Figure 8.7 the effect of the base angle is evident from a

comparison of the results in (a) and (b). The average cycle time doubled and a wider

distribution was obtained as the included cone angle increased.

Gross mixing of sawdust was evaluated

in a continuously operating spouted bed drier

in terms of the RTD. A tracer was introduced as a pulse and sampled after entrainment.

The drying reactor (D = 0.3 m, height = 1.9 m) behaved as an almost perfectly mixed

unit: it was modeled ﬁrst as a continuous stirred-tank reactor (CSTR) connected to a

plug ﬂow reactor and later as a dispersed plug ﬂow system, with a Peclet number, Pe,as

the ﬁtting parameter. Both descriptions were demonstrated to be in excellent agreement,

148 Giorgio Rovero and Norberto Piccinini

048121620

time (s)

024 6810

(a) (b)

time (s)

frequency (%)

Figure 8.7. Cycle time frequency.

Histograms: experimental results. Lines: calculated from the

trajectories. Experimental conditions: D = 0.152 m, D

= 0.03 m, H

= 0.20 m, d

= 4 mm, U =

1.02 U

:(a)θ = 45

◦

(b) θ = 120

◦

. Reprinted with permission of American Chemical Society,

by Copyright Clearance Center.

with Pe < 1, indicating that the material in the drying chamber is well mixed, regardless

of the discharge mode. Another mixing model, which considers elutriation of ﬁnes from

a continuous spouted bed, is also available

; the authors claim good agreement between

experimental data and ﬁtted model predictions.

Spouted beds as well-mixed reactors for coating applications were reviewed by

Piccinini

for batch pyrolytic carbon deposition. The deposition reaction, homogeneous

on the nuclear fuel particles circulating in the system, maintained excellent performance

throughout the many hours required for multilayer coating with simple adjustment of

gas ﬂowrate and gas composition. Continuous processes may be conceived for coating

operations, b ut variation of particle diameter and density with time and the extent of

coating may be challenging issues.

8.2 Mixing in a pulsed spouted bed

Spouting mechanism, mixing properties, maximum spoutable bed depth, and solids

circulation rates were studied in a pulsed spouted bed.

The pulsing is intended to

reduce energy consumption and to be applied where mass transfer controls the process.

The authors operated a cylindrical column of 0.17 m ID, D

= 10 and 20 mm, with

3.1 < d

< 6.7 mm, 0.61 < particle sphericity < 0.85, and 930 <ρ

< 1280 kg/m

.Air

pulsations at frequencies from 0.2 to 2 Hz were induced through a solenoid valve, with

the low frequency being the minimum required by the inertial time of particles to start

their circulation. Colored particles permitted determination of the stagnant zone height

at the column base. Flow regime diag rams (spouting/transition/slugging) were traced as

a function of frequency for different bed depths.

Particle mixing and segregation 149

350

PE-PS

wheat-PS

soya-PS

soya-PE

soya-wheat

300

250

200

150

100

0.4 0.8 1.2 1.6 2.0

Frequency (Hz)

Mixing time (s)

Figure 8.8. Time to obtain well-mixed state for different particulate mixtures.

D = 0.7 m, D

10 mm, U = 0.21 m/s, H

= 0.2 m (equal height layers).

The mixing effectiveness was determined by spouting 50 percent v/v binary mixtures

and sampling at different times to detect concentration differences less than 5 percent,

deﬁned as the mixing time criterion; this procedure was repeated at various bed locations.

An example of the inﬂuence of the frequency of pulsations on mixing is plotted in

Figure 8.8: the mixing time increased with frequency for all the binary mixtures tested,

whereas solids circulation at the top of the annulus reached a maximum at a frequency

of 1.2 Hz. This apparent inconsistency might be caused by local nonhomogeneity (i.e.,

segregation) or zones characterized by a l ower circulation (e.g., next to the bottom

stagnant zone).

8.3 Origin of segregation studies

Most studies on granular materials mixing have been carried out with particle tracers that

satisfy the requirement of being typical of the bulk in terms of size, shape, and density.

In most practical cases, however, there is a distribution of properties. In addition, these

properties may vary with time, for instance, because of drying, coating, or gas–solid

chemical reactions. In such cases, segregation or demixing can take place because of

the hydrodynamics of the spout and fountain, percolation of ﬁnes in the interstices of

coarse particles, and buoyancy differences between light and dense components.

Understanding and being able to control segregation phenomena leads to improved

process control. Another important consideration is whether the process is batch or

continuous. In the for mer case, segregation mainly gives rise to zones of different

concentration, whereas in the latter, after attaining steady state, the bed composition

eventually differs from that of the incoming mixture. If virtually well mixed, the outlet

composition is very similar to the bed composition.

150 Giorgio Rovero and Norberto Piccinini

bed

discharge

feed

bed

0 0.5 1.0 1.5 2.0

Dischar

ed solids, k

Coarse particles, wt %

Figure 8.9. Composition in bed and in discharge stream

: D = 80 mm, D

= 6 mm, m

0.67 kg, Q

= 1.64 × 10

−5

kg/s, U = 0.66 m/s, θ = 40

◦

, H

= 130 mm, ρ

= 2,650 kg/m

= 1.58, coarse material: glass, d

= 1.24 mm; ﬁne material: glass, d

= 0.78 mm.

____

and

•

submerged discharge D

= 7 mm, N

= 1.72;

−·−·− and −·−−·− overﬂow discharge D

= 14 mm, N

= 1.44.

Spouted beds often generate an inverted segregation with respect to ﬂuidized beds.

Because of entrainment in the spout, jetsam material is raised into the upper portion

of the bed. Then the fountain separates the components differing in mass according to

stochastic trajectories, whereas the annulus keeps circulating the particulate solids along

well-deﬁned streamlines.

8.4 Segregation in continuously operated spouted beds

A particular application of spouted beds that motivated an early study

was the coating

of prosthetic devices with pyrolytic carbon. In this process, characterized by a slow

deposition of material on the circulating solids, few particles represent the product,

whereas the bulk acts as a buffer. Spouting features must be maintained over time.

Control is provided by selectively discharging some of the ever-growing coarse particles.

The spouting vessel had D = 0.08 m, θ = 40

◦

, and D

= 6 mm. A 14-mm ID overﬂow

pipe was positioned 130 mm above the base to control the bed depth and to sample the

solids. A binary mixture of glass ballotini was used, with solids fed independently to

prevent upstream segregation. Figure 8.9 depicts the system dynamics from an initial bed

composition matching the feed solids concentration to a stationary discharge identical

to the feed. The solids feed rate did not appreciably affect the concentration proﬁles.

An equilibrium condition, displayed in Figure 8.10, was demonstrated to exist between

the internal (averaged over the entire bed) and the outgoing solids. It was expressed by

Y = X

, (8.4)

Particle mixing and segregation 151

0.8

20.6

30.2

41.1

50.5

70.4

80.2

Coarse part. %

0.6

0.4

0.2

0 0.2 0.4

Y = X

1.7

0.6 0.8 1

Fraction of coarse particles in the bed, X

Fraction of coarse particles in the discharge, Y

Figure 8.10. Relationship between bed and discharge mass fraction of coarse component for feed

compositions shown in the legend

; H

= 130 mm, D = 80 mm, D

= 6 mm, θ = 40

◦

, ρ

2,650 kg/m

, N

= 1.7 ± 0.1, d

ﬁne material = 0.55 mm, d

coarse material = 0.92 mm.

Reprinted with permission of John Wiley & Sons, Inc.

where n depends on the gas ﬂowrate in the vessel and the particle mixture according to

the relationship

n = c − d log

(U/U

− 1), (8.5)

where c and d depend on the particle mixture. If we consider a different situation

with a higher gas ﬂowrate (a more developed fountain and more vigorous mixing), the

equilibrium curve approaches the diagonal, signifying less segregation. The controlling

mechanism is then due primarily to trajectories and collisions in the fountain, rather than

to ﬁne particle buoyancy at the bed surface. Different segregation may be obtained in

deeper beds, owing to higher gas velocity in the annulus.

An additional contribution and quantiﬁcation of segregation phenomena, as well as

of the dynamics to reach steady state, was presented

to study the effect of the height

of the discharge port on the side and in the freeboard, with overﬂow, submerged, and

bottom openings. The composition of the stream collected directly from the fountain was

typically richer in ﬁnes, except for a fully overdeveloped and particle-crowded fountain

that generated local chaotic mixing (with U/U

approaching 2). An overﬂow opening

receives the solids according to fountain trajectories, bouncing on the bed surface or

entrainment, so discharge of ﬁnes is more probable. A submerged opening can release

a stream either richer or leaner in coarse material, depending on the gas ﬂowrate,

with the U/U

ratio affecting the composition of the discharge stream. Segregation

152 Giorgio Rovero and Norberto Piccinini

owing to strain-induced interparticle percolation generates some voidage increase and

preferential rolling out of the coarser particles. Depending on the operating conditions

and the geometry, a spouted bed of identical binary mixtures can evolve toward different

steady state composition distributions. In summary, the dynamics of a continuously

operating spouted bed can be shortened by using two different openings with their total

surface area chosen to obtain adequate solid material discharge.

During continuous operation, segregation induces substantial modiﬁcations in the

bed that can cause the system to change its behavior – for example, with the fountain

undergoing a transition to an underdeveloped state

and even with spouting collapse.

Contours of the particle velocity vectors were deﬁned in the three zones of a spouting

unit with D = 0.19 m, for both shallow and deep beds, based on stereophotogrammetric

measurements. The fountain height was shown to be linearly related to the gas mass ﬂux,

by having as a parameter the bed depth. Comparing these vectors clearly demonstrates

particle recirculation. Given the major role of fountain trajectories, particle demixing is

expected to play a signiﬁcant role in large-scale units.

A case in which steady state segregation of coarse particles occurred in a continuous

coating process was reported

for a thermochemical reactor in which large bodies (heart

valves or bone prostheses) were circulated in a spouting unit. When all s urfaces in direct

contact with a reacting hydrocarbon (or silane) underwent coatings as thick as 500 μm,

the increase of bed volume could be controlled by continuously feeding ﬁne particles

and removing the grown ones.

Segregation was compared in half and full beds by Cook and Bridgwater

:the

qualitative particle concentration proﬁles demonstrated that angular and radial segrega-

tion occurred, indicating that half-bed experiments are questionable for particle mixing

measurements. Batch experiments in a 0.193-m ID unit, with glass beads dispersed in

mustard seeds, allowed relative concentration proﬁles to be traced. By comparing the

results of tests carried out at different gas ﬂowrates, an overdeveloped fountain caused

the glass beads to land closer to the outer wall; however, the concentration proﬁle was

reversed by percolation along the annulus, favored by appreciable entrainment of the

lighter particles.

Experiments were carried out by Kutluoglu et al.

in a 0.152-m ID half-column

with D

= 12.7 mm, θ = 60

◦

, and four types of spherical particles (980 <ρ

2890 kg/m

,1.1< d

< 2.2 mm). The trajectories of colored particles were ﬁlm-

recorded at high frequencies and analyzed frame by frame. The mixing properties of the

fountain were evaluated by relating the landing radial position of particles to the radial

proﬁle of axial velocity component at the top of the spout exit, which is well described

by a parabolic distribution. Figure 8.11 accounts for this effect. Light particles were

deﬂected more than heavier particles because of collisions at the top of the fountain,

whereas collisions of particles against the column wall caused counteracting motion.

The sloping proﬁle of the annulus-top free surface also provided some redistribution.

Binary systems were tested to evaluate the cumulative distributions at the annulus–spout–

fountain boundaries for segregating conditions. An effective representation was provided

by triangular diagrams depicting the three regions: whereas segregation/demixing was

generated in the fountain, the annulus and particularly the spout promoted remixing

Particle mixing and segregation 153

1.0

0.5

H = 110 mm

H = 430 mm

0 0.5 1.0

MAXIMUM HEIGHT ACHIEVED/H

RADIAL LANDING POSITION / R

0.5

Figure 8.11. Radial landing position of polystyrene particles on the annulus surface as a function

of the maximum height achieved by the particle.

Reprinted with permission of John Wiley &

Sons, Inc.

and desegregation. An important conclusion was reached by operating with a mixture

formed by the same binary components of different particle densities and diameters, but

virtually identical particle masses: in this case no segregation occurred.

Bed depth affects the fountain solids load: the deeper the bed, the more pronounced the

component separation becomes. Shallow beds counteract segregation owing to an inward

sloping top bed surface, which generates a preferential inward rolling of light particles,

counteracting the greater outward motion of the light par ticles because of collisions in

the fountain. Surface bouncing, on the contrary, has a random effect, with the heavier

component having a tendency to be embedded and follow the particle streamlines. Fine

particles, depending on their mass and local gas velocity, may percolate or be entrained:

both mechanisms act in favor of generating concentration proﬁles in the axial and radial

directions. Installing conical deﬂectors in the fountain region was shown

to reduce

segregation.

Uemaki et al.

studied segregation of silica sand in a 0.20-m ID spouted bed by means

of batch tests with d

ratios from 1.47 to 3.40. In addition to generating a correlation

for the minimum spouting velocity of particle mixtures, the experimental program led

to detailed mapping of the coarse component concentration in the annulus without

interrupting the spouting. The particle size ratio and gas ﬂowrate were the test variables.

It was demonstrated that the degree of segregation increased with increasing particle

size ratio. With the solids tested and U = 1.20 U

, homogeneity was not achieved in

the bed for the mixtures tested.

8.5 Top surface segregation

Local segregation at the free surface of a spouted bed was demonstrated by Rovero.

Any particle characterized by a minimum ﬂuidization velocity (owing to its density or

154 Giorgio Rovero and Norberto Piccinini

size) lower than that typical of the solids bulk has a tendency to separate, provided that the

local gas velocity is sufﬁcient to promote ﬂuidization. Fines or fragments of the material

constituting the bed of particles could frequently be observed to concentrate at the vessel

wall, particularly when the fountain mixing properties were hindered, owing to moderate

spouting with a narrow fountain, or by insertion of a horizontal bafﬂe. Bafﬂe segregation

could be induced by having U

> U

of the ﬂotsam particle, locally at a given vertical

coordinate z. With this local segregation near the exit por t, a highly concentrated stream

of ﬂotsam particles could be discharged, while maintaining well-mixed conditions in the

annulus.

Bafﬂe-induced segregation can be relevant to continuous processes in which a reacting

solid phase undergoes a thermochemical reaction and the product particles differ in

size or density from the reactant particles. This bafﬂe segregation phenomenon was

proven to be useful in an autothermal pyrolysis-gasiﬁcation process under controlled

devolatilization conditions.

A possibly similar mechanism, in which the discharge pipe itself offers some cover

from fountain pouring, was mentioned

for the continuous release of light char dropping

from the freeboard and preferentially segregated to the region near the vessel wall.

8.6 Mixing and segregation in conical spouted beds

The success of conical spouted beds (CcSBs) for dr ying/granulation of pasty material

has been replicated in other applications with solids of irregular shapes. Fast reactions,

such as combustion, gasiﬁcation, and pyrolysis, do not need deep beds. Spout stability,

linked to solids circulation and homogeneity, has been demonstrated to beneﬁt from a

decrease in the diameter ratio of binary mixtures.

In the same paper, the mixing index,

, between 0.95 and 1.05 corresponded to negligible segregation. The mixing index

was found to be a function of the geometry of the bed and the air velocity.

The same authors

performed tests in a conical column unit with binary and tertiary

mixtures of glass beads (1 < d

< 8 mm). By optimizing the sampling conditions,

detailed radial and vertical proﬁles of the coarse fraction were obtained. Two empirical

correlations were proposed for the two phases, each giving good ﬁt to the experimental

results. The highest M

was obtained for 50 percent by mass of the coarser solid. Fig-

ure 8.12 plots the relationship between M

and U/U

, showing increasing homogeneity

with increasing U/U

. A similar mixing i ndex was also evaluated for tertiary solids

mixtures (M

), with a maximum for similar proportions by mass of all three components

(see Figure 8.13).

The mixing characteristics of conical spouted beds were evaluated indirectly in terms

of the solids circulation patterns.

D, d

, ρ

, , θ , solids l oading, and U were varied in

the tests. The mean radial and vertical particle velocities v

and v

were detected by an

optical probe and the streamtube mapping traced. The volumetric solids circulation was

then computed by cross-sectional integration of the particle ﬂux. The circulation rate

increased as the particle sphericity, , decreased, and as the particle density increased.

The spout-to-annulus volume ratio was much higher in the conical conﬁguration, with

Particle mixing and segregation 155

1.3

1.2

=8 (Mixture

39)

=7 (Mixture 33)

=6 (Mixture 27)

=5 (Mixture 21)

1.1

1.0

1.0 1.1 1.2 1.3

1.4 1.5

= 0.22 m

= 0.03 m

Figure 8.12. Effect of relative air velocity, u

= u

msi

, on mixing index for binary mixtures,

. θ = 36

◦

, H

= 0.22 m, D

= 0.03 m. Reprinted with permission of American Chemical

Society via Copyright Clearance Center.

1.3

1.2

1.1

1.0

0.9

0 0.1 0.2

)

= 0.22 m

= 0.03 m

0.3 0.4 0.5

Key d

Figure 8.13. Values of the mixing index for ternar y mixtures, M

, versus bed average value of

Sauter mean diameter distribution function, f

)

, for different particle diameter ratio,

, θ

= 36

◦

, H

= 0.32 m, D

= 0.03 m. Reprinted with permission of American Chemical Society via

the result that the radial component of particle velocity was more effective in causing

mixing, thus countering segregation. The non-monotonic radial concentration proﬁles

of coarse particles provide a qualitative indication of the improved mixing effectiveness.

Bacelos and Freire

demonstrated that spouting stability and particle segregation are

related. Spouting stability was evaluated by calculating the standard deviation of pressure

ﬂuctuations in the bed. Some particle mixtures generated unstable spouting, in particular

for ﬁne materials and mixtures of high particle diameter ratio. It seems that decreased

bed permeability, which is likely to cause incipient instability, also r esulted in increased

156 Giorgio Rovero and Norberto Piccinini

segregation. Percolation of a coarser fraction and/or entrainment of a ﬁner fraction was

enhanced by moderate system pulsation. For the range of experimental conditions tested,

a deeper bed improved spouting stability while decreasing segregation.

8.7 Mixing and segregation in a multispouting vessel

A novel ﬂuid–solids contactor featuring an annular geometry was studied by Huang and

Hu.

The degree of mixing was investigated in both the axial and the circumferential

directions. To compensate for peripheral elongation, an alternative axisymmetric circu-

lar feeding device was also proposed. Both the axial and the lateral mixing rates were

demonstrated to increase as the spouting airﬂow rate increased. The static bed depth had

a noticeable effect on the ﬁnal degree of mixing, ﬁrst increasing and then decreasing

with height, although the degree of lateral mixing showed a monotonic decrease with

height. It is likely that this contradictory result is caused by interference of the experi-

mental method, with some segregation occurring in the vertical direction for the coarser

tracer particles used, especially for deeper beds. In a second study,

the authors used

inclined conical nozzles to enhance the peripheral circulation of the granular solids. They

observed minor dead zones on the sides of their V-shaped deﬂectors. This unforeseen

ﬁnding is believed to be caused by the nature of the material used.

Taha and Koniuta

reported work on the Cerchar ﬂuidization distributor, which has all

the characteristics of 2×2 and 3×3 modules in a multiple spouting unit ( see Chapter 17).

The mixing obtained with this grid was compared to that resulting from a conventional

ﬂuidized bed distributor. By operating over a range of particle size and at density ratios

between 1 and 7, it was demonstrated that adequate homogeneity was obtained at a

superﬁcial velocity exceeding 50 percent of the minimum operating conditions, whereas

an excess of 150 percent was unable to disperse the jetsam in standard ﬂuidization.

Stimulus–response experiments were conducted

in four different rectangular

columns containing two and three spout cells. Each cell had a square cross-section

with 0.075, 0.10, or 0.15 m sides and a 60

◦

included angle at the bottom. The ﬂuid inlet

to each cell was 12 mm in diameter, independent of the side dimension. This geometry

caused different spouting conditions. Polymeric cylindrical chips (d

= 1.8 mm and l =

3.4 mm, ρ

= 556 kg/m

) constituted the bed material. After achieving steady state by

carefully adjusting the air supply to individual cells and continuous feeding through a

screw feeder, colored tracer was added as a pulse. Samples at the outlet were collected at

regular time intervals over two to ﬁve mean residence times. A plug ﬂow compartment

in series with mixed ﬂow was used to ﬁt the experimental data, giving an internal age

distribution of

(

)

= exp[−(V /V

)

(

θ − V

)

]. (8.6)

The solids ﬂow rate and superﬁcial gas velocity were recognized as important operating

parameters affecting the mixing properties of a multiple spouted bed. A dimensionless