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

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Scaleup, slot-rectangular, and multiple spouting 287

0.4 1.0

0.6

1.0

0.8

0.4

0.2

0.0

0.8

0.60.20.0

(b)

0.6

1.0

0.8

0.4

0.2

0.0

0.0 0.2

0.4

0.30.1

1.2

Dimensionless radius, r/R

Dimensionless vertical level, z/H

Dimensionless height z/H

(a)

Figure 17.1. Dimensionless (a) spout diameter and (b) pressure proﬁles for two scaled columns: a

0.152-m diameter column with glass beads at 500

◦

C, and a 0.051-m diameter column with steel

shot at room temperature, after He et al.

or two at a time, led to signiﬁcant lack of agreement. The authors found that all the

dimensionless groups included in (17.2) were important for the range of conditions

studied. This approach was also supported by experimental results for three similar

slot-rectangular columns,

and by computational ﬂuid dynamic (CFD) simulations.

The degree of agreement for matched columns is illustrated in Figures 17.1 and 17.2.

This agreement suggests that the hydrodynamics of spouted beds can be scaled (upward

or downward) by geometrically similar physical cold models, providing it is possible to

maintain equality of all important independent dimensionless groups (geometric sim-

ilarity implies equality of all groups such as H/D, D/D

and D

). Moreover, the

approach can be employed to test the effects of operating pressure and temperature, in

addition to the inﬂuence of scale (D).

Several CFD studies of spouted beds

20–24

have demonstrated that the coefﬁcient

of restitution for particle–particle collisions, η

, should also be added to the set of

dimensionless groups to be matched for spouted beds. This arises because interparticle

collisions play an important role in the fountain and spout regions. With this addition,

(17.2) becomes

ρd

,φ

,ε

,ϕ,PSD ,η

. (17.3)

It is clearly difﬁcult in practice to match as many as 10 dimensionless groups, but if

this can be done, coupled with geometric similarity, there is a sound basis for scaleup.

It should be remembered in practice, however, that this approach may well fail in some

cases, for example:

288 John R. Grace and C. Jim Lim

predicted for larger bed / Q

predicted in smaller bed

observed in larger bed / Qms observed in smaller bed

0.80 and 0.30 m wide columns

0.30 and 0.15 m wide columns

0.80 and 0.15 m wide columns

Figure 17.2. Matching of dimensionless minimum spouting velocities for three dimensionally

similar units of slot-rectangular spouted bed geometry, after Costa and Taranto.

When particles of the same sphericity (a single parameter representing complex three-

dimensional forms) have signiﬁcantly different shapes.

When more than one parameter is needed to describe particle size distributions.

For “overdeveloped” fountains (those in which the particles bounce off the inner wall)

of the column, so the particle wall coefﬁcient of restitution is also important.

For vessels with very rough inner surfaces that may behave ver y differently from

smooth walls.

If substantial pulsations are provided by the blower, then their amplitude, frequency

and waveform may all play signiﬁcant roles.

If other forces, such as those caused by electrostatics or surface moisture, play major

roles, additional dimensionless groups will be required.

If physical properties change during the course of the operation – for example, as a

result of particle attrition, agglomeration, or drying in batchwise operation – similarity

between the model and the prototype may be destroyed.

It should also be remembered that cold modeling based on dimensional similitude is

readily suited only to physical modeling of hydrodynamics. It may be extended to other

physical phenomena such as convective heat transfer if it is also possible to match other

key dimensionless groups such as the Prandtl number, but it is unlikely to be able to deal

with situations in which there are other complications, such as substantial temperature or

concentration gradients, signiﬁcant radiant heat transfer, chemical reactions, or erosion

(wear) of surfaces.

On the other hand, in some cases it may be possible to simplify the matching. For

example, it may be possible on occasion

to replace the Reynolds number by U/U

which is easier to match. Alternatively, it may be possible to use the minimum ﬂuidization

Scaleup, slot-rectangular, and multiple spouting 289

width α

β = thickness

α ≥β

η≤β

slot of width λ and length η

Figure 17.3. Schematic of slot-rectangular spouted bed geometry with a single slot.

velocity, U

, or the terminal free settling velocity in formulating a reduced set of

dimensionless groups.

If particles are very uniform in size, the PSD parameter may be

disregarded; the same applies to the sphericity if the particles are very nearly spherical.

17.5 Slot-rectangular spouted beds

In order to facilitate scaleup, Mujumdar

promoted the concept of two-dimensional

spouted beds (2DSBs), in which planar symmetry replaces axial symmetry. Two facing

walls are completely vertical and parallel, whereas the other two are ver tical, with a

sloping lower section so that the gas ﬂow, which enters through an open slot at the

bottom, diverges as it rises. This geometry is shown schematically in Figure 17.3. A

“half-column” geometry is also possible,

in which one installs only one side of what

is shown. In comparison with conventional (conical-cylindrical) spouted beds, which

are limited in their volumetric processing capacity, it is stated

26,27

that the volumetric

capacity of a 2DSB can be easily increased by extending the bed thickness. As a further

advantage, it is proposed

that different ﬂow regimes can be achieved by small changes

in inlet slot width. If this geometry is adopted, it is claimed

that scaleup can be achieved

by increasing the width and/or the thickness, with or without separating walls.

The implication of referring to the planar geometry as two-dimensional is that there

would be negligible variations in the direction (referred to here as “thickness”) normal

to the column width, so scaleup could be achieved by simply increasing that dimension.

However, tests with columns of different column thickness

29,30

have shown clear three-

dimensional behavior – for instance, with two or more discrete jets or spouts forming

along the slot length. In view of this three-dimensional behavior, Freitas et al.

suggested

290 John R. Grace and C. Jim Lim

that the name “slot-rectangular spouted bed” would be more appropriate for this generic

geometry; we adopt this terminology i n the rest of this chapter.

Zhao et al.

suggest that the thickness of such columns should not be less than 5d

to avoid excessive wall effects. However, the multiple of 5 is likely applicable only

for narrow particle size distributions and smooth spherical particles in smooth-walled

vessels, as experience with ﬂuidized beds, in which particle size distributions tend to be

broader and particle shapes less regular, suggests a more conservative ratio, for example,

that the column thickness ( or other gaps) not be less than about 20 particle diameters to

prevent bridging.

A number of experimental studies have been performed on many of the same hydro-

dynamic features (e.g., minimum spouting velocity, maximum spoutable bed depth) for

slot-rectangular spouted beds, as are covered by several chapters of this book for the

more conventional cone-cylindrical spouted bed geometry. Up to eight

or nine

sep-

arate ﬂow regimes have been identiﬁed. The greater number of ﬂow regimes than for

conventional conical-cylindrical beds can be attributed to the three-dimensionality of

the geometry, as well as to the greater number of independent variables. Some hysteresis

has been observed in the ﬂow regimes, with regime boundaries differing for increasing

and decreasing ﬂow.

Hydrodynamic studies have generally shown that slot-rectangular

vessels have similar qualitative behavior to conventional cone-cylindrical columns, but it

is not possible to simply adapt relationships obtained for conical-cylindrical units to the

slot-rectangular geometry. Instead, the experimental work on slot-rectangular columns

has led to a series of separate empirical and semiempirical correlations for such proper-

ties as minimum spouting velocity, maximum spoutable bed depth, maximum pressure

drop, and ﬂow regimes, speciﬁc to the slot-rectangular geometry. These studies have been

summarized by Chen

in tabular form. The results are not summarized here because, in

the judgment of the authors, they lack generality, given the sheer number of independent

variables and the limited ranges of these covered in the reported experimental work.

Figure 17.4 shows a top view and side view of a slot at the base of a symmetrical

slot-rectangular column to deﬁne the geometry. Chen

carried out an extensive study

on the effects of slot geometry, including cases in which the slot length, η, < column

thickness, β, and conﬁgurations in which the slot length η perpendicular to the column

width is less than the slot width λ parallel to the column width, α. In all cases, the

slot was symmetrically located at the center of the column base. Chen

also tested

extensions of the slot into the windbox, where the depth, κ, was substantially greater

than the plate thickness, as well as cases in which the slots converged or diverged along

their lengths. Slots of greater κ, smaller λ, and smaller η/λ ratio provided more stable

spouts. Stable spouting could be achieved if

√

ηλ/d

≤ 21.3 and either η/λ ≤ 15 or

κ/d

≥ 25. Higher pressure drop across the slot and divergence of the ﬂow through the

slot gave more stable spouting.

Slot-rectangular columns are useful for testing multiphase CFD codes, with several

different software packages tested in this manner, giving predictions that are generally

in good agreement with experimental results.

19–25,32

Given this favorable agreement

and the difﬁculties, discussed previously in correlating results for systems with so many

Scaleup, slot-rectangular, and multiple spouting 291

η = slot

length

(a)

(b)

λ=slot width

β = column

thickness

κ = slot depth

Figure 17.4. Slot geometry and deﬁnition of dimensions: (a) plan view; (b) side view.

variables, we recommend that CFD simulations be used as a primary vehicle for scaleup

of columns of this geometry, with proper validation, whenever possible, of the particular

software in spouted beds of similar geometry.

17.6 Multiple spout geometries

Another possible way to scale up spouted beds is to provide multiple discrete entry

points for the incoming spouting gas, essentially dividing the overall system into modular

spouted beds in parallel. This is likely to involve oriﬁces of circular cross-section in a

horizontal distributor plate (as in many ﬂuidized beds), or multiple rectangular slots

in parallel. The bottom plate may be ﬂat

or dished above each oriﬁce.

2,34,37

The

multiple entry points can be fed from a common plenum chamber or “windbox,” or

each entry point may be connected separately to a common gas supply – for instance,

served by a separate pipe and control valve from a common manifold. The overall vessel

can then be rectangular with an aspect ratio of horizontal width and length of order

unity,

2,33–35

thin,

38,39

or even annular

2,40

in cross-section. Draft plates or draft tubes may

be installed above each gas-entry opening.

28,39

Gas can enter only at the major oriﬁces

or with auxiliary gas from surrounding smaller ports to provide a multiple-spout-ﬂuid

bed.

The most widely studied multiple-spout geometry is shown schematically in

Figure 17.5.

When oriﬁces are fed from a common plenum chamber, it is difﬁcult to ensure

uniformity of ﬂow through the various oriﬁces owing to instability.

30,38,41

Some of

the entry points can even become inactive, that is, with no spout above them. When

292 John R. Grace and C. Jim Lim

(a)

(b)

Figure 17.5. Geometry of a typical multiple spouted bed, adapted from Murthy and Singh

(a) plan view; (b) side view.

adjacent slots are fed from the same plenum chamber, instability is likely to occur, with

a substantial increment in ﬂow needed after each spout becomes active for the next one to

be activated. This is easily explained, as when spouting starts at one oriﬁce, its pressure

drop decreases relative to the one at which s pouting has not yet started, resulting in

more gas going to the actively spouting oriﬁce and less to the others. Ensuring a high

pressure drop through the distributor can help to prevent instabilities and keep all oriﬁces

active.

41,42

Full or partial vertical partitions may be installed at the boundaries between adjacent

geometrically similar compartments, or there may be no partitions. Vertical bafﬂes may

also be installed in multiple spouted beds to reduce short-circuiting of particles, resulting

in residence time distributions that approach those for plug ﬂow.

One of t he problems

encountered with multiple spouted beds is interference among the spouts, sometimes

even leading to their merging. Partial bafﬂes between modules that extend from the base

to the bed surf ace have not been found to be very helpful.

30,33

However, vertical plates

suspended from above, extending from approximately the top of the fountains to the top

of the dense bed, have been found

to be very helpful in isolating adjacent spouts and

fountains, while still allowing transfer of solids among adjacent modules.

When stable spouting i s achieved with multiple oriﬁces, results from single-oriﬁce

spouted beds (e.g., from Chapter 3) can usually be employed to predict the most important

spouting properties such as minimum spouting velocity and maximum spoutable bed

depth.

33,35

If the modules are rectangular or square in cross-section, then the diameter,

D, needed in the correlations can be taken to be the area-equivalent diameter of the

cross-sectional area of the module.

Another option for multiple spouted beds is to use multiple slots, rather than oriﬁces of

circular cross-section. It is then recommended

that the slots be located symmetrically

within each module, that the maximum module width be 225d

, and that the guidelines

provided in Section 17.5 be followed with respect to the length ratios for the slots.

Scaleup, slot-rectangular, and multiple spouting 293

17.7 Scaleup of spout-ﬂuid beds

Spout-ﬂuid beds have several extra degrees of freedom, compared with conventional

spouted beds and the other geometries covered in this chapter. In particular, the ratio of

auxiliary gas ﬂow to primary (central oriﬁce) gas ﬂow can be varied, and there are many

different possible conﬁgurations for the delivery of the auxiliary gas. As spout-ﬂuid beds

are covered in detail in Chapter 6, they are not dealt with explicitly here, except to note

that the methodologies and many of the comments in the present chapter also apply to

the design and scaleup of spout-ﬂuid beds.

17.8 Final comments and recommendations related to scaleup

Scaleup is an area of uncertainty for spouted beds, in terms of both the changes in

behavior as equipment size is varied and how best to conﬁgure and design units for

commercial-scale operation. A number of methods are available for scaling up (or

down) spouted beds:

In some cases, such as spouted bed dryers,

speciﬁc design criteria and procedures

are available.

Building a series of columns of identical geometry, but different scale, for spouting

of the same material is quite common when scaling up ﬂuidized beds, and may prove

to be useful for some complex spouted bed processes. However, this approach does

not appear to have received much attention in the spouted bed literature.

Empirical and semiempirical correlations and simpliﬁed mechanistic hydrodynamic

models of the kind reviewed in Chapter 3, may be helpful in predicting the performance

and behavior of columns of different geometry or the effect of changes in temperature

or pressure. However, there are commonly too many variables for these correlations

to be reliable beyond the range of variables covered in deriving them.

CFD codes, discussed in detail in Chapter 4, provide potentially powerful tools for

predicting the inﬂuence of spouted bed scale, geometry, and operating conditions.

CFD is likely to be the primary tool for scaleup in the future.

Scaleup based on dimensional similitude can provide useful information on hydrody-

namics, but the number of dimensionless groups to be matched is large, so it is difﬁcult

to carry out tests in which similitude is ensured by strict adherence to matching of

all important independent dimensionless groups. The task of matching is even more

difﬁcult if other variables, such as those related to heat transfer and chemical reaction,

are also important in the particular application.

Multioriﬁce spouted beds can be used to provide scaleup. However, instabilities and

interference between adjacent spouts can lead to serious operability issues. Although

these can be alleviated by high-pressure-drop distributors or separate control valves

to each gas-entry point, such measures add to the operating and capital cost of the

equipment.

294 John R. Grace and C. Jim Lim

Slot-rectangular units, with or without bafﬂe plates and auxiliary ﬂuidizing gas, pro-

vide alternative geometries to the conventional cone-cylinder spouted bed geometry,

which may be helpful in designing larger units. The two-dimensional approach,

whereby scaleup would be achieved by simply extending the thickness of a thin planar

column, is oversimpliﬁed, as signiﬁcant three-dimensional effects become evident as

the thickness of slot-rectangular columns is varied. Suspended vertical bafﬂes separat-

ing adjacent units appear to be useful to prevent instabilities while retaining simplicity

of design and the ability of particles to transfer between adjacent compartments.

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