Solids Mixing

\ 5.1 1NTRODUITlON

part~miXing is' of importance in the design of both batch and continuous fluidized beds. For example, the axial and radial transport of solids within the bed can influence:

(a) Gas-solid contacting

(b) Thermal gradients between a reaction zone and the zone in which heat transfer surfaces are located

(d) The position and number of solids feed and withdrawal points (e) The presence and extent of dead zones at distributor level.

Problems of mixing in fluid beds fall into four categories:

1. Particles have uniform size and density.

2. Particles have uniform size but variable density.

3. Particles are all of same density but vary in size.

4. Particles vary in both size and density, e.g. small/heavy - large/light;

small/light - large/heavy.

In category 1 the main problem, generally, is to ensure that the overall solids transport or circulation flux is high enough to eliminate temperature gradients; in categories 2,3, and 4 an additional concern is whether the local composition of the powder - however defined - is everywhere equal to the overall average. The amount of solids circulation and degree of local mixing or segregation is primarily determined by the gas velocity, but particle shape,

size, density, stickiness, and size distribution all playa part. Bed and column geometry can also be important.

Although mechanisms of mixing are now better understood, there is still much to be learnt and experimentation is essential.

5.2.1 Experimental Methods

A selection of the most frequently used methods is listed in Table 13.5 of Chapter 13. None is entirely satisfactory; they either make use of indirect measurements (e.g. heat transfer) from which circulation has to be inferred or involve the use of tracers in batch experiments or in artificial systems such as two-dimensional beds. There is a great need for a reliable on-line technique so that mixing can be monitored continuously. 'Freezing' the bed is the most tedious but simplest technique and is often used. In one version a layer of tracer is positioned in the bed, the gas flow is turned on for a given time, then suddenly shut off, and the bed removed a section at a time. In another, a tracer is released into an already fluidized bed and the bed shut down after a specified elapsed time.

Where the process demands that solids are fed and removed continuously it is often important to know the residence time distribution (RID); experi-mental techniques to determine RID are generally more straightforward and depend on taking continuous samples of magnetic, chemically active, or radioactive tracers.

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5.2.2 Bubble-Induced Particle Mixing and Circulation

It is well known that vertical,mixing in fluidized beds is many times faster than lateral mixing. Indeed it seems likely that solids move in a net horizontal direction largely by being (a) carried up to the surface where they are dispersed sideways by bursting bubbles and (b) carried down to, and across, the distributor by bubble-free flows of dense phase material.

Much of the early work on mixing mechanisms was done by Rowe and Partridge (1962, 1965). Layers of coloured and colourless particles were disturbed by injected bubbles and photographed in two-dimensional beds:

These studies showed that in an idealized case, particles are carried upwards in the wake of the bubble (defined as the solids occupying the bottom of the completed sphere) and in the ^drift (defined as the region behind the completed sphere) (see Figs 5.1 and 5.2). Particles appear to be pulled into the wake or drift, carried up the bed for a distance, and then shed. Thus, particles travel upwards where there are bubbles and, by continuity, downwards where there are not.

original tracer level

"- --~

^//

:'~"'\

""-:f":

Mfl~dl

···_~····,:t...···

"o.,'t'"

;. ~ ',!

~jltil

(0) Colourless solid (b) Coloured solid

··..···~r··..···

~L "

l.~

Figure 5.2 Displacement and mixing of solids by a rising bubble (Rowe and Partridge, 1962).

In freely bubbling beds non-uniform bubble distribution patterns become established because of the directional probability of bubble coalescence (Geldart and Kelsey, 1968; Grace and Harrison, 1969; Whitehead, Gartside, and Dent, 1976). Areas near the wall are almost bubble free. Bubbles which are initiated close to the wall at the distributor are attracted towards other bubbles near the centre but can themselves attract only a limited number; the probability of a bubble moving into the centre of the bed is therefore high, and of a bubble moving towards the wall, low. As a consequence of there being fewer bubbles close to the wall, there is a predominantly downward flow of particles close to the wall. Once established, this return flow of solids tends to maintain the tendency for bubbles to move inwards from the walls (Rowe and Everett, 1972). Both these factors are largely responsible for the characteristic bubble flow profile found in studies of bubble distribution (Werther and Molerus, 1973; Whitehead, Gartside, and Dent, 1977;

Whitehead and Young, 1967; (see also Fig. 4.7 in Chapter 4).

The apparently random movement of individual particles within a fluidized bed, as shown in tracks of radioactive tracer particles, led a number of authors (May, 1959; Lewis, Gililand and Girouard. 1961/62; Kondukov, 1964;'de Groot, 1967;Miyauchi, Kaji, and Saito, 1968)to express mixingdata in terms of a radial and axial dispersion (diffusion) coefficient obtained by fitting experimental results to the diffusion differential equation under specific boundary conditions.

However, due largely to the wide scatter in experimental values and the lack of correlation in terms of the bubbling phenomenon, this approach has been abandoned for some time.

Having noticed that most of the earlier work was carried out in the slugging mode (which is anyway easier to characterize than the freely bubbling mode), Thiel and others (Thiel and Potter, 1978) fitted the results of th~ir own and earlier work in terms of a diffusive mixing model for slugging beds. Although the model relates the diffusion coefficient to actual slugging parameters and achieves a reasonable agreement, its use is limited since slugging beds are of little or no industrial importance except in pilot plant work.

5.3 VARIABLES WHICH INFLUENCE SOUDS CIRCULATION Whitehead and others (Whitehead, Gartside, and Dent, 1976, 1977;

Whitehead and Dent, 1978) studied the circulation patterns of solids in large fluidized beds and reported them in a series of papers. The solids used were largely in Geldart's group B. Their results and those of other workers are summarized below:

(a) In a bed 1.22 m square by about 1.5 m deep, sand was fluidized at velocities up to 0.3^mls (see Fig. 5.3). At low velocities bubble-rich

Bubble-lean regions

I

00 00

00 00 o

Figure 5.3 Effect of gas velocity on circulation patterns in a 1.22 x 1.22 m bed of group B sand (Whitehead et ai" 1977).

areas occurret\, near the corners leaving bubble-free regions close to the walls and in the centre. Solids were carried upwards with bubbles and moved downwards elsewhere. At higher velocities the bubble-rich regions increased in size at the expense of the bubble-free regions; at still higher velocities the pattern changed entirely to upflow in the centre and downflow at the walls.

(b) In shallow beds ^(HID <0.5), at most velocities the predominant flow pattern is as shown in Fig. 5A(a) with the central solids downflow deflecting bubbles towards the walls. In deep beds(HID> 1) the flow pattern in the distributor region resembles that in a shallow bed but changes into a central upflow-wall downflow pattern higher up (Fig.

5Ab). The relative size of the regions is a function of gas velocity, with the 'shallow bed' zone becoming smaller as U - Umf increases.

(c) At equal excess gas velocities, the flow patterns and solids downflow velocities are similar in different sizes of bed having the same aspect ratio ^(HID). This has been explained by Geldart (1980)as follows: The ratio of bubble size at the surface divided by the bed diameter (deq,/D) is approximately the same for different bed sizes at equal

'"

^II

tI tI

~L1J

~ ~

o t

~ ~ Q

+ t:J.

.~ )°1

(d) The solids flow is not easily changed from its 'natural' circulation pattern, though gross deliberate 'mal-distribution' at the distributor can be effective in shallow beds (Fig. 5.4c).

(e) The presence of tubes or baffles modifies the flow patterns shown:

with vertical tubes radial mixing is reduced slightly; with horizontal tubes, depending on the fraction of the cross-section occupied, vertical mixing can be inhibited to the point where the bed effectively becomes staged.

(f) Flow patterns can be time-dependent and cyclic, with changes occurring over several minutes.

(g) In group A powders bubble sizes and velocities are limited by the properties of the powder and gas (see Chapter 4, Section 4.2.3). Also, because the dense phase has a low effective viscosity, circulation velocities are similar to or higher than the isolated bubble velocities, and the absolute bubble velocities, ^UA, turn out to be relatively independent of bubble size.

Figure 5.4 Solids circulation patterns in beds having different aspect ratios and distributors at approximately equal velocities (after Whitehead and Dent, 1982).

values of HID and U - Urnf• This is likely to give rise to similar circulation patterns because solids are transferred laterally from bubble-rich regions to the downward-moving dense phase largely by bubbles bursting at the surface and scattering the solids sideways (Fig.

5.5).

, . 5.4.1 The Parameters

~t is evident from the foregoing that the mixing rate (J) ought to be defined in terms of the volumetric flowrate of bubbles through the bed, the amount of terial each bubble drags up with it, the velocity at which the solids rise, and the fraction of the bed consisting of bubbles. Thus:

=

visible bubble flowrate

UA =rise velocity of bubbles relative to the wall

=

the fraction of bed consisting of bubbles

Parameter f3

Rowe and Partridge (1962) showed that the amount of solids travelling in the the bubble wake Vw, expressed as a fraction of the bubble volume Vh, decreases with increasing particle size. Baeyens and Geldart (1973) studied the fraction of the solids in the driftf3d, defined as volume of the drift divided by bubble volume, and found that this also decreases with increasing particle

Figure 5.5 Beds containing the same powder, operated at equal values of gas velocity and of similar aspect ratio, have similar circulation patterns.

size. Their data are shown in Table 5.1 and expressed, somewhat specu-latively, as functions of the Archimedes number in Fig. 5.6. For most group B powders /3d is larger than f3w which averages about 0.35. For group D and

Table 5.1 Wake and drift fractions (Baeyens and Geldart, 1973)

Powder f3w {3d y

Catalyst 47 0.43 1.00 1.00

Angular sand 252 0.26 0.42 0.50

470 0.20 0.28 0.25

Rounded sand 106 0.32 0.70 0.82

195 0.30 0.52 0.65

group A solids,f3w may be, respectively, 0.1 and 1. Thus, a bubble of a given volume produces a much greater degree of particle movement in, for example, a bed of cracking catalyst than in a bed of coal ash.

-- ---

--om

Parameter ^UA

Analysis of movie films of particles in two-dimensional beds (Baeyens and Geldart, 1973) showed that the particles in the wake travel at a velocity similar to that of the rising bubble while particles carried up on the drift travel on average at about 38 per cent. of the bubble velocity, ^UA, a figure later confirmed by Ohki and Shirai (1976). Equations (4.41) and (4.9) or (4.10) may be used to find ^UA'

Parameter Qb

The quantity of gas appearing as bubbles should be, according to the two-phase theory, equal to (U - Umf)A (see Section 4.5.2). It is in general less than this, and Eq. (4.38) can be rewritten:

A

Qb = Y(U - Urnf)

where Y decreases with increasing particle size. Baeyens (1981) has correlated Y speculatively with the Archimedes number in Fig. 5.7.

c---

~- • _•

0.5

•....

0.4

•

03 02

0.1

102 103

Refs. +Geldart. D. (l96B) o Werlher.J. (1975)

c Werther.J. and Molerus. D. (1972)

•• Grace. J.R. and Harrison. D. (1969)

• Everell. D.J. (1970)

v Chavarie. C. (1973) .., Geldart. D. (1970)

X Geldarl. D. and Cranlield,R.R. (1972)

• Baeyens.J. and Geldart. D. (1981)

Parameter ^Eb

The fraction of the bed consisting of bubbles can be obtained by measuring the bed expansion so that:

H - Hrnf

Alternatively, it can be predicted approximately from Eqs (4.46) and (5.2):

QJA Y(U - Urnf) Y(U - Urnf)

= --;;;:: =

^UA U - U^rnf

+

^Ub (5.4)

5.4.2 Particle Velocities

Assuming that solids move upwards in the wake and drift of bubbles, and

downwards elsewhere, a mass balance in any horizontal plane cutting the bed gives:

( ~~a~:~O:o~~sbed)x(~~~~~:rd~

=(

^~:~t~~e~: .) x (~JI~~rds) (5.5)

move down particle sohdsmove up velOCIty

velocity

1 - Eb - (f3w + f3d) Ebvp

=

^{UA f3w Eb}+0.38 UA f3d Eb (5.6) substituting for Eb from Eq. (5.4) and rearranging:

{ f3w+0.38 f3d } )

V - --- Y (U - Urnf

p - 1 - Eb - Eb(f3w + f3d)

The term within the first bracket is largely dependent on the particle properties and decreases with increasing particle size. Experimentally measured values of vp(Baeyens and Geldart, 1973) are shown in Fig. 5.8 and seen to be straight lines; separate measurements of f3 and Y, and values of

Ebcalculated from Eq. (5.4), gave good agreement with the slopes over the Vp 5

(em/s)

\

10 12

U - Umf (emIs) cracking catalyst

fine malachite sand sauthpart sand medium malachite sand caarse malachite sand

47 }Am 106pm

195 JoArn 252 I'm

470)-1m

Figure 5.8 Particle velocities at bed wall as a function of excess gas flow (Baeyens and Geldart, 1973).

velocity range covered. Local values of the particle velocity may be several times smaller or larger than the average (Nguyen, Whitehead, and Potter, 1978).

5.4.3 Circulation Flux

Equations (5.5) and (5.6) can be reformulated to give an expression for the solids circulation rate:

( ~~~Iation) =(~~~~ity) x ( ~~~c~~~~~ere) x(~e;~rdS) x (~:o~s- )

rate of dense solIdsmove solids sectIOnal

phase upwards velocity area

(5.1S) and the solids flux:

=

^{Pp (1 -} Emf) (UAf3wEb

+

0.38 UAf3dEb)

As before, substituting for ^Eb:

=

Pp (1 - Emf) (U - Urnf) Y (f3w +0.38f3d) (5.10) This can be compared with the empirical equation of Talmor and Benenati (1963) obtained in a 0.1 m diameter bed with ion exchange resin particles of 67to 660JLm:

J (kg/m²s) = 785 (U - Urnf)e-^6,630d^p (5.11) The two equations agree reasonably well for group B particles but Eq. (5.11) increasingly underestimates J for larger group D materials. In Fig 5.9 experimental values from the literature are compared with predicted values (Eq. 5.10) and reasonable agreement is obtained.

At equal values of excess gas velocity, U - Urnf, the circulation flux decreases as particle size increases; however, the circulation fluxes in beds of large particles can be made large by increasing U - Urnf•

5.4.4 Bed Turnover Time The time required to turn the bed over once is:

mass of powder in the bed M

=

^JA

Substituting for M, and for J from Eq. (5.10):

H^rnf

=

^(f3w ⁺0.38f3d) Y (U - Urnf)

Whitehead, and Potter (1978) injected CO2 gas near the bed surface and measured the concentration at 49 positions below the injection point. They used two sands having Urnf values of 2.5 and 10.7 cm/s and found that the CO2

concentration profiles reflected strongly the downflow patterns of the solids at various superficial fluidizing velocities (see Section 5.3 (a)). They maintain that for non-absorbing particles, backmixing commences when the ratio U/Urnf is about 3, and this reflects the fact that, for a given value of U - Urnf, both solids mixing and gas backmixing decreases as particle size increases.

However, in view of the wide range of values for Y, f3w, and f3d as particle size changes, it would be surprising if the critical ratio at which backmixing commences remained at 3 for all solids.

On the basis of Eq. (5.7) and the criterion that gas backmixing becomes significant when vp > Urnfi, there are grounds for believing that for group A and group D solids, the critical values of U/Urnf may be smaller and larger, respectively.

Gas backmixing is influenced considerably by the degree to which the gas is absorbed on the particles (Nguyen and Potter, 1974), and Bohle and van Swaaij (1978) showed that the mean residence of a strongly adsorbing gas (freon-12) injected into the bed can be a factor of ten longer than that for a weakly absorbing gas (helium). Thus the critical velocity ratio at which gas backmixing commences decreases as gas adsorption on the particle increases.

102 J pred (kg/m2s)

Many applications of fluidized beds involve the continuous processing of solids; e.g. the feed may be wet solids and the product dry, or the feed limestone and the product lime. In a plug flow system all particles have the same residence time tR, while in a fully mixed system the solids have a wide range of residence times; this gives a non-uniform solid product and is inefficient for the high conversion of solids. Consider a quantity of tracer particles mkg introduced instantaneously at time zero into a bed containing M kg solids when the overall feed rate isFkg/so If the bed is in plug flow, no tracer should appear at the solids offtake until the average residence time tR

has elapsed, where:

• Whitehead et al (1979) + Cranfield - Geldart (1978) t. Werther (1976)

Figure 5.9: Comparison of experimental values of mixing flux with Eq~

For a bed to which solids are continuously added and from which reacted products are removed (e.g. fluidized bed limestone calcination), the turnover time should be short compared with the solids residence time: i.e. good dispersion requires that the feed material should experience as many circulations as possible before discharge. Little research has been done on this but a ratio of residence time/turnover time of 5 to 10 seems reasonable.

If the bed is fully mixed, tracer will appear immediately in the offtake at a concentration Co

=

m/M and the concentration in the exit, C, will then fall

according to:

This is a function of the downwards velocity of the dense phase, vp' If vp

exceeds the interstitital gas velocity, UrnriEmt. then gas will be carried downwards with the solids. Working in a 1.22 m square bed, Nguyen,

C -tit

-= e ^R

110

A bed may be 'well fluidized' in the sense that all the particles are fully supported by the gas may still be segregated in the sense that the local composition does not correspond with the overall average. Defluidization can be regarded as a special case of segregation in that some or all of the bed, usually that near the distributor, may be immobile. Segregation is likely to occur when there is a substantial difference in drag/unit weight between different particles. Particles having high drag/unit weight migrate to the surface while those with low drag/unit weight migrate to the distributor.

When fluidized, the upper part of the bed will attain a fairly uniform composition, while the component that tends to sink forms a concentrated bottom layer. If the particles differ only in size, the larger particles settle to the bottom. Nienow and Rowe, who have done a considerable amount of work on segregation caused by density differences (e.g. Nienow, Rowe, and Cheung, 1978) have used the words flotsam and jetsam to describe the solids which occupy, respectively, the top and bottom of the bed. In non-technical English flotsam means 'floating wreckage' and jetsam, goods thrown out to lighten a ship and later washed ashore! A quantitative measure of segregation is required and two parameter are often used:

(a) The coefficient of segregation Csis defined as:

(XB -XT) x 100

XB +XT

where XB and XT are the concentration of the material of interest in the bottom and top halves of the bed, respectively. Clearly Cscan have values between -100 and

+

100 per cent., 0 per cent. being perfect mixing.

(b) The mixing index M1is defined as x/x, where x is the concentration of'the material under scrutiny at some level in the bed and

x

is its average concentration.

J -0 Bed size 0.61x 0.61m U-Umf (em Is) 18 25 35 Symbol 0 "" •••

Weir height =15 em

Rate of solids flow =8kg/min Mean residenCe time 7 R =2.6 min Mean particle size = 1.6 mm

Figure S.10 External age distribution of traeer solids in a fluid bed with constant solids feed - tracer added instantaneously at tflR = 0 (Cranfield, 1978)

Typical experimental data are shown in Fig. 5.10.

Similarly, the fraction of solids

f

spending less than time tin a completely

mixed bed is: ~

-f=

1 - e-^t1^tp. (5~

A significant percentage of solids (18.2 per cent.) spends less than 20 p~r cent.

of the average residence time tRin a fully mixed bed. This problem can be solved in shallow beds (

<

0.15 m) by installing vertical baffles or making the bed in the form of a long channel (see Chapter 10). Baffles are sometimes used in deeper beds but become progressively less effective in preventing short-circuiting of solids as bed depth increases. There is a need for further work on baffled deep beds.

5.7.1 Methods of Investigation

A qualitative indication of defluidization can be obtained from the bed pressure drop-gas velocity curve. Consider a bed which consists of materials likely to segregate and which is either premixed outside the bed or vigorously bubbled and then collapsed rapidly. If the gas velocity is gradually increased,

In document Gas Fluidization Technology (Page 52-65)

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