gas distributor and plenum design in fluidized beds

6

Gas Distributor and Plenum Design in Fluidized Beds

S. B. Reddy Karri

Particulate Solid Research, Inc., Chicago, Illinois, U.S.A.

Joachim Werther

Technical University Hamburg-Harburg, Hamburg, Germany

1 INTRODUCTION

The gas distributor (also called a grid) in a fluidizedbed reactor is intended to induce a uniform and stablefluidization across the entire bed cross section, preventnonfluidized regions on the grid, operate for long per-iods (years) without plugging or breaking, minimizeweepage of solids into the plenum beneath the grid,minimize attrition of the bed material, and supportthe weight of the bed material during startup and shut-down. In practice, grids have taken a variety of forms,a few of which are discussed in subsequent pages.Whatever the physical form, all are fundamentallyclassifiable in terms of the direction of gas entry:upward, laterally, or downward. The choice dependson prevailing process conditions, mechanical feasibil-ity, and cost. In the past, grid design has been more ofan art than a science. However, more recent studiesnow allow grid design based on scientific principles.

2 TYPES OF GRIDS

2.1 Perforated Plates (Upwardly Directed Flow)

Main Advantages

Simple fabrication; most common; inexpensive; easy tomodify hole size; easy to scale up or down; easy to

clean can be flat, concave, convex, or double dished;ports are easily shrouded.

Possible Disadvantages

Bed weepage to plenum; can be subject to buckling orthermal distortion; requires peripheral seal to vesselshell; requires support over long spans; high pressuredrop required if weepage during operation is to beminimized

2.2 Bubble Caps and Nozzles (Laterally Directed

Flow)

Main Advantages

Depending on the design, weeping is reduced or totallyavoided; good turndown ratio; can incorporate caps asstiffening members; can support internals.

Copyright © 2003 by Taylor & Francis Group LLC


Expensive; difficult to avoid stagnant regions; moresubject to immediate bubble merger; difficult toclean; difficult to modify; not advisable for stickysolids; requires peripheral seal; ports not easilyshrouded.

Details of some nozzles that are currently used incirculating fluidized beds (CFB) combustors are shownin Fig. 1 (VGB, 1994). There are significant differencesbetween bubble caps (No. 7 in Fig. 1) and nozzles (No.1 in Fig. 1) with respect to the prevention of solidsback flow: in the case of nozzles, the high velocity ofthe gas jet prevents the solids from flowing back intothe wind box. On the other hand, in the case of thebubble cap design, the gas flowing out of the bubblecap into the bed has a rather low velocity. In this case,the backflow of solids is avoided by letting the gas flowdownward from the holes in the inner tube to the lower

edge of the cap. The separation distance sbc is respon-sible for the sealing effect of the bubble cap.

2.3 Sparger (Laterally or Downwardly Directed

Flow)

Main Advantages

Can minimize weeping; good turndown ratio; low pres-sure drop; can support internals; can undergo thermalexpansion without damage; ports are easily shrouded;well suited to multilevel fluid injection; solids can flowfrom above the grid to below.


Defluidized solids beneath the grid; can be a lessforgiving mechanical design.

Figure 1 Distributors and nozzles used in large circulating fluidized bed combustors. (After VGB, 1994.)


2.4 Conical Grids (Laterally Directed Flow)

Main Advantages

Promotes solid mixing; prevents stagnant solidsbuildup; minimizes solids segregation. Facilitates theeasy discharge of solids.


Difficult to construct; requires careful design to ensuregood gas distribution; requires high pressure drop forgood gas distribution.

2.5 Pierced Sheet Grids (Laterally Directed Flow)

Produced by punching holes in a relatively thin plate.Holes are of a semielliptical shape with slanting,strongly conical openings in the direction of entry. Itis primarily used in fluid bed drying applications.Holes can be oriented in such a way to promote certainmixing patterns or drive the solids toward dischargenozzle.

Main Advantages

Promotes solid mixing; prevents stagnant solidsbuildup. Facilitates discharge of most of the solids.The holes are angled so that the grids can be non-weeping for coarse solids.


Difficult to construct, facilitates only small hole sizes,requires reinforcement underneath the sheet to supportthe bed.

Among the foregoing advantages and limitations,the designer must select those most pertinent or criticalto the process application. There are, for example,instances in which solids below the grid level are toler-able, where grid thermal expansion is significant,where bed solids are very friable, where pressuredrop, and therefore the cost of compressive horse-power, is critical, where solids are ‘‘sticky’’ and mustbe kept in motion throughout, where internal impellersor stirrers must be provided, or where grids areexpected to have a short life due to corrosion. Theseand many other specifics have dictated a host of designvariations, some of which are illustrated below. Itshould be emphasized that each application requiresthoughtful engineering consideration before finaldesign selection.

3 GRID DESIGN CRITERIA

3.1 Jet Penetration

Gas flowing from the grid holes can take the form ofeither a series of bubbles or a permanent jet, dependingon system parameters and operating conditions.However, a permanent jet prevails for most industrialconditions. Jet penetration is one of the most impor-tant design parameters since it helps in

1. Determining how far to keep the bed internals,such as feed nozzles, heat exchanger tubes, etc.,away from the grid to minimize erosion ofinternals.

2. Deciding on grid design parameters such ashole size and the gas jet velocity required toachieve a certain jetting region.

3. Minimizing or maximizing particle attrition atgrids.

Knowlton and Hirsan (1980) reported that the jetpenetration for upwardly directed jets fluctuatedgreatly. Karri (1990) noted that jet penetration canvary as much as 30% for upwardly directed jets.However, the jet emanating from a downwardly direc-ted grid hole is stable, and its penetration length doesnot significantly fluctuate with time. Figure 2 indicatesjet penetration configurations for jets orientedupwardly, horizontally, and downwardly. According


to Karri, the jet penetrations for various orientationscan be approximately related by:

Lup � 2Lhor � 3Ldown ð1Þ

There are numerous jet penetration correlations (Zenz,1969; Shakhova, 1968; Merry, 1971; Yang andKeairns, 1979; Knowlton and Hirsan, 1980; Yates etal., 1986; Blake et al., 1990; Roach, 1993) in the litera-ture. Massimilla (1985) and Karri (1990) have shownthat the jet penetrations predicted by these correlationscan vary by a factor of 100 or more. Among them,Merry’s correlation for horizontal jets was shown(Karri, 1990; Chen and Weinstein, 1993; Roach,1993) to give reliable predictions, although this corre-lation was derived for horizontal jets issuing into anincipiently fluidized bed, which is not exactly the samesituation as for a grid jet. Merry’s correlation to calcu-late the penetration of horizontal jets is

Lhor

dh¼ 5:25

rg;hU2h

rpð1� emf Þgdp

!0:4rg;brp

!0:2dp

dh

� �0:2

ð2Þ

The jet penetration lengths for upwardly and down-wardly directed jets can be calculated from Eq. (1).These equations take into account the effects of pres-sure and temperature on jet penetration. Knowltonand Hirsan (1980) and Yates et al. (1986) found thatthe jet penetration increases significantly with systempressure. In addition, Findlay and Knowlton (1985)found that the jet penetration decreases with increasingsystem temperature. Bed internals should not be placed

in the jetting zone near the grid, otherwise the internalscould be severely eroded.

3.2 Grid Pressure Drop Criteria

For a grid, achieving equal distribution of gas flowthrough many parallel paths requires equal resistancesand sufficient resistance to equal or exceed the maxi-mum value of any unsteady state pressure fluctuation.It has been determined experimentally that the ‘‘head’’of solids in some fluidized beds above an upwardlydirected grid port can vary momentarily by as muchas 30%. This is due to large fluctuations in the jetpenetration for an upwardly directed jet, as discussedin the previous section. The equivalent variation down-stream of a downwardly directed port is less than 10%.Thus as a rule of thumb, the criteria for good gasdistribution based on the direction of gas entry are(Karri, 1990):

1. For upwardly and laterally directed flow:

�Pgrid � 0:3�Pbed ð3Þ2. For downwardly directed flow

�Pgrid � 0:1�Pbed ð4Þ

and

3. Under no circumstances should the pressuredrop across a large-scale commercial grid beless than 2500 Pa, i.e.,

�Pgrid � 2; 500 Pa ð5Þ

Figure 2 Jet penetrations at grid holes for different orientations.


Several investigators (Hiby, 1964; Zuiderweg, 1967;Whitehead, 1971; Siegel, 1976; Mori and Moriyama,1978) have found the ratio of distributor pressure dropto bed pressure drop to be in the range of 0.015 to 0.4.

If turndown is desired, the grid pressure dropcriteria (Eqs. 3 and 4) should apply at the minimumgas flow rate. This can be a problem for circulatingfluidized bed combustors, since this means that underfull load the grid pressure drop will be unacceptablyhigh. Also, if the grid is curved, i.e., concave, convex,or conical, the criterion must apply with respect to thelowest hole on the grid. Take an example of a fluid bedwith curved grid, as shown in Fig. 3.

A pressure balance across the curved grid can bewritten as

�Ph (Highest holeÞ ¼ �Ph (Lowest hole)

þ rB g ðHhigh �HlowÞð6Þ

i.e.,

�Ph (Highest holeÞ ¼ �Ph (Lowest holeÞþ 480� 9:8� 0:9

¼ �Ph (Lowest holeÞ þ 4235 Pa

ð7Þ

Therefore the lowest grid hole has the lowest pressuredrop, and hence the pressure drop criterion must applywith respect to the lowest hole on the grid.

3.3 Design Equations

The following equations can be used to design perfo-rated plates, spargers, and bubble cap types of grids:

Pressure drop across the grid:

�Pgrid ¼ KgrBLB �Pgrid � 2; 500 Pa ð8Þ

where K ¼ 0:3 for upward and lateral gas entry and 0.1for downward gas entry.

The gas velocity through the grid hole (orifice equa-tion):

Uh ¼ Cd

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�Pgrid

rg;h

sð9Þ

The orifice discharge coefficient, Cd, is typically about0.6 for gas flowing through an orifice in a pipe (for aratio of orifice diameter to pipe diameter in the rangeof 0 to 0.2). This value of the orifice coefficient is for asharp-edged orifice. However, grids are not sharpedged, and the orifice coefficient is then greater than0.6. A typical value of Cd for a grid hole is about 0.8.Actually, the value of Cd depends on the grid platethickness and the hole pitch. It can be calculatedfrom Fig. 4 (Karri, 1991).

Volumetric flow rate of gas:

Q ¼ Npd2

h

4Uh ð10Þ

Figure 3 A typical fluid bed showing a curved perforated plate.


3.3.1 Hole Size

To increase the gas residence time in the bed, it isdesirable to introduce the greatest number of smallgas bubbles as possible into the bed. This can beachieved by maximizing N at the expense of dh inEq. (10) (within the limits of mechanical, cost, andscaleup constraints). To minimize stagnant zones, the

number of grid holes per m2 should be � 10. In prac-tice, the number of grid holes per square meter shouldbe greater than 20.

3.3.2 Hole Layout

To increase the uniformity of fluidization, it is com-mon to lay out the holes in triangular or square pitch,as shown in Fig. 5. All the holes in a grid with trian-gular pitch are equidistant. This is not the case for agrid with square pitch. Triangular pitch will also resultin more holes per unit area.

The relationship between the grid hole pitch, Lh,and the number hole density (holes per unit area ofthe bed), Nd, depends on whether the holes are laidout in triangular or square pitch.

3.4 Additional Criteria for Sparger Grids

Additional distribution criteria are used for spargergrids. To keep the pipe header pressure drop downto acceptable levels and to ensure good gas distribu-tion, the following criteria (Karri, 1990) should be met:

1. The manifold should be sized based on thefollowing equation:

D2m

Nhd2h

!2

> 5 ð11Þ

Figure 4 Grid hole discharge coefficient design chart.

Figure 5 The relationship between hole density and grid hole pitch for both triangular and square pitch.


The parameters in Eq. (11) are defined in Fig.6. Eq. (11) ensures that the pressure drop in themanifold is negligible compared to the pressuredrop in the holes, which are determining thegrid pressure drop.

Similarly, the main header pipe should besized based on the equation

D2head

NmD2m

!2

> 5 ð12Þ

2. In some instances, two to three different holesize are used on a given manifold to get bettergas distribution.

3. The gas velocity in the header/manifold pipeshould be < 25m=s for best distribution.

4. Holes should not be located closer than oneDm from any sharp bend or tee in theheader/manifold to prevent solids from beingsucked into the manifolds due to the venacontracta effect.

3.5 Port Shrouding or Nozzle Sizing

Shrouds are generally placed around grid holes toreduce the velocity at the gas–solid interface andreduce particle attrition (de Vries et al., 1972).Shrouds simply consist of short pipes centered overthe smaller grid holes that have been selected in sizeand number to operate at a hole velocity defined byEq. (9).

To be effective, shrouds must be long enough to‘‘contain’’ the expanding (11� included angle) gas jetleaving the grid orifice (Karri, 1991).

As can be seen from Fig. 7, the minimum shroudlength should be:

Lmin ¼ Ds � dh2 tan 5:5�

ð13Þ

In practice, it is prudent to increase Lmin by a factor of50 to 100%. A shroud length less than Lmin causessignificantly more erosion and attrition than no shroudat all. Significant attrition can also occur if the shroudis not centered over the smaller hole.

The nozzle or shroud details inside a sparger pipegrid are illustrated in Fig. 8.

If properly sized and installed, particle attrition isreduced by a factor (Karri, 1990) calculated from

particle attrition without shrouds

particle attrition with shrouds¼ Ds

dh

� �1:6

ð14Þ

4 PARTICLE ATTRITION AT GRIDS

Solids immediately surrounding the gas jets issuingfrom the grid are ingested into the jets. These particlesare accelerated and collide with the particles near thetip of the jet. Figure 9 depicts how the particlesare picked up and slammed into a fluidized, yieldingbed for an upwardly directed jet. However, downward-pointing jets generally issue into a nonfluidized area ofparticles. Therefore particles picked up by downwardlydirected jets, issuing into a nonyielding unaerated bed,result in a greater degree of particle attrition than thosefor upwardly directed jets. Karri (1990) reported thatdownwardly directed jets have approximately twice thesteady-state attrition rate as that of upwardly directedjets. The attrition rates for upwardly and laterallydirected jets are essentially the same. Grid jet attritionis discussed in greater detail in Chapter 8 of this book.

5 EROSION

5.1 Erosion at Bed Walls and Internals

Erosion in the grid region is primarily due to high-velocity submerged jets impinging on distributorparts, bed walls, or bed internals. Therefore one shouldestimate the jet penetration heights for a given griddesign and check for the following:

1. Bed internals should not be placed in the jet-ting zone near the grid, otherwise the internalscould be severely eroded.

Figure 6 Manifold sparger grid showing the definitions of

various parameters.


2. Nozzles should not be located any closer thanhalf the jet penetration height from the bedwall.

The basic equation for erosion rate is of the form(Karri, 1990)

Erosion / Ker2g;hU

3hd

2hd

3pr

2p

’ð15Þ

5.2 Erosion at Distributor Nozzles

Erosion in the nozzle or orifices is often associated withweepage of solids. This can be avoided by carefully

designing a grid with the proper pressure drop criteria,as presented in Sec. 3.2. Poorly designed bubble capstend to have erosion problems due to the secondarycirculation of solids. Therefore bubble caps should bedesigned to minimize secondary circulation of solids.

Erosion has often been experienced at the nozzlesused in CFB combustors (Fig. 1). A dominant mechan-ism leading to erosion is the pressure-induced gas flowreversal that will be discussed below in Sec. 6. Solidswhich have entered into the nozzle during a period offlow reversal are entrained out once the gas flows athigh velocity in the outward direction again. Theentrained solids in the high-velocity flow in the nozzlehole may cause severe erosion of the wall of the hole. A

Figure 7 (a) Diverging free jet; (b) shroud too short to contain the jet; (c) minimum shroud length required to contain jet.

Figure 8 Shroud design for a sparger grid.


second mechanism of erosion was observed by high-speed video in cold models (Hartge and Werther,1998): even when the gas was flowing out of the holeinto the bed, a region near the mouth of the orificecould be observed where the gas jet entrained particlesinto the hole. These entrained particles caused erosionat the outer edge of the hole. Figure 10 shows thephotography of a nozzle that had been painted inblack before the experiment. After 60 hours of opera-tion, the erosion marks were clearly visible. They wereparticularly obvious at the lower edges of the holes,which is due to the fact that the jet issuing from ahorizontal bore tends to bend into the upward direc-tion (see Fig. 2), which gives more surface area toentrain solids at the lower edge of the hole.

6 WEEPAGE OF SOLIDS

Solids weepage has been a major problem during thedevelopment of circulating fluidized bed (CFB)combustors in the past two decades. Seemingly well-designed nozzle grids experienced weepage to such anextent that CFB boilers had to be shut down afterseveral days or weeks of operation, because most ofthe bed inventory had wept through the grid. Morerecent investigations (Hartge and Werther, 1998;Karri, 1991) have revealed that pressure fluctuationsin the dense bottom bed of the CFB riser may causethe backflow of solids through the grid hole. Figure 11

shows measurements of the pressure drop between thewind box and at a height of 0.3m above the distributorin a circulating fluidized bed. The average pressuredrop of gas distributor and bed was about 40mbarduring these measurements. As can be seen, sometimesnegative pressure drops occurred, i.e., the pressure at aheight of 0.3m above the distributor was higher than

Figure 9 The mechanism of particle attrition at a sub-

merged jet.

Figure 10 Erosion marks around the gas outlet holes of

the nozzle with 5mm diameter holes. (From Hartge and

Werther, 1998.)

Figure 11 Pressure flucutations measured in a circulating

fluidized bed between the windbox and at a height of 0.3m

above the distributor (riser diameter, 0.4m; superficial gas

velocity, 3m/s; solids mass flux, 22 kg/m2s).


the pressure below the distributor. In such cases, gasflow reversal occurs, which results in weepage of solidsinto the nozzles (Fig. 12).

In order to prevent such a flow reversal, the designpressure drop of the nozzle in the example of Fig. 11should be roughly 20mbar larger, i.e., the pressuredrop of the grid has to take into account the largestpossible pressure fluctuations. These pressure dropfluctuations are significantly higher for Group B par-ticles with a wide particle size distribution which aretypical of CFB combustion. Another reason thatmakes it difficult to keep the grid pressure drop alwayshigher than the largest pressure fluctuations in the bedis the necessity of frequent turndown operations forCFB combustors. Reducing the load to 50% means areduction of the grid pressure drop to 25% of its valueat full load. In CFB combustion, the bubble cap designof Fig. 1 (case 7) has shown to be more effective. Herethe solids have to be transported upwards in the annu-lus between the bubble cap and central tube againstgravity during the gas flow reversal. The solids areprevented from entering the central tube if the separa-tion length sbc is kept between 70 and 100mm. Figure13 shows solids inflow during the period of gas flowreversal.

7 EFFECTS OF TEMPERATURE AND

PRESSURE

System temperature and pressure affect the momentumof grid jets via the gas density. The momentum of thegas jets is proportional to rg;hUh. When the tempera-

ture is increased, the gas density decreases. For thesame gas jet velocity, this decreases the momentumof the jets and therefore decreases the jet penetrationand the attrition at the grid. Similarly, when systempressure is increased, gas density increases, gas jetmomentum increases, and therefore the jet penetrationand the attrition at the grid are increased.

8 PLENUM DESIGN

The plenum, or windbox, is the chamber immediatelybelow the grid. If the bed-pressure-drop-to-grid-pressure-drop ratio is high enough, the plenum designwill probably not be too important. However, for thecase where this ratio is low, the plenum design maydetermine whether the bed will operate satisfactorily.

The typical plenum designs showing various config-urations for introducing gas into the plenum areillustrated in Fig. 14. Common sense dictates that cer-tain plenum designs be preferred over others. If the gasenters the plenum from the bottom it is preferable thatthe plenum have a large enough distance between theoutlet of the supply pipe and the grid to prevent the gasfrom preferentially passing through the middle of thegrid. When gas enters a plenum from the side, it ispreferable to rout the gas to the middle of the plenum(Fig. 14c) rather than have the supply pipe end at thewall of the plenum. In addition, horizontal-to-verticaldown gas entry (Fig. 14c) is preferable over thehorizontal-to-vertical up gas entry (Fig. 14b).

If the gas–solid or gas–liquid suspension needs to beintroduced into the plenum, as for example in a poly-ethylene reactor and some FCC regenerators, it is

Figure 12 Solids flowing into the nozzle shaft during gas

flow reversal.

Figure 13 Solids flowing into the cap during gas flow rever-

sal.


preferable to introduce the suspension at the lowestpoint of the plenum (Fig. 14a,d,e) to minimize theaccumulation of solids or liquids in the regions in-accessible to reentrainment For two-phase systems, itis preferable to have some sort of deflection device(Fig. 14d,e,f) between the outlet of the supply pipeand the grid to prevent the solids from preferentiallypassing through the middle of the grid due to their highmomentum. This preferential bypassing of solidscauses maldistribution of gas. In addition, the config-uration of Figs. 14e and 14f are preferable over theconfigurations of Figs. 14a,d.

9 POWER CONSUMPTION

Since the grid contributed a considerable fraction oftotal pressure drop across a given fluid bed system, itis always important to estimate the power consump-tion of the blower that drives the gas through thissystem. Suppose a stream of gas is to be compressedfrom an initial pressure of P1 to a higher pressure of P2

to pump it through the entire fluid-bed system. Usingthermodynamics for adiabatic reversible compressionwith negligible kinetic and potential energy effects, the

ideal shaft work to compress each kilogram of gas isgiven by

�Ws;ideal ¼ðP2

P1

dP

rgð16Þ

If an ideal gas behavior is assumed, then Eq. (16) trans-forms into

�Ws;ideal ¼g

g� 1P1Q1

P2

P1

� �ðg�1Þ=g�1

" #ð17Þ

or

�Ws;ideal ¼g

g� 1P2Q2 1� P1

P2

� �ðg�1Þ=g" #ð18Þ

Due to heat of compression, the raise in temperaturecan be calculated from

T2 ¼ T1

P2

P1

� �ðg�1Þ=gð19Þ

where g ¼ ratio of specific heats of gas ffi 1:67, 1.4, and1.33 for monatomic, diatomic, and triatomic gases,respectively.

Figure 14 Different plenum configurations.


However, for real operations with its frictionallosses, the actual work required is always greaterthan the ideal and is given by

Ws;actual ¼Ws;actual

Zð20Þ

where Z is the blower efficiency, approximately givenby

Z ¼ 0:55–0.75 for a turboblower¼ 0:6–0.8 for a roots blower¼ 0:8–0.9 for an axial blower or a two-

stage reciprocating compressor

Equation (20) can be used not only for power con-sumption but also to size the correct horse powermotor to drive the blower.

The actual temperature of gas leaving a well-insu-lated (adiabatic) but not 100% efficient compressor isthen calculated from

T2 ¼ T1 þT1

Z1

P2

P1

� �ðg�1Þ=g�1

" #ð21Þ

10 DESIGN EXAMPLES

10.1 FCC Grid Design

Example 1. A 13-m-ID bed of FCC catalyst(dp ¼ 60 mm) 3m deep is to operate at a superficialgas velocity of 0.6m/s. The bed density is 480 kg=m3.the density of the gas entering the bed is 0:64 kg=m3.Design the following grid types: (1) a flat perforatedplate, and (2) concentric-ring type downflow sparger.Assume the grid thickness to be 0.025m.

Solution. Perforated Plate Design

Determine �Pbed and �Pgrid:

�Pbed ¼ grBLB ¼ 9:8� 480� 3 ¼ 14,112 Pa

Choose �Pgrid to be 30% of �Pbed

�Pgrid ¼ 0:3 �Pbed ¼ 4,234 Pa

Determine the gas velocity through the grid holes(assume a typical value for cd ffi 0:77):

Uh ¼ Cd


rg;h

s¼ 0:77

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� 4234

0:64

r¼ 88:6m=s

Determine the volumetric gas flow rate at the con-ditions below the grid. For this example, assumethat the temperature of the gas below the grid is

the same as in the bed. This may not be the casein an actual plant.

Q ¼ Usup

pD2

4¼ 0:6

pð13Þ24

¼ 79:6m3=s

Determine the number of grid holes required:

Since Q ¼ Nd2h4Uh

Therefore

N ¼ Q

Uh

1

pd2h=4

¼ 79:6

88:6

1

pd2h=4

¼ 1:14

d2h

The hole density is

Nd ¼ N

ðp=4ÞD2¼ 1:14

d2h

1

ðp=4Þð13Þ2 ¼0:0086

d2h

Determine the hole pitch for a triangular arrange-ment:

Lh ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNd sin 60

�p ¼ 11:59 dh

Downwardly Directed Gas Sparger Design

Choose �Pgrid to be 10% of �Pbed

�Pgrid ¼ 0:1�Pbed ¼ 1,411 Pa ¼ 14:4 cmH2O

1411 Pa is less than the minimum of 2500 Pa �Prequired for a grid. Therefore use �Pgrid ¼2500 Pa.

Uh ¼ 0:77

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� 2500

0:64

r¼ 68m=s

N ¼ 79:6

68

1

pd2h=4

¼ 1:5

d2h

Various combinations of N and dh satisfy the pres-sure drop requirements for the two grid type asshown in the table:

To proceed with the design, it is necessary to select ahole size (judgment call). For the purpose of this

dhNumber of holes (N)

m perforated plate downflow sparger

0.005 45,600 60,000

0.01 11,400 15,000

0.025 1,824 2,400

0.05 456 600


example, a hole size of 0.025m will be chosen tocompare the different grid types. This hole dia-meter does not result in an excessive number ofholes for both types of grids.

Check the value for Cd for the perforated plate:

Nd ¼ 13:8 holes=m2 and Lh ¼ 0:29m

t

dh¼ 0:025

0:025¼ 1

From Fig. 3

Cd

Lh

dh

� �0:1

¼ 0:96

Cd ¼ 0:960:025

0:29

� �0:1

¼ 0:75 vs. 0.77 (initial guessÞ

There is a fairly good agreement between the initialand calculated values for Cd. If not, one mustrepeat the calculations using the calculated Cd

until both values agree.Therefore, for a 0.025 m hole diameter, the

perforated plate has 1,824 holes arranged in atriangular pitch of 0.29 m. The hole density is13:8 hole=m2.

For the sparger grids, it remains to determine thesparger configuration and pipe-header size. Pipeheaders can be laid out in various configurations.The design calculations will depend on the con-figuration one chooses.

Concentric-Ring Sparger. Consider for example,a configuration of four concentric rings of 0.4 m dia-meter supplied by a number of gas entry points.

This design results in 2,401 holes.

Determine the hole pitch:

Lh ¼ 97:13

2401¼ 0:04m

To determine the header-pipe size, first determinethe maximum number of holes in ring sectionsupplied by a single effective entry of gas. If out-ermost ring is supplied by four gas entry points,then the number of effective gas entry points is 8,and the number of holes in each section of ringNo. 4 would be Nh ¼ 978=8 ¼ 122. Then Eq. 11gives

D2head

Nhd2h

!2

> 5

D2head

122� 0:0252

!2

> 5 or Dhead > 0:41m

Summary. For an orifice diameter of 0.025 m, thedownwardly directed concentric-ring sparger has2,401 nozzles placed on four concentric rings.The pitch is 0.04 m. Sometimes the holes arestaggered on the sparger pipe. Also it is a com-mon practice to place two nozzles at a given crosssection as shown in Fig. 8.

Example 2. For the conditions of Example 1 ofperforated plate design, estimate the submerged jetheight in the fluidized bed.

Solution. Perforated Plate

Uh ¼ 88:6m=s rg;h ¼ 0:64 kg=m3

rg;b ¼ 0:5 kg=m3 dh ¼ 0:025m N ¼ 1; 824

dp ¼ 60 mm rp ¼ 1440 kg=m3 emf ¼ 0:42

Gas jet penetration depth using Merry’s correlation(Eq. 3.4.2) for horizontal jets

Lhor

dh¼ 5:25

rg;hU2h

rpð1� emf Þgdp

!0:4rg;brp

!0:2dp

dh

� �0:2

Sparger Grid, Concentric Ring Type

Ring no.

(i)

Radius of each ring

(ri), m

Length of each ring

(Li) 2�ri, m % of total length

Number of holes on each ring

(Ni)

1 1.43 8.98 9.24 222

2 3.05 19.16 19.73 474

3 4.68 29.41 30.28 727

4 6.30 39.58 40.75 978

Total = — 97.13 — 2,401


Lhor ¼ 5:250:64� 88:62

1440ð1� 0:42Þ9:8� 65� 10�6

!0:4

0:5

1440

� �0:265� 10�6

0:025

!0:2

� 0:025 ¼ 0:32m

From Eq. (1),

Lup � 2Lhor � 2� 0:32 � 0:64m

Example 3. For the conditions and the perfo-rated plate defined in Example 1, design a shroudhaving an ID twice that of the grid hole, i.e.,DS ¼ 2dh ¼ 0:05m

Solution. Perforated Plate

The minimum length of the shroud should be

Lmin ¼ 0:05� 0:025

2 tan 5:5�¼ 0:13m

The gas jet velocity emanating from the shroud is

Uh;s ¼ Uh

dhDs

� �2

¼ 88:60:025

0:05

� �2

¼ 22:2m=s

Particle attritions rate will be reduced by a factorcalculated from Eq. (14):

particle attrition without shrouds

particle attrition with shrouds¼ Ds

Dh

� �1:6

¼ 0:05

0:025

� �1:6

¼ 3:0

Thus adding a shroud to the grid reduces the attri-tion rate to 67% of the rate without a shroud.

10.2 Polyethylene Reactor Grid Design

Example 4. Design a flat perforated-plate gridfor the polyethylene reactor schematically shown inFig. 15 and calculate the gas jet penetration depth.Use a triangular pitch. System parameters are

Usup ¼ 0:5m=s rg;h ¼ 19:2 kg=m3

rg;b ¼ 17 kg=m3 rp ¼ 641 kg=m3

rB ¼ 272 kg=m3 �Pgrid ¼ 0:4�Pbed

dh ¼ 0:01m dp ¼ 508 mm emf ¼ 0:45

t ¼ 0:019m

Solution

Determine �Pbed and �Pgrid

�Pbed ¼ grBLB ¼ 9:8� 272� 12:2 ¼ 32,520 Pa

�Pgrid ¼ 0:4�Pbed ¼ 13,008 Pa

Determine the gas velocity through the grid hole(trial and error). Assume Cd ¼ 0:8:

Uh ¼ Cd


rg;h

s¼ 0:8

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� 13008

19:2

r¼ 29:5m=s

Determine the volumetric flow rate of gas

Q ¼ Usup

pD2

4¼ 0:5

pð4:6Þ24

¼ 8:3m3=s

Determine the number of grid holes required:

N ¼ Q

Uh

1

pd2h=4

¼ 8:3

29:5

1

ðp=4Þð0:01Þ2 ¼ 3582

Hole density:

Nd ¼ 3582

ðp=4Þð4:6Þ2 ¼ 215 holes/m2

Figure 15 Schematic of polyethylene reactor.


Determine the hole pitch:

Lh ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNd sin 60

�p ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi215 sin 60�

p ¼ 0:073m

Check the value for Cd:

t

dh¼ 0:019

0:01¼ 1:9

From Figure 3.4.4,

Cd

Lh

dh

� �0:1

¼ 0:98

therefore

Cd ¼ 0:980:01

0:073

� �0:1

¼ 0:803 � 0:80 (great guess)

Gas jet penetration depth using Merry’s correlation[Eq. (2)] for horizontal jets:

Lhor

dh¼ 5:25

rg;hU2h

rpð1� emf Þgdp

!0:4rg;brp

!0:2dp

dh

� �0:2

Lhor ¼ 5:2519:2� 29:52

641ð1� 0:45Þ9:8� 508� 10�6

!0:4

17

641

� �0:2508� 10�6

0:1

!0:2

� 0:01 ¼ 0:55m

From Eq. (1),

Lup � 2Lhor � 2� 0:55 � 1:1m

Coalescence factor:

l ¼ Lh

Lup=2¼ 0:073

1:1=2¼ 0:13 < 1

Therefore Jets coalesce. The low value of l indicatesthat the bed of solids is probably suspendedabove the coalesced jets. Therefore the solidsrarely come into contact with the grid. Thistype of design reduces the chances of grid plug-gage due to ‘‘sticky’’ polyethylene solids.

Summary: The perforated plate has 3,582 holes, eachof 0.01 m diameter, arranged in a triangular pitchof 0.073 m. The hole density is 215 holes=m2.

10.3 Power Consumption

Example 5. Determine the compressor power topass reactant gas into the plenum of the fluid bedsystem. Also calculate the temperature rise due toheat of compression. The system parameters are

�Pgrid ¼ 6 kPa; �Pbed ¼ 15 kPa; �Pcyclonesþfilters

¼ 12 kPa; pressure at the exit of the filters ¼ 350 kPa.Gas entering the compressor: T1 ¼ 20�C; P1 ¼

101 kPaq; Q1 ¼ 10m3=s.Use Z ¼ 0:85; g ¼ 1:4

Solution

Determine compressor discharge pressure, P2:

P2 ¼ Pexit þ�Pcyclonesþfilters þ�Pbed þ�Pgrid

¼ 350þ 12þ 15þ 6 ¼ 388 kPa

Determine ideal power consumption, Ws;ideal

�Ws;ideal ¼g

g� 1P1Q1

P2

P1

� �ðg�1Þ=g�1

" #

�Ws;ideal ¼1:4

1:4� 1101� 10

383

101

� �ð1:4�1Þ=1:4�1

" #¼ 1638 kW

Determine actual power consumption, Ws;actual:

Ws;actual ¼Ws;ideal

Z¼ 1638

0:85

¼ 1927 kW (or 2587 hp)

Determine the temperature rise, T2:

T2 ¼ T1 þT1

Z1

P2

P1

� �ðg�1Þ=g�1

" #

T2 ¼ 293þ 293

0:85

383

101

� �ð1:4�1Þ=1:4�1

" #¼ 453 (or 180�CÞ

NOMENCLATURE

Cd = discharge coefficient; see Fig. 4

dh = grid hole diameter, m

dp = Sauter mean particle size, m

D = diameter of fluid bed, m

Dhead = diameter of the main header pipe, m

Dm = diameter of the manifold pipe, m

Ds = shroud or nozzle diameter, m

g = gravitational acceleration 9:8m=s2

Hhigh = elevation of highest grid hole for curved grid,

m

Hlow = elevation of lowest grid hole for curved grid,

m


K = grid pressure-drop coefficient; see Eq. (8)

0.3 for upward gas entry;

0.1 for lateral and downward gas entry

Ke = erosion constant, Eq. (15)

LB = operating bed depth, m

Ldown = jet penetration for downwardly directed jet, m

Lh = grid hole pitch, cm

Lhor = jet penetration for horizontally directed jet, m

Lmin = minimum shroud or nozzle length, m

Ls = shroud or nozzle length, m

Lup = jet penetration for upwardly directed jet, m

N = number of grid holes

Nd = number of hole density (holes per unit area of

the bed), holes=m2

Nh = maximum number of holes per manifold pipe

section supplied by gas entry

Nm = number of manifolds on the main header

supplied by single gas entry point

P1 = pressure of gas entering the blower, Pa

P2 = pressure of gas leaving the blower, Pa

Q = total volumetric gas flow entering the grid,

m3=sQ1 = total volumetric gas flow entering the blower,

m3=sQ2 = total volumetric gas flow leaving the blower,

m3=st = grid thickness, m

T1 = temperature of gas entering the blower, �KT2 = temperature of gas leaving the blower, �KUh = velocity of gas through the grid hole, m/s

Usup = superficial gas velocity, m/s

Ws;actual = actual power consumption due to shaft work,

W

Ws;ideal = ideal power consumption due to shaft work,

W

a = energy efficiency factor

g = ratio of specific heats of gas

rB = operating bed density, kg=m3

rg;b = density of gas at bed operating conditions,

kg=m3

rg;h = density of gas entering the grid hole (plenum

conditions), kg=m3

rp = particle density, kg=m3

emf = voidage at minimum fluidizing conditions

y = included angle of gas jet, degrees

�Pbed = pressure drop across the dense bed, Pa

�Pgrid = pressure drop across the grid, Pa

�Ph = pressure drop across the grid hole, Pa

’ = particle shape factor

Z = compressor efficiency

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gas distributor and plenum design in fluidized beds

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