Yang Fluidization, Solids Handling, and Processing

Gas Distributor and Plenum Design 215

lowest hole on the grid. Take an example of a fluid bed with curved grid as shown in Fig. 2.

		Dilute Phase
	Overflow		Bed Density
	Well
			480 kg/m3
	4.6 m	5.5 m
			Curved
	Highest	0.9 m	Peforated
			Plate
	Grid	Plenum
	Hole
	Lowest		Riser
	Grid		Typical Hole
	Hole

Figure 2. A typical fluid bed showing a curved perforated plate.

A pressure balance across the curved grid can be written as:

Eq. (6)	Ph (Highest Hole) =	Ph (Lowest Hole) + ρB g (Hhigh - Hlow)
i.e.,
Eq, (7)	Ph (Highest Hole) =	Ph (Lowest Hole) + 480 × 9.8 × 0.9
	Ph (Lowest Hole) + 4235 Pa

Therefore, the lowest grid hole has the lowest pressure drop, and hence for pressure drop, the criterion must apply with respect to the lowest hole on the grid.

3.3Design Equations

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

216 Fluidization, Solids Handling, and Processing

Pressure drop across the grid:

Eq. (8) Pgrid = Kg ρB LB

where K = 0.3 for upward and lateral gas entry, and 0.1 for downward gas entry.

The gas velocity through the grid hole (orifice equation):

2 Pgrid

Eq. (9) Uh = Cd

ρg,h

The orifice discharge coefficient, Cd , is typically about 0.6 for gas flowing through an orifice in a pipe (for a ratio of orifice diameter to pipe diameter in the range of 0 to 0.2). This value of the orifice coefficient is for a sharp-edged orifice. However, grids are not sharp-edged, and the orifice coefficient is greater than 0.6. A typical value of Cd for a grid hole is about 0.8. Actually, the value of Cd depends on the grid plate thickness and the hole pitch. It can be calculated from Fig. 3.

1.0

0.9

1 . 0

) h /d

h (L d C

0.8

0.7
0.0		0.4	0.8	1.2	1.6	2.0	2.4	2.8
		Thickness-to-Diameter Ratio, t / d

Figure 3. Grid hole discharge coefficient design chart.

Gas Distributor and Plenum Design 217

Volumetric flow rate of gas:

π d 2

Eq. (10) Q = N h Uh

4

Hole Size. To increase the gas residence time in the bed, it is desirable to introduce the greatest number of small gas bubbles as possible into the bed. This can be achieved by maximizing N at the expense of dh in Eq. (10) (within the limits of mechanical, cost, and scale-up constraints). To minimize stagnant zones, the number of grid holes per m2 should be ³10. In practice, the number of grid holes per square meter is generally about 2 to 3.

Hole Layout. To increase the uniformity of fluidization, it is common to lay out the holes in triangular or square pitch as shown in Fig. 4. All the holes in a grid with triangular pitch are equidistant. This is not the case for a grid with square pitch. Triangular pitch will also result in more holes per unit area.

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

• Triangular Pitch

• Square Pitch

		60o
			dh		dh
			Lh	Lh
	Eq. (11) Lh	=	1	Eq. (12) Lh =	1
			Nd sin 60°		Nd

Figure 4. The relationship between hole density and grid hole pitch for triangular and square pitch.

218 Fluidization, Solids Handling, and Processing

3.4Additional Criteria for Sparger Grids

Additional distribution criteria are used for sparger grids. To keep the pipe header pressure drop down to acceptable levels and to ensure good gas distribution, the following criteria (Karri, 1990) should be met:

(a)The manifold should be sized based on the following equation:

	æ	D2		ö2
Eq. (13)	ç	m		÷	> 5
		N d
	ç		2	÷
	è	h	h	ø

The parameters in Eq. (13) are defined in Fig. 5.

no holes within one Dm

Dm

					Nm	= no. of manifolds on
Nh = no. of holes			Dhead			the main header
		on this manifold				supplied by single
						gas entry point

Figure 5. Manifold sparger grid showing the definitions of various parameters

Similarly, the main header pipe should be sized based on the following equation:

		æ	D2		ö2
	Eq. (14)	ç		head	÷	> 5
			N	D2
		ç			÷
		è		m m ø

(b)In some instances, two to three different hole sizes are used on a given manifold to get better gas distribution.

Gas Distributor and Plenum Design 219

(c)The gas velocity in the header/manifold pipe should be <25 m/s for best distribution.

(d)Holes should not be located closer than one Dm from any sharp bend or tee in the header/manifold to prevent solids from being sucked into the manifolds due to the vena contracta effect.

3.5Port Shrouding or Nozzle Sizing

Shrouds are generally placed around grid holes to reduce the velocity at the gas-solids interface and reduce particle attrition. Shrouds simply consist of short pipes centered over the smaller grid holes which have been selected in size and number to operate at a hole velocity defined by Eq. (9).

To be effective, shrouds must be long enough to “contain” the expanding (11-degree included angle) gas jet leaving the grid orifice.

Ds

o	o	Lmin
11	5.5
		d h
a.	b.	c.

Figure 6. (a) Diverging free jet; (b) shroud too short to contain the jet; (c) minimum shroud length required to contain jet.

As can be seen from the Fig. 6, the minimum shroud length should be:

	Eq. (15)	Lmin	=	Ds - dh
				2 tan 5.5°

In practice, it is prudent to increase Lmin by a factor of 50 to 100%. A shroud length less than Lmin causes significantly more erosion and attrition than no shroud at all. Significant attrition can also occur if the shroud is not centered over the smaller hole.

220 Fluidization, Solids Handling, and Processing

The nozzle or shroud details inside a sparger pipe grid are illustrated in Fig. 7.

		erosion confined
		to surface
	refractory			refractory
				header wall
	sparger		Ds
	pipe
		Ls		gas expands to completely
	nozzle /		θ	fill the tube, thereby reducing
		θ = 11O		chance for solids to get into
	shroud
				eddies near orifice
	drain			dh
	sparger cross-section	small restriction orifice

Figure 7. Shroud design for a sparger grid.

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

	particle attrition without shrouds	æ	D	ö1.6
Eq. (16)		= ç		s	÷
	particle attrition with shrouds	ç		÷
		è dh ø

4.0PARTICLE ATTRITION AT GRIDS

Solids immediately surrounding the gas jets issuing from the grid are ingested into the jets. These particles are accelerated and collide with the particles near the tip of the jet. Figure 8 depicts how the particles are picked up and slammed into a fluidized, yielding bed for an upwardlydirected jet. However, downward-pointing jets generally issue into a nonfluidized area of particles. Therefore, particles picked up by downwardlydirected jets issuing into a non-yielding unaerated bed, results in a greater degree of particle attrition.

Gas Distributor and Plenum Design 221

Figure 8. The mechanism of particle attrition at a submerged jet.

The attrition rate, i.e., the rate of generation of fines, 0–dp microns, at the submerged jets in a fluidized bed, tends to fall off asymptotically with time to a steady-state rate as shown in Fig. 9. Initially the attrition rate is high due to the wearing off of angular corners. Typically, it takes long time, hours to days, for the particles to reach steady-state (equilibrium) where the particles tend to be more rounded. For most catalytic fluidized bed processes, the bed operates at equilibrium. That means the most significant part of the attrition rate curve is the “steady-state” rate.

	irregular shape	more rounded
gm/min	unsteady-state	steady-state
,
p		equilibrium bed
d
-
0
of
Rate		Material 'A'
Attrition
		Material 'B'
	dh , N, U h= constant
	Time

Figure 9. Typical attrition rate curve for submerged jets.

222 Fluidization, Solids Handling, and Processing

4.1Attrition Correlation

There is no general correlation available to date to predict the steady state attrition rates for various materials. Zenz and Kelleher (1980) gave a simple correlation to predict steady-state attrition rates for FCC catalyst and glass beads. This is an empirical dimensional equation as given by:

		φ			2.5	π dh2
	Eq. (17)		(kg/m/hole) = Ka (U h	ρ g,h )
		N				4

The following table gives the attrition-rate constant (Ka) for FCC catalyst as a function of particle size range (0–dp) for upwardly-directed jets.

Attrition to particles of	Numerical Constant, Ka
0 to dp (μm)	in Eq. 17
0 to 2	1.11 X 10-6
0 to 23	9.03 X 10-6
0 to 50	2.29 X 10-5

For glass beads, the values of Ka were found to be about 1/12 those for FCC catalyst. For other materials, one should obtain a relative attrition index with respect to either FCC or glass beads and then obtain a value of Ka based on that index.

Karri (1990) reported that downwardly-directed jets have approximately twice the steady-state attrition rate as that of upwardly directed jets. The attrition rates for upwardly and laterally directed jets are essentially the same.

If excessive particle attrition is expected, it is a common practice to place a shroud/nozzle around a grid hole as discussed in Sec. 3.5. For properly sized nozzles, one can derive from Eq. (17), particle attrition is reduced by a factor:

	particle attrition without shrouds		æ	D	ö3
Eq. (18)		=	ç		s	÷
	particle attrition with shrouds		ç		÷
			è d h ø

However, it has been determined experimentally that the exponent in Eq. (18) is more like 1.6 as shown in Eq. (16) instead of 3 as indicated in Eq. (18).

Gas Distributor and Plenum Design 223

5.0EROSION

Erosion in the grid region is primarily due to high velocity submerged jets impinging on distributor parts, bed walls, or on bed internals. Therefore, one should estimate the jet penetration heights for a given grid design and check for the following:

(a)Bed internals should not be placed in the jetting zone near the grid, otherwise the internals could be severely eroded.

(b)Nozzles should not be located any closer than half the jet penetration height from the bed wall.

Erosion in the nozzle or orifices is often associated with weepage 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 caps tend to have erosion problems due to the secondary circulation of solids. Therefore, bubble caps should be designed to minimize secondary circulation of solids.

6.0EFFECTS OF TEMPERATURE AND PRESSURE

System temperature and pressure affect the momentum of grid jets

via the gas density (see Ch. 2). The momentum of the gas jets is ρg,hUh. When the temperature is increased, the gas density decreases. For the

same gas jet velocity this decreases the momentum of the jets and, therefore, decreases the jet penetration and the attrition at the grid. Similarly, when system pressure is increased, gas density increases, gas jet momentum increases and, therefore, the jet penetration and the attrition at the grid are increased.

7.0PLENUM DESIGN

The plenum, or windbox, is the chamber immediately below the grid. If the bed-pressure-drop–to–grid-pressure-drop ratio is high enough, the plenum design will probably not be that important. However, for the case where this ratio is marginal, the plenum design may determine whether the bed will operate satisfactorily.

224 Fluidization, Solids Handling, and Processing

The typical plenum designs showing various configurations for introducing gas into the plenum, are illustrated in Fig. 10. Common sense dictates that certain plenum designs may be preferred over others. If the gas enters the plenum from the bottom, it is preferable that the plenum has a large enough distance between the outlet of the supply pipe and the grid to prevent the gas from preferentially passing through the middle of the grid. When gas enters a plenum from the side, it is preferable to route the gas to the middle of the plenum (Fig. 10 c) rather than have the supply pipe end at the wall of the plenum. In addition, horizontal-to-vertical down gas entry (Fig. 10 c) is preferable over the horizontal-to-vertical up gas entry (Fig. 10 b).

(a) Vertical Entry

(b) Horizontal-to-

(c) Horizontal-to-

Vertical (Up) Entry

Vertical (Down) Entry

(d) Deflection Plate

(a) Chinese Hat

(e) Inverted Bowl

Figure 10. Different plenum configurations.

If the gas-solid or gas-liquid suspension needs to be introduced into the plenum, as for example in a polyethylene reactor and some FCC regenerators, it is preferable to introduce the suspension at the lowest point of the plenum (Fig. 10 a, d, e) to minimize the accumulation of solids or liquids in the regions inaccessible to reentrainment. For two-phase systems, it is preferable to have a some sort of deflection device (Fig. 10 d, e, f ) between the outlet of the supply pipe and the grid to prevent the solids from preferentially passing through the middle of the grid due to their high