Design Of Perforated Plate 2d5m72

Procedure # 2 Design of perforated plate distributor Cedric Briens, 1992 04 20, 2002 06 10 General design criteria A good gas distributor must be such that: - the flowrate of gas through each hole is the same. - the gas flow through the holes is not too sensitive to pressure perturbations and fluctuations in the fluidized bed. - there are enough holes per m2 of bed cross-section to provide a fairly uniform distribution of gas. - the jets exiting from the holes do not merge (then, it would be useless to have many holes). One exception may be when the main objective is the elimination of stagnant zones. - the jets exiting from the distributor should not reach internals. In shallow beds, they should not pierce the bed surface. - if the jet velocity is very high and might lead to unacceptable solids attrition rates, consider the use of shrouds.

Step-by-step procedure

1. Set the grid to bed pressure drop ratio. It should be large enough to minimize the impact of pressure perturbations and fluctuations in the bed on the gas distribution between the various holes. Note that this is the dry grid pressure drop, i.e. the grid pressure drop in the absence of particles. Normally, take: 0.1 <

∆Pgrid ∆Pbed

< 0.3

Knowing the bed pressure drop ∆Pbed, this gives the grid pressure drop ∆Pgrid.

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One should then check that this grid pressure drop is greater than 3400 Pa. One should also check that it is larger than (100 ∆Pexp) where ∆Pexp is the expansion pressure drop of the gas into the wind-box. In practice, ∆Pgrid is set and the size of the gas inlet(s) into the wind-box are set so as to keep the expansion pressure drop ∆Pexp below 1% of the grid pressure drop ∆Pgrid. 2. Select the grid thickness The grid thickness is usually set by mechanical considerations. Note: the grid thickness is obtained from mechanical considerations. The perforated plate must be thick enough to withstand the mechanical constraint to which it will be exposed. In volume 6 of Chemical Engineering by Coulson, Richardson and Sinnot, page 635, the minimum thickness for a flat plate is given as: P t = C D column f C is an empirical constant: you may take C = 0.45. f is the design stress which depends on the material and the temperature. For carbon steel at temperatures between 50 and 100 oC, take f = 125 x 106 N/m2. P is the intensity of loading in N/m2. Consider the highest possible value when calculating the plate thickness. 3. Select the grid hole diameter Advantages of a large hole diameter: • not too many holes (i.e. cheaper grid) • less risk of merging of jets or bubbles rising from adjacent grid holes • solids segregation may be less likely due the fact that the bubbles in the grid region are large enough to re-entrain large or heavy particles (this a bit controversial). • more resistant to plugging by any particles from upstream gas lines. Drawbacks of a large hole diameter: • larger volume of stagnant defluidized zones on the plate, in-between the holes. • if the orifice is jetting, the jets will penetrate further and internals such as heat exchanger tubes or diplegs will have to be located farther away from the grid. • particles entrained into the jets will remain longer inside the jet. This may lead to problems if, for example, the particles can thus become sticky. • with group B particles, the bubbles in the whole bed will be larger and bubbleemulsion mass transfer will not be as effective. With group A particles, it usually page 2 of procedure 2

• •

does not matter since the bubble size in most of the bed is not set by the grid design but by the maximum stable bubble size. the fluidization in the grid region may be less smooth. for a given grid thickness, the vena contracta is more likely to occur in the bed rather than inside the grid hole. Flow through the grid hole may be less stable.

For most applications, a hole diameter dh between 1 and 10 mm should be OK (as a start, you may want to try 3 or 4 mm). 4. Calculate the number of grid holes Nh From the total gas flowrate, using the selected hole diameter and grid thickness, find the number of grid holes which will give the dry grid pressure drop obtained in step 1. If the gas properties (e.g. viscosity, density) vary between the wind-box and the bed, use the wind-box properties. A correlation for the prediction of the dry pressure drop through a perforated plate is required to perform the above calculation. If a correlation such as the correlations from McAllister et al. or Tyagi et al. is used, an iterative calculation will be required. 5. Set the wall clearance This is the distance between the outer holes and the inner column wall. If this clearance is too small, grid jets or bubbles may erode the wall. On the other hand, in some processes, this clearance is set to zero to minimize the formation of stagnant defluidized zones near the column wall. Once the wall clearance w is set, calculate the effective distribution area:

A de =

π 2 ( Dcolumn − 2w − d h ) 4

6. Select equilateral or square pitch

This does not matter too much. 7. Calculate the grid hole pitch s (i.e. center-to-center distance)

This is calculated from the number of required grid holes, taking into the wall clearance. For a square pitch, there is on the average one hole per square, so that: page 3 of procedure 2

s = 0.88623

Dcolumn − 2w − d h Nh

For an equilateral triangular pitch, there is on the average one half hole per triangle, so that: s = 0.952313

Dcolumn − 2w − d h Nh

In practice, the number of grid holes may be adjusted slightly to give a "nice" pattern. The dry grid pressure drop should, then, be recalculated. 8. Estimate the actual, "wet" grid pressure drop

The presence of a fluidized bed may greatly affect the grid pressure drop which may be as much as doubled. In the absence of actual industrial data and to be on the safe side for the compressor specifications, assume that the "wet" grid pressure drop will be twice the "dry" grid pressure drop. 9. Calculate the grid jet characteristics

In this section, jetting is assumed (whether the grid is jetting or bubbling will be determined in section 11). The jet penetration depth (or "jet length") is obtained from a standard correlation such as reviewed in the course notes (e.g. a correlation from Zenz). As a first approximation, take a jet width equal to 50% of the jet length. The axial profile of the gas velocity, along the jet axis, may be obtained directly from the correlation by Yang and Keairns (1981). Alternately, it may be obtained by adjusting the profile obtained from Yang and Keairns (1981) so that the axial velocity is only 5% of the hole velocity at the previously calculated jet penetration depth. The effective diameter of the bubbles detaching from the jets is about 50% of the jet length.

10. Bubble diameter at the orifice page 4 of procedure 2

In this section, the grid holes are assumed to be bubbling. The bubble diameter at the orifice can be calculated from one of the correlations reviewed in the chapter on Bubble Properties. 11. Determine whether the grid holes are jetting or bubbling.

Assume that the flow regime will be such that the bubble size is maximized (giving the lowest energy expenditure). If the jet length is greater than twice the diameter of a bubble which would be formed at the grid hole if it was bubbling, then the grid will be jetting. Set the effective diameter of the bubbles formed at the grid accordingly. 12. Final checks

Check whether the wall clearance is large enough, i.e. whether the jets or bubbles formed at the orifice will reach to the wall. • If the holes are bubbling, consider that wall erosion would be caused by the shell of emulsion phase solids which surrounds each bubble. The diameter of this shell is about 50% larger than the bubble diameter. • If the holes are jetting, include a 50% safety factor on the jet width to for the observed lateral fluctuations of grid jets. Check whether bubbles or jets will merge at the grid. If they do, this means that the diameter of the bubbles formed at the grid and/or the effective jet penetration depth would not be increased by increasing the hole diameter. Be aware that if bubbles or jets merge, their penetration depth will be much larger than predicted (important when considering the safe distance from the grid for internals). • If the holes are bubbling, consider that bubbles will coalesce at the grid if there is intersection of the shells of emulsion phase solids which surrounds each bubble. The diameter of this shell is about 50% larger than the bubble diameter. • If the holes are jetting, include a 50% safety factor on the jet width to for the observed lateral fluctuations of grid jets. In case of a shallow bed, check that the jets do not pierce the bed surface. As a rough guideline, the jet penetration depth should be less than about 65 % of the minimum bed height. 13. Bubble formation frequency at the grid

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The bubbling frequency, at the grid, can be obtained from the effective diameter db0e of the bubbles formed at the grid (i.e. db0 if bubbling occurs, db0e = half the jet length if jetting occurs). 3( Vg − U mf ) Then, the bubbling frequency is given by: f B0 = 2 N h (d B0e ) 3 This frequency is interesting since it is usually the highest possible frequency of perturbations inside a fluidized bed (it is certainly the highest possible frequency coming from bubbles; note that, although there is no definite ing data, the bubbles coming from all the grid holes are assumed to be in phase). This frequency can, thus, with an appropriate safety factor, be used to design the ing structure of internals such as heat exchanger tubes.

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