Yang Fluidization, Solids Handling, and Processing

Gas Distributor and Plenum Design 225

momentum. This preferential by-passing of solids causes maldistribution of gas. In addition, the configurations of Figs. 10 (e) and 10 (f) are preferable over the configurations of Figs. 10 (a) and 10 (d).

8.0DESIGN EXAMPLES

8.1FCC Grid Design

Example 1: A 13-m-ID bed of FCC catalyst 3 m deep, is to operate at a superficial gas velocity of 0.6 m/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: (i) a flat perforated plate, and (ii) concentric-ring type downflow sparger. Assume a grid thickness to be 0.025 m.

Solution:

LB = 3.05 m; D = 13 m; Usup = 0.6 m/s; ρB = 480 kg/m3;

ρg,h = 0.64 kg/m3; dp = 60 μm; t = 0.025 m

Perforated Plate Design:

• Determine Pbed and Pgrid

Pbed = g ρ BLB = 9.8× 480 × 3 = 14,112 Pa

Choose Pgrid to be 30% of Pbed

Pgrid = 0.3; Pbed = 4,234 Pa

•Determine the gas velocity through the grid holes (assume a typical value for Cd 0.77)

•Determine the volumetric gas flow rate at the conditions below the grid. For this example, assume the temperature of the gas below the grid is the same as in the bed. This may not be the case in an actual plant.

Gas Distributor and Plenum Design 227

Various combinations of N and dh satisfy the pressure drop requirements for the two grid types as shown in the table below.

To proceed with the design, it is necessary to select a hole size (judgement call). For the purpose of this example, a hole size of 0.025 m will be chosen to compare the different grid types. This hole diameter does not result in an excessive number of holes for either type of grid.

Check the value for Cd ,

t0.05

== 2

There is a good agreement between the initial and calculated value for Cd . If not, one must repeat 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 a triangular pitch of 0.29 m. The hole density is 13.8 holes/m2.

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

228 Fluidization, Solids Handling, and Processing

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

Sparger Grid - Concentric Ring Type

This design results in 2,400 holes.

• Determine the hole pitch

97.13

Lh = 2400 = 0.04 m

•To determine the header-pipe size, first determine the maximum number of holes in ring section supplied by a single effective entry of gas. If outer most 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 ring No. 4 would be Nh = 978/8 = 122. Then Eq. (13) gives:

or Dhead > 0.41 m

230 Fluidization, Solids Handling, and Processing

Example 3: For the conditions defined in Example 1 and 2, design a shroud having an ID twice that of the grid hole, i.e., Ds = 2dh = 0.05 m.

Solution: Perforated Plate

The minimum length of the shroud should be:

• The gas jet velocity emanating from the shroud is

•Particle attrition rate will be reduced by a factor calculated from Eq. (16)

Thus, adding a shroud to the grid reduces the attrition rate to 67% of the rate without a shroud, i.e., attrition rates with and without shrouds are 0.42 and 1.25 ton/day, respectively.

8.2Polyethylene Reactor Grid Design

Example 4: Design a flat, perforated-plate grid for the polyethylene reactor schematically shown in Fig. 11, and calculate the gas jet penetration depth. Use a triangular pitch. System parameters are:

Gas Distributor and Plenum Design 231

Usup = 0.5 m/s; ρg,h = 19.2 kg/m3; ρg,b = 17 kg/m3; ρp = 641 kg/m3; ρB = 272 kg/m3; Pgrid = 0.4 Pbed; dh = 0.01 m; dp = 508 mm; εmf = 0.45; t = 0.019 m

TO COMPRESSOR

7 m

6.1 m

11o 4.6 m

3 m

12.2 m

FLAT PERFORATED

PLATE

ETHYLENE

IN

Figure 11. Schematic of polyethylene reactor

Determine the gas velocity through the grid hole, (trial and error)- assume Cd = 0.8

232Fluidization, Solids Handling, and Processing

•Determine the volumetric flow rate of gas

·Check the value for Cd

234 Fluidization, Solids Handling, and Processing

K= grid pressure-drop coefficient; Eq. (6) for upward gas entry;

0.1for lateral and downward gas entry

θ= included angle of a gas jet, degrees