Gas Emission Control - Mathematics and Statistics for the Environment - page 465

Solution : From Examples 16.2 and 16.3:

Gas flow rate = Q = 84.9 m 3 /min
Density = ρ g = 1.17 kg/m 3

From Table 16.2 for a bubble cap tray:

Ψ = 0.0162 m 0.25 hr 0.50 /kg 0.25

Before Equation 16.13 can be used, Q must be converted to m 3 /hr:

Q = 84.9 m 3 /min × 60 min/hr = 5094 m 3 /hr

Substituting these values into Equation 16.13 for a minimum diameter d ,

05 .

= () Ψρ 05

. 0 5

05 .

d Q g = 0 0162 5094 117 . ( .) = 12 . m

Correct this diameter for a tray spacing of 0.53 m. From Figure 16.10, read a correction factor of
1.05. Therefore, the minimum diameter is

d = 1.2 × 1.05 = 1.26 m (4.13 ft)

Note: This estimated diameter is a minimum acceptable diameter based on actual conditions. In
practice, a larger diameter (based on maintenance and economic considerations) is usually
chosen.

16.3.4.4 Theoretical Number of Absorber Plates or Trays
The several methods used to determine the number of ideal plates or trays required for a given
removal efficiency can become quite complicated. One method used is a graphical technique
(USEPA, 1981, p. 4-34). The number of ideal plates is obtained by drawing “steps” on an operating
diagram. This procedure is illustrated in Figure 16.11. This method can be rather time consuming,
and inaccuracies can result at both ends of the graph. Equation 16.14 is a simplified method of esti-
mating the number of plates. It can only be used if both the equilibrium and operating lines for the
system are straight. This is a valid assumption for most air pollution control systems.

YmX
YmX

−
−

mG
L +

mG
L

1 2 m m

m

ln 1 −

2 2 m

N = (16.14)

p

L
mG

m
m

ln

where
N p = Number of theoretical plates.
Y 1 = Mole fraction of solute in entering gas.
X 2 = Mole fraction of solute entering the tower.
Y 2 = Mole fraction of solute in exiting gas.
m = Slope of equilibrium line.
G m = Molar flow rate of gas (kg-mol/hr).
L m = Molar flow rate of liquid (kg-mol/hr).