Wet Scrubbers for Emission Control - Mathematics and Statistics for the Environment - page 543

Express the fractional collection efficiency (η i ) in terms of d pi ( d p in ft):

=− − (

(

)

)

η 1 exp kQ LG Ψ

( )

( ) ( ) ()

2

11

η =− − 1 exp(.)(.). 0 28513945 × 10 QQ d

i LG p

( )

5

=− − 1 exp 6 348 . × 10 d

pi

Now calculate the collection efficiency for each particle size appearing in Table 18.1. For d p = 0.05
µm (1.64 × 10 -7 ft), for example:

( ) ( ) ( )

5

=− −

5 − 7

=

η==− − 1 exp 6 348 . × 10 d pi 1 exp 6 348 . × 10 16410 . × 0 0989 .

Table 18.2 shows the results (rounded) of the above calculations for each particle size. Now calculate
the overall collection efficiency:

η = ∑w i η i = (9.89 × 10 -4 ) + 0.0975 + 0.6325 + 12.980 + 16.00 + 12.00 + 8.00 + 50.00 = 99.71%

■ EXAMPLE 18.7
Problem: A vendor proposes to use a spray tower on a lime kiln operation to reduce the discharge
of solids to the atmosphere. The inlet loading is to be reduced in order to meet state regulations.
The vendor's design calls for a certain water pressure drop and gas pressure drop across the tower.
Determine whether this spray tower will meet state regulations. If the spray tower does not meet
state regulations, propose a set of operating conditions that will meet the regulations (USEPA,
1984b, p. 81).

Given:
Gas flow rate = 10,000 acfm
Water rate = 50 gal/min
Inlet loading = 5.0 grains/ft 3
Maximum gas pressure drop across the unit = 15 in. H 2 O
Maximum water pressure drop across the unit = 100 psi
Water pressure drop = 80 psi
Gas pressure drop across the tower = 5.0 in. H 2 O
State regulations require a maximum outlet loading of 0.05 grains/ft 3 . Assume that the contact
power theory applies (USEPA, 1984a, p. 9-15).

TABLE 18.2
Particle Size Data
d p (ft)

w i (%) η i w i η i (%)

1.64 × 10 -7 0.01 0.0989 9.89 × 10 -4

9.84 × 10 -7 0.21 0.4645 0.0975

2.62 × 10 -6 0.78 0.8109 0.6325

9.84 × 10 -6 13 0.9981 12.98

2.62 × 10 -5 16 1 16

4.27 × 10 -5 12 1 12

5.91 × 10 -5 8 1 8

6.56 × 10 -5 50 1 50