Wet Scrubbers for Emission Control - Mathematics and Statistics for the Environment - page 536

The overall penetration is 0.009, and the geometric standard deviation is 2.5. The figures in USEPA
(1984c, p. 9-12) provide us with the following information:

P t * = 0.009
σ gm = 2.5
( d p ) cut / d pg = 0.09

The cut diameter ( d p ) cut is calculated from

( d p ) cut = 0.09(12.6 µmA) = 1.134 µmA

■ EXAMPLE 18.3
Problem: A particle size analysis indicated the following (USEPA, 1984a, 9-14):

d gm = Geometric mean particle diameter = 12 µm
σ gm = Standard deviation of the distribution = 3.0
η = Wet collector efficiency = 99%

If a collection efficiency of 99% were required to meet emission standards, what would the cut
diameter of the scrubber have to be?

Solution: Write the penetration ( P t ) equation:

P t * = 1 - η = 1 - 0.99 = 0.01

From the figures in USEPA (1984c, p. 9-12), we read ( d p ) cut / d gm , for P t * = 0.01 and σ gm = 3.0; [ d p ] cut /
d gm equals 0.063. Because d gm = 12 µm, the scrubber must be able to collect particles of size 0.063 ×
12 = 0.76 µm with at least 50% efficiency to achieve an overall scrubber efficiency of 99%.

18.2.5.4 Contact Power Theory
A more general theory for estimating collection efficiency is the contact power theory. This theory is
based on a series of experimental observations made by Lapple and Kamack (1955). The fundamen-
tal assumption of the theory can be expressed as: “When compared at the same power consumption,
all scrubbers give substantially the same degree of collection of a given dispersed dust, regardless
of the mechanism involved and regardless of whether the pressure drop is obtained by high gas flow
rates or high water flow rates” (Lapple and Kamack, 1955). In other words, collection efficiency is a
function of how much power the scrubber uses, and not of how the scrubber is designed. This has a
number of implications in the evaluation and selection of wet collectors. Once we know the amount
of power needed to attain a certain collection efficiency, the claims about specially located nozzles,
baffles, etc. can be evaluated more objectively. The choice between two different scrubbers with the
same power requirements may depend primarily on ease of maintenance (USEPA, 1984a, p. 9-16;
USEPA, 1984c, p. 9-13).
Semrau (1960, 1963) developed the contact power theory from the work of Lapple and Kamack
(1955). The theory, as developed by Semrau, is empirical in approach and relates the total pressure
loss ( P T ) of the system to the collection efficiency. The total pressure loss is expressed in terms of
the power expended to inject the liquid into the scrubber plus the power needed to move the process
gas through the system (USEPA, 1984c, p. 9-13):

P T = P G + P L , P G = 0.157∆ p , P L = 0.583 p t ( Q L / Q G ) (18.16)