Page 178 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

6.1 General Consideration 153

P
g d pi m pi d pi
i
g ¼ P ð6:7Þ
m pi d pi
i
With the fractional efficiency curve of a device determined, the total efficiency
for polydisperse particles can be calculated using above equation. In the following
analyses, only fractional efficiency will be introduced to avoid duplication of work.

6.1.2 Particle Separation Efficiency of Multiple Devices

In engineering applications, usually more than one unit is employed in order to
achieve high efficiency or to handle a great amount of air flow. The former is
achieved by connecting more than one unit in serial and the latter in parallel.
Consider k identical devices arranged in serial, the number of particles entering the
ith unit is the same as that penetrating through the (i − 1)th unit. Then the pene-
tration through all the k units is

P ¼ PP i ¼ P 1 P 2 ...P k ð6:8Þ

And the corresponding efficiency is

g ¼ 1 P ¼ 1 P 1 P 2 ...P k ð6:9Þ
In this analysis, we actually made a critical assumption that the particle sepa-
ration efficiencies of the identical units are the same. In reality, it is actually invalid
because the particle separation efficiency of a unit depends on the incoming particle
concentration, which keeps decreasing when the units are connected in serial.
Therefore, careful interpretation of this equation should be executed.

Example 6.1: General particle separation efficiency
A filter has an efficiency of 85 %. What is the total efficiency if two of them
working in serial.

Solution
With a single filter efficiency of 85 %, the corresponding penetration efficiency is
15 %. For two filters in serial, the total efficiency is thereby
g ¼ 1 P 1 P 2 ¼ 1 0:15 0:15 ¼ 0:9775

The total filtration efficiency is 97.75 %.