Page 177 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

152 6 Separation of Particles from a Gas

Consider a particle separation device, which could be any of the devices to be
introduced shortly. N i and N o are the numbers of particles with size d p before and
after the device, respectively. The total amount of particles collected by the device
is N c ¼ N i N o . Then the separation efficiency for particles with a size d p is
defined as the

N c N o
g d p ¼ ¼ 1 : ð6:1Þ
N i N i
The performance of a particle separation device can also be described with a
penetration efficiency (P).

N i
Pd p ¼ : ð6:2Þ
N o
Obviously, the relationship between P and g is defined as

g ¼ 1 P ð6:3Þ

g d p represents the efficiency for the particles having same diameter, d p .Itis
also referred to as grade collection efficiency.
An important parameter in fractional efficiency is the so-called “cut size”, d 50 ,
which is the particle size for which the separation efficiency is 50 %.
In air pollutant control, we deal with polydisperse particles. It leads to another
term called total efficiency. The total efficiency by considering all the particles is
1 1
R R
p
N o d p dd p g d p N i d p dd p
0 0
1 1
g ¼ R ¼ R ð6:4Þ
0 N i d p dd p 0 N i d p dd p
When the particle size distribution is measured using discrete data, it can be
estimated by
P
g d pi N i d pi
g ¼ P ð6:5Þ
N i d pi
If the particle density m is assumed to be the same before and after the device
and all the particles with the same size have the same mass, we can replace number
N with mass m; Eq. (6.4) becomes
1 1
R R
0 m po d p dd p 0 g d p m pi d p dd p
¼ ð6:6Þ
g ¼ R R
1 1
m pi d p dd p m pi d p dd p
0 0
Similarly, when the particle size distribution is measured using discrete data,
Eq. (6.5) can be rewritten as