Particulate Emission Control - Mathematics and Statistics for the Environment - page 513

TABLE 17.6
Particle Size Distribution

Weight Range Average Particle Size d p (µm)

0-20% 3.5

20-40% 8

40-60% 13

60-80% 19

80-100% 45.5

A Deutsch-Anderson type of equation describing the collection efficiency of an electrostatic pre-
cipitator is

η = 1 - exp(- Kd p )

where
η = Fractional collection efficiency.
K = Empirical constant.
d p = Particle diameter.
Solution: Is the overall efficiency of the electrostatic precipitator equal to or greater than 98%? Since
the weight fractions are given, collection efficiencies of each particle size are needed to calculate the
overall collection efficiency. Determine the value of K by using the given cut diameter. Because the
cut diameter is known, we can solve the Deutsch-Anderson type equation directly for K :

η = 1 - exp(- Kd p )

0.5 = 1 -exp[- K (0.9)]

Solving for K , K = 0.77. Now calculate the collection efficiency using the Deutsch-Anderson equa-
tion where d p = 3.5:

η = 1 - exp[(-0.77)(3.5)] = 0.9325

Table 17.7 shows the collection efficiency for each particle size. Calculate overall collection efficiency:

∑ w ii
(0.2

η = η

=× +× +× 0.9325) (0.2 0.9979) (0.2 0.9999) +× +× (0.2 0.9999) (0.2 0.9999)

= 0.9861 = 98.61 %

TABLE 17.7
Collection Efficiency for Each Particle Size

Weight Fraction w i Average Particle Size d p (µm) η i

0.2 3.5 0.9325

0.2 8 0.9979

0.2 13 0.9999

0.2 19 0.9999

0.2 45 0.9999