The most common efficiency theory is the DeutschAndersen equation. The theory assumes that particles are at their terminal electrical drift velocity and well-mixed in every plane perpendicular to the gas flow direction due to lateral turbulence. The theory also assumes plug flow through the ESP, no reentrainment of particles from the collector plates, and uniform gas velocity throughout the cross section. Collection efficiency is expressed as follows:
where A is the total collecting area of the precipitator and Qg is the volumetric gas flow. The derivation of this equation is identical to that for gravity settling chambers except that the terminal settling velocity under a gravitational field is replaced with terminal drift velocity in an electric field.
The precipitator performance can differ from theoretical predictions due to deviations from assumptions made in the theories. Several factors can change the collection efficiency of an idealized precipitator. These factors include particle agglomeration, back corona, uneven gas flow, and rapping reentrainment.
Cooperman (1984) states that the Deutsch-Andersen equation neglects the role of mixing (diffusional and large-scale eddy) forces in the precipitator. These forces can account for the differences between observed and theoretical migration velocities and the apparent increase in migration velocity with increasing gas velocity. He postulates that the difference in particle concentration along the precipitator length produces a mixing force that results in a particle velocity through the precipitator that is greater than the gas velocity. At low velocities, the effect is pronounced, but it is masked at higher velocities. He presents a more general theory for predicting collection efficiency by solving the mass balance equation as follows:
32C 32C 3C 3C D1 3x2 + D2 3^ - Vg 3^ + VP 3^ = 0 5.17(16)
C = the particle concentration
Dj and D2 = the longitudinal and transverse mixing coefficients, respectively
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