Electrostatic Precipitation

General Description

The process of electrostatic precipitation involves (a) the ionization of contaminated gas (usually air) flowing between electrodes, (b) the charging, migration and collection of contaminants (particles) on oppositely charged plates, and (c) the removal of the particles from the plates. The particles can be either dry dusts or liquid droplets. The air flows through the electrostatic precipitator (ESP) but the particles are left behind on the plates. The material is knocked off or washed off the plates and is collected in the bottom of the ESP. The ESP is unique among air pollution control devices in that the forces of collection act only on the particles and not on the entire air stream. This phenomenon typically results in high collection efficiency with a very low air pressure drop.

Unit Procedure Availability

● Electrostatic Precipitation Procedure

Electrostatic Precipitation: Modeling Calculations

We use the Deutsch Equation as the central equation for ESP design. The Deutsch equation relates the collection area with the efficiency of an ESP as follows:

eq. (A.123)

where:

● η is the collection efficiency of the ESP

● C_out is the concentration of particles in the outlet stream (g/L)

● C_in is the concentration of particles in the inlet stream (g/L)

● w is the terminal velocity of the particles under the collection field (m/min)

● A is the overall collection area (m²)

● Q is the volumetric flow of the inlet stream (m³/min)

In case we want to distinguish among several particle ranges, each with a different typical average diameter (and therefore a distinct drifting velocity), the overall efficiency will be a weighted sum of all efficiencies, where the mass fraction of each range is used as the weight in the summation.

The Deutsch equation can be derived by considering the continuity equation for particles flowing between two collection plates, in one collection section, separated by a given distance, and taking into account the fact that the only removal mechanism is a particle flux (with velocity equal to the drift velocity) perpendicular to the flow and towards the plates. More precisely, the Deutsch equation relies on the following assumptions:

Gases (and particles) move in the direction of the flow (-x) with constant velocity and no longitudinal mixing.

The particles are uniformly distributed in the other two directions (-y and -z).

The charging and collecting fields are constant and uniform; the particles quickly attain terminal velocity w in the y direction.

Re-entrainment of collected particles is negligible.

If the user does not set the drifting velocities, they are calculated based on field strength data and the permitivity of the flowing gas and several properties of the particles, as follows:

eq. (A.124)

where:

● d_pi is the diameter of a particle in the i-th range (in m)

● ε is the relative dielectric constant of the gas

● ε₀ is the permitivity of free space (constant; 8.85E-12 C/V-m)

● ρ_p is the density of the particles (in g/L)

● E_ch is the strength of the charging field (in V/m)

● c₀ is the strength of the collecting field (in V/m)

● τ_i’ is the slip-corrected, characteristic time the particles (in s)

The characteristic time of a particle with a given diameter is calculated as follows:

eq. (A.125)

where:

● μ is the viscosity of the gaseous phase

● ρ is the density of the particles (in g/L)

● C_Di is the drag coefficient of a particle in the i-th range

● C_i’ is the slip-correction (Cunningham) factor

● Re_i is the Reynolds Number

The Reynolds number is given by:

eq. (A.126)

The drag coefficient is estimated from an empirical correlation with Re, and the slip correction factor (Cunningham factor) is calculated from the gas’s mean free path and the particle’s diameter.

Equipment Sizing

In Design Mode of calculation we must first understand the role of the overall efficiency percentage. As described in the input data section, the user has to declare which components are likely to be removed by the ESP. Then, by default, the model estimates an overall efficiency of solids retention, using particle size data and the Deutch equation. Then the model makes the assumption that all components withheld by the ESP are evenly distributed in all particle ranges, and sets the removal efficiency for each component set to be removed, to be equal to the overall efficiency. If this assumption is not adequate, the user can specify his/her own removal percentages for each component, and then the program will calculate the overall efficiency.

During design mode, typically there is some design constraint that restricts the size of each equipment selected. In this case, the design constraint is a maximum limit for the sizing of the collection plates’ width and height.

In summary, an electrostatic precipitator step in design mode calculates as follows:

Given

● Particle Drift Velocities (Set or calculated)

● Aspect Ratio

● Number of Sections

● Corona Power Consumption Data

● Fan Efficiency

● Overall Pressure Drop,

and,

● Overall Retention Efficiency (Set or calculated)

● Linear Velocity

● Max Plate Height

● Max Plate Width

● Calculate

● Number of Units Required

● Number of Ducts in Each Unit

● Plate Separation in Each Unit

● Plate Length

● Plate Height

In Rating Mode, the component retention coefficients are always calculated by the program and set equal to the (calculated) overall efficiency of the ESP.

In summary, an electrostatic precipitator step set in rating mode calculates as follows:

Given

● Particle Drift Velocities (Set or calculated)

● Aspect Ratio

● Number of Sections

● Corona Power Consumption Data

● Fan Efficiency

● Overall Pressure Drop,

and,

● Number of Units Required

● Number of Ducts in Each Unit

● Plate Separation in Each Unit