Electrostatic Precipitator Collection Efficiency (Deutsch)

The collection efficiency an electrostatic precipitator reaches, by the Deutsch equation, and what buying more of it costs. Efficiency is one minus the exponential of the plate area times the migration velocity over the gas flow, and the exponential is what governs ESP design and economics. Each equal increment of plate area removes the same FRACTION of the remaining penetration rather than the same amount of dust, so efficiency approaches 100 percent asymptotically and never reaches it -- and going from 99 to 99.9 percent requires exactly as much additional plate as going from zero to 90 percent did. That is why high-efficiency precipitators are enormous and why the last increment of performance is the expensive one, and it is reported here as a per-decade area rather than left as an observation. The migration velocity is the weak input and it is entered rather than predicted. It is the speed at which charged particles drift toward the plate, and it depends on particle size, on the electrical field, and above all on the dust's RESISTIVITY -- so in practice it is fitted backwards from the performance of a similar installation on a similar dust rather than calculated from first principles. A Deutsch calculation is therefore only as good as the migration velocity it was given, and quoting one to three figures overstates what is known. Resistivity is the dominant variable in real performance and it cuts both ways. Too high and the collected layer holds its charge, the field across it breaks down, and back corona destroys collection; too low and particles lose their charge on contact and re-entrain. Conditioning the gas, usually by temperature or by an additive, is how resistivity is managed, and it can matter more than plate area. Rapping is the other loss: the plates must be rapped to release the cake, and each rap re-entrains some of it, which is why measured efficiency falls short of the Deutsch value. The modified Deutsch-Anderson form with a fitted exponent is often used instead for that reason. This is a screening calculation on an ENTERED migration velocity; it does not model resistivity, conditioning, rapping re-entrainment, sneakage around the fields, or gas distribution, and it does not size the fields, the transformer-rectifier sets or the hoppers. The precipitator manufacturer's data and a qualified air quality engineer govern.

Deutsch: efficiency = 1 - exp(-A w / Q) with the flow on a per-second basis; the area a target needs is -ln(1 - target) x Q / w; and the area per factor of ten off the penetration is ln(10) x Q / w, the same for every decade.

The Deutsch equation for electrostatic precipitator collection. The migration velocity is ENTERED because it depends on particle size, field strength and above all dust RESISTIVITY, and in practice is fitted from the performance of a similar installation rather than predicted. A screening calculation: it does not model resistivity, back corona, gas conditioning, rapping re-entrainment, sneakage or gas distribution, and it does not size the fields, transformer-rectifier sets or hoppers.

One exponential; no manufacturer data is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: plate_area_ft2, gas_acfm, migration_velocity_fps, target_efficiency_pct, deutsch_exponent, efficiency_pct, penetration_pct, area_for_target_ft2, area_per_decade_ft2, area_999

• Migration velocity is entered it is fitted from performance, not predicted from first principlesa similar installation on a similar dust
• Resistivity is not modelled it is the dominant variable and is managed by conditioningthe precipitator manufacturer
• Rapping re-entrainment is not included measured efficiency commonly falls short of the Deutsch valuethe stack test