Air Pollution Control, Power-Plant Flue Gas & Electrostatic Separation
Deutsch-Anderson Electrostatic Precipitator (ESP) SCA Formula
Calculate Electrostatic Precipitator Specific Collection Area (s/m), Deutsch-Anderson Collection Efficiency (%), Outlet Stack Dust Concentration (mg/m³), and Plate Area Required for 99.9% Removal (m²).
Why jumping from 99.0% to 99.9% ESP capture requires +50% more steel plate area—not +1%!
Under the Deutsch-Anderson Equation, electrostatic precipitator (ESP) dust capture follows exponential decay eta = 1 - EXP(-w_e * SCA), where Specific Collection Area is SCA = A_plate / Q_gas (m² per m³/s = s/m) and w_e (m/s) is the effective electrostatic drift migration velocity! Because outlet penetration P = 1 - eta = EXP(-w_e * SCA) scales logarithmically, cutting stack emissions 10-fold from 99.0% capture (P = 0.01) to 99.9% capture (P = 0.001) increases LN(1 / P) from 4.605 to 6.908—requiring 1.50x (+50%) more grounded steel collecting plate area!
Verify on a 100 m³/s Utility Boiler ESP—Total_Plate_Area = 4,800 m² (B2), Flue_Gas_Flow = 100.0 m³/s (B3 -> SCA = 48.00 s/m in E2), Effective_Migration_Velocity w_e = 0.10 m/s (10 cm/s, B4), and Inlet_FlyAsh_Loading = 10.0 g/m³ (10,000 mg/m³, B5): Deutsch-Anderson Collection Efficiency reaches (1 - EXP(-4.8)) * 100 = 99.18% (E3), Outlet Stack Dust Concentration drops to 10,000 * EXP(-4.8) = 82.30 mg/m³ (E4), and Plate Area Required for 99.9% Capture equals -(100 / 0.10) * LN(0.001) = 6,907.76 m² (E5)!
| Deutsch-Anderson ESP Metric (4,800 m² Plate, 100 m³/s, w_e = 0.10 m/s, 10 g/m³) | Formula | Verified Output |
|---|---|---|
| Specific Collection Area SCA (s/m) | Total_Plate_Area_m2 / Gas_Flow_m3_s | 48.00 s/m |
| ESP Collection Efficiency (%) | (1 - EXP(-w_e * SCA)) * 100 | 99.18% (94.39% High-Resistivity) |
| Outlet Stack Dust Loading (mg/m³) | Inlet_g_m3 * 1000 * EXP(-w_e * SCA) | 82.30 mg/m³ (561.35 mg/m³ @ 0.06) |
| Plate Area for 99.9% Capture (m²) | -(Q_gas / w_e) * LN(1 - 0.999) | 6,907.76 m² |
Deutsch-Anderson Exponential ESP Efficiency Formula
Validate Plate_Area > 0, Gas_Flow > 0, Migration_Velocity in (0, 1.0], and Inlet_Loading > 0!
=LET(ar_p, B2, q_fl, B3, w_em, B4, c_in, B5, IF(OR(ar_p <= 0, q_fl <= 0, w_em <= 0, w_em > 1, c_in <= 0), "Invalid ESP Design Input", LET(sc_a, ar_p / q_fl, ROUND((1 - EXP(-w_em * sc_a)) * 100, 2))))Low-Sulfur Coal Back-Corona Check (Set Migration Velocity w_e = 0.06 m/s)
Switch to low-sulfur high-resistivity coal that depresses w_e B4 from 0.10 m/s down to 0.06 m/s: Collection Efficiency E3 falls from 99.18% to 94.39%, causing stack dust emissions E4 to surge nearly 7x from 82.30 mg/m³ to 561.35 mg/m³!
=IF(ISTEXT(E3), E3, ROUND(B5 * 1000 * EXP(-B4 * (B2 / B3)), 2))Try the example
Use the original values or change them to test your understanding.