---
name: electrostatic-precipitator
description: Electrostatic precipitator (ESP) — Deutsch-Anderson equation, collection efficiency, specific collecting area, corona discharge, resistivity effects, rapping, gas flow, NFPA 496, EPA AP-42, industrial stack emission control.
metadata:
  priority: 7
  promptSignals:
    phrases:
      - "electrostatic precipitator"
      - "ESP"
      - "Deutsch Anderson"
      - "particle collection efficiency"
      - "corona discharge"
      - "dust collection ESP"
    minScore: 3
---

# Electrostatic Precipitator (ESP) — Complete Skill

## ESP Operating Principle

**Process:**
1. Inlet gas with particles enters ESP
2. Discharge electrode (corona wire) creates corona discharge → ionizes gas → negative ions
3. Ions migrate to collecting plate (positive) → charge particles in transit
4. Charged particles migrate toward collecting electrode (Coulomb force) → deposit
5. Electrodes rapped periodically → dislodge collected dust → hopper

**Particle charging:**
Field charging (d > 0.5 μm): particle in electric field accumulates ions on surface
Diffusion charging (d < 0.5 μm): thermal diffusion of ions to particle surface
Combined: most particles charged by both mechanisms

**Saturation charge (field charging):**
q_sat = 3ε/(ε+2) × π ε₀ d_p² × E  [C; ε = dielectric constant; ε₀ = 8.85×10⁻¹² F/m; d_p = particle diameter; E = field strength]

## Deutsch-Anderson Equation

**Collection efficiency:**
η = 1 - exp(-w × A / Q)  [dimensionless]
w = migration velocity [m/s]; A = collecting electrode area [m²]; Q = volumetric flow rate [m³/s]

**Effective migration velocity:**
w = q × E_p / (3π μ d_p)  [Stokes law; q = particle charge; E_p = precipitating field; μ = gas viscosity]
Typical w: 0.05–0.15 m/s for fly ash; 0.05–0.10 for cement; 0.15–0.30 for paper

**Modified Deutsch (White, accounts for gas distribution):**
η = 1 - exp(-(w/A_correction × SCA))
SCA = A/Q = specific collecting area [m²/(m³/s) = s/m]

**SCA for high efficiency:**
| Efficiency target | Required SCA [s/m] |
|------------------|-------------------|
| 90% | 15–25 |
| 99% | 30–50 |
| 99.5% | 40–70 |
| 99.9% | 80–120 |

## Corona Discharge

**Corona wire field:**
E_corona = V / (r_w × ln(R_plate / r_w))  [V/m; r_w = wire radius; R_plate = wire-to-plate half-spacing]
Onset voltage: V_onset = 3.1×10⁶ × r_w × ln(R_plate / r_w) [V; Peek's law approximation]

**Operating voltage:** 30–70 kV DC (negative corona preferred for most applications; more stable, higher efficiency)
**Spark rate:** optimal: 50–150 sparks/min (controlled by voltage regulation); sparks → momentary field collapse

**Wire-plate ESP geometry:**
Wire spacing: 300 mm typical; Plate spacing: 250–400 mm; Collection plate height: 5–15 m

**Precipitating field:**
E_p = V / S_half  [S_half = half plate spacing; average field between discharge and collecting electrode]

## Resistivity Effects

**Particle resistivity critical parameter:**
Low resistivity (< 10⁷ Ω·cm): particles discharge quickly → re-entrainment; negative corona back-ionization
Optimal resistivity: 10⁸–10¹⁰ Ω·cm
High resistivity (> 10¹⁰ Ω·cm): back corona → positive ions from surface → reduce charge → efficiency drops

**Back corona:** flashover/sparking on collecting electrode surface from high resistivity particles
Detection: rapid rise in secondary current at low voltage; erratic voltage waveform

**Resistivity control:**
Flue gas conditioning: SO₃ injection (reduces resistivity of fly ash) — 10–30 ppm SO₃ lowers resistivity from 10¹² to 10⁹ Ω·cm
Moisture injection: increases conductivity of surface film
Temperature: resistivity minimum at 150–200°C for many materials; design operation at minimum resistivity temperature

## Rapping System

**Purpose:** dislodge accumulated dust without re-entraining it
**Rap frequency:** 0.1–10 raps/hour per electrode
**Rap force:** impact generates acceleration > 100 g on electrode
**Re-entrainment:** main loss mechanism; minimize by:
  - Rap with gas flow off (intermittent flow rapping)
  - Use "sonic rapping" (vibration at resonance)
  - Collect rapped dust in hopper quickly (steep hopper angle > 55°)

**Sneakage:** gas bypassing active field (under/over electrodes)
Mitigation: gas distribution plate at inlet; anti-sneakage baffles around hoppers

## Gas Flow Distribution

**Inlet duct:** gas must be distributed uniformly across ESP cross-section
Non-uniformity → hot spots in velocity → local re-entrainment + low efficiency at high-velocity zones
**Coefficient of variation:** CV = σ_v / v̄ < 15% (target); < 25% (acceptable)
**Perforated plate:** pressure drop ΔP/q_dyn = 0.5–2.0 (achieve uniform distribution)

**Gas volume and velocity:**
Inlet velocity: 1–2 m/s (typical); > 2.5 m/s → excessive re-entrainment
Treatment time: t = L_ESP / v_gas ≈ 5–15 s (collection time)

## Sizing Example

**Given:** Q = 100 m³/s (gas flow), target η = 99.5%, w = 0.10 m/s
Required A = -Q × ln(1-η) / w = -100 × ln(0.005) / 0.10 = 100 × 5.30 / 0.10 = 5300 m²
SCA = A/Q = 53 s/m

**Physical dimensions:**
Collection plate height H = 10 m, plate length L = 10 m; plate area = 100 m²/plate pair
Number of plate pairs = A / (H × L) = 5300 / 100 = 53 plates → 26.5 plate pairs
Total ESP width = 27 × 0.3 m (plate spacing) = 8.1 m

## Emission Calculation

**Outlet particle concentration:**
C_out = C_in × (1 - η)  [mg/m³]
**Emission rate:**
ṁ_emission = Q × C_out  [g/s or kg/hr]

**US EPA emission limits:** PM2.5 from coal: 0.020 lb/MMBtu (ESP needed to achieve)
**EU ELV (for coal plants):** PM < 10–30 mg/m³ at standard conditions

## Standards

| Standard | Scope |
|---------|-------|
| NFPA 496 | Purged/pressurized equipment (electrical in dusty environments) |
| EPA AP-42 | Emission factors for EPS performance estimation |
| IEEE 548 | ESP performance |
| ASME PTC-21 | Particulate matter collection equipment performance testing |
| ASHRAE 52.2 | MERV rating for filters (alternative to ESP) |

## Output
Provide: gas flow Q [m³/s], inlet particle concentration C_in [mg/m³], target η [%] and resulting C_out [mg/m³], migration velocity w [m/s], required SCA [s/m], total collecting area A [m²], operating voltage [kV] and polarity, corona wire spacing [mm], plate spacing [mm], number of plate pairs, gas velocity [m/s] and treatment time [s], particle resistivity [Ω·cm] and back corona risk, gas conditioning method (if high resistivity), rap frequency [raps/hr], emission rate [kg/hr] and compliance with EPA/EU limit, and applicable standard (ASME PTC-21, EPA AP-42).