75.7 s/m (3,888 m² ÷ 51.4 m³/s)
Design-basis SCA
Resources · Engineering tools
ESP efficiency calculators and sizing methods
Four calculation methods, published with their formulas and worked design-basis numbers: Deutsch-Anderson ESP efficiency η = 1 − exp(−wA/Q), migration-velocity back-calculation from any quotation, economizer savings from ΔT × flow × cp, and boiler efficiency by the BS 845 indirect method. Reproduce our arithmetic — or check anyone else's.
w ≈ 4.5 cm/s
Back-calculated migration velocity
≈ 15.3 cm/s
Matts-Öhnfeldt wk (k ≈ 0.5)
24 mg/Nm³ @ 6 % O₂ dry
Design-basis ESP outlet
01 — The calculator set
Four methods, stated in full
The formulas are the content. Interactive versions follow; the arithmetic works today with a hand calculator.
This page documents the four calculations Arrow Energy uses daily: ESP efficiency and sizing by Deutsch-Anderson, migration-velocity back-calculation for checking any quotation, economizer savings, and boiler efficiency by the indirect (losses) method. Each is stated with its formula and worked through with the numbers of the standing design basis used across this site and the electrostatic precipitator pillar. Everything here is part of the open engineering resources; terms are defined in the ESP terminology glossary. CONFIRM: interactive calculators to be wired at build
| Calculator | Inputs | Output | Governing relation |
|---|---|---|---|
| ESP efficiency (Deutsch-Anderson / SCA) | w (m/s), A (m²), Q (m³/s) | η, % | η = 1 − exp(−wA/Q) |
| Migration-velocity back-calculation | A, Q, measured or quoted η | w, cm/s | w = −(Q/A) · ln(1 − η) |
| Polydisperse correction (Matts-Öhnfeldt) | wk, SCA, k ≈ 0.5 | η, % | η = 1 − exp[−(wk · SCA)0.5] |
| Economizer savings | V̇ (Nm³/s), cp (kJ/Nm³·K), ΔT (K) | Q̇, kW | Q̇ = V̇ · cp · ΔT |
| Boiler efficiency, indirect method | Flue-gas O₂ and temperature, fuel analysis | ηboiler, % | η = 100 − Σ losses (BS 845) |
02 — ESP efficiency
Deutsch-Anderson and specific collecting area
One exponential relation carries the whole sizing argument.
How do I calculate ESP collection efficiency?
Apply the Deutsch-Anderson equation, η = 1 − exp(−w·A/Q): w is the effective migration velocity of charged particles toward the plates (m/s), A the collecting-plate area (m²), Q the gas volume flow (m³/s). The ratio A/Q is the specific collecting area, SCA (s/m) — the single strongest sizing lever an ESP has.
DESIGN BASIS — ILLUSTRATIVE CALCULATION, NOT A GUARANTEE · all concentrations @ 6 % O₂ dry
- Collecting area A
- 3,888 m²
- Gas flow Q
- 51.4 m³/s (= 3,888 ÷ 75.7)
- SCA = A/Q
- 75.7 s/m
- Migration velocity w
- 0.0449 m/s (4.5 cm/s)
- η = 1 − exp(−0.0449 × 75.7)
- = 1 − exp(−3.40) = 96.67 %
- Outlet: 720 mg/Nm³ × (1 − 0.9667)
- = 24 mg/Nm³
The same relation prices redundancy. With one of four fields out of service, SCA falls to 56.8 s/m and, at unchanged w, η = 1 − exp(−0.0449 × 56.8) = 92.2 % — an outlet of 57 mg/Nm³ from the same 720 mg/Nm³ inlet. That is the n−1 figure quoted throughout this site, and it drops out of the formula rather than being asserted. Note what the exponential implies: each equal increment of SCA cuts penetration by the same factor, so the last milligram is always the most expensive one.
03 — Back-calculation
Migration velocity: the honesty check for any quotation
Invert the equation and every ESP quote becomes testable.
Rearranged, Deutsch-Anderson gives w = −(Q/A) · ln(1 − η). Take any quotation's collecting area, design gas flow and promised efficiency, and out comes the migration velocity the vendor is implicitly claiming for your dust. For the design basis: w = −(1/75.7) × ln(0.0333) = 3.40/75.7 = 0.0449 m/s. Effective values for biomass fly ash typically fall around 4–15 cm/s depending on resistivity and particle size; an offer whose numbers imply substantially more deserves the question "measured where, on what dust?"
How accurate is the Deutsch-Anderson equation?
It is exact only for its own assumptions — uniform gas distribution, a single migration velocity, no re-entrainment, no sneakage. Real dust is polydisperse: the easy coarse particles vanish in the first field and the surviving fines migrate slower, so measured efficiency undershoots the ideal curve at high SCA. Practical sizing therefore uses the Matts-Öhnfeldt form, η = 1 − exp[−(wk·SCA)k] with k ≈ 0.5.
The flattened exponent models the progressive hardening of the residual dust. Back-calculating the design basis in Matts-Öhnfeldt terms: (wk × 75.7)0.5 = 3.40 requires wk ≈ 0.153 m/s. The k ≈ 0.5 form is the honest planning curve for upgrades — it is why doubling SCA does not halve the outlet twice over, and why the ESP upgrade service sizes added fields from measured, not brochure, performance.
04 — Heat recovery
Economizer savings: ΔT × flow × cp
Three numbers you already have, multiplied.
Recovered duty is Q̇ = V̇ · cp · ΔT — flue-gas flow times volumetric heat capacity times the stack-temperature drop. Illustratively, on the design basis: taking the 51.4 m³/s flow at an operating temperature near 160 °C corresponds to ≈ 32.4 Nm³/s (× 273/433); with cp ≈ 1.38 kJ/Nm³·K and a stack drop from 203 °C to 160 °C (ΔT = 43 K), Q̇ ≈ 32.4 × 1.38 × 43 ≈ 1,900 kW into feedwater. The rule-of-thumb cross-check agrees in direction: every ~20 °C of stack reduction is worth about 1 percentage point of boiler efficiency, and full economizer retrofits typically return 3.1–4.0 pp. The lower bound on stack temperature is corrosion, not ambition — the calculation is always run against the acid-dewpoint margin, working the 203 °C stack toward the 55 °C margin rather than through it.
05 — Boiler efficiency
Indirect method: efficiency as 100 minus the losses
You cannot manage a loss you have not itemised.
The indirect (losses) method per BS 845 practice computes η = 100 − Σ losses, itemised as: dry flue-gas loss (sensible heat in stack gas — set by stack temperature and excess air), loss due to moisture in fuel, loss due to hydrogen in fuel (both latent-heat terms), loss due to unburned combustible in ash, loss due to CO in flue gas, and radiation and unaccounted losses. It beats the direct method on solid fuels because fuel-flow measurement of bagasse or rice husk is unreliable, while flue-gas O₂ and temperature are cheap to measure well — and because each loss line is itself an action item.
On a ~50 % moisture bagasse (LHV 7.2–7.5 MJ/kg) the moisture-in-fuel term dominates and is fixed by the fuel; the recoverable lines are the dry flue-gas loss (attack with heat-recovery surface) and the excess-air multiplier on it — trimming toward λ ≈ 1.15 is typically worth 0.7–0.8 percentage points on biomass units running high excess air. A measured loss map on this method is the first deliverable of the plant energy audit. CONFIRM: interactive calculators to be wired at build
FAQ
Engineering questions, answered
How do I calculate electrostatic precipitator efficiency?
Use the Deutsch-Anderson equation: η = 1 − exp(−wA/Q), with w the migration velocity in m/s, A the collecting area in m² and Q the gas flow in m³/s. In the design basis, w = 0.0449 m/s and SCA = A/Q = 75.7 s/m give η = 96.67 %, taking 720 mg/Nm³ down to 24 mg/Nm³ at 6 % O₂ dry.
What migration velocity should I assume for biomass fly ash?
Do not assume — back-calculate. From any real installation, w = −(Q/A) × ln(1 − η). Our bagasse design basis yields 4.5 cm/s; effective values for biomass fly ash typically fall in the 4–15 cm/s range depending on resistivity and particle size. A quotation whose promised outlet implies a higher w than the dust supports is optimistic.
How do I estimate economizer fuel savings?
Recovered duty is flow × volumetric heat capacity × temperature drop: Q̇ = V̇ × cp × ΔT. Illustratively, 32.4 Nm³/s of flue gas × 1.38 kJ/Nm³·K × 43 °C ≈ 1.9 MW into feedwater. As a cross-check, each ~20 °C of stack reduction is worth about 1 percentage point of boiler efficiency; economizer retrofits typically return 3.1–4.0 pp.
Send us your plant data
Fuel, boiler capacity, gas flow, current emission and the limit you must meet. An Arrow engineer replies with a technical assessment basis — not a brochure.