Introduction
A scrubber efficiency formula predicts how much of a target pollutant your wet scrubber removes — before you build it, before you test it, and before the regulatory agency asks for the numbers. The two most common approaches are the empirical removal rate model (η = 95%, simple but imprecise) and the mass transfer unit model (NTU × HTU = packing height, rigorous but requiring more data). This guide covers both: the quick removal rate formula that engineers use for initial sizing, and the NTU/HTU model that determines packing height from first principles — inlet concentration, outlet target, L/G ratio, and the overall mass transfer coefficient Ka. The target audience is process engineers who need to specify a scrubber from a datasheet, not researchers writing a paper. Every formula below is expressed with industrial units (mg/Nm³, L/m³, m) rather than laboratory units (mol/m³, dimensionless), and each worked example uses a real exhaust scenario. For the complete scrubber sizing methodology that uses these formulas, see our PP wet scrubber sizing guide.
Key Takeaways
– The simplest scrubber efficiency formula is the removal rate: η = (Cin − Cout) / Cin × 100%. For HCl, 95–99% removal is standard. For H₂S, 90–97%. For NH₃, 95–99%.
– NTU (Number of Transfer Units) measures how hard the scrubber must work: higher inlet/outlet concentration ratios require more NTUs. NTU = ln(Cin/Cout) / (1 − 1/A), where A is the absorption factor.
– HTU (Height of a Transfer Unit) measures packing efficiency: higher Ka values mean shorter HTU and less packing height needed. Typical HTU for PP pall rings: 0.3–0.8 m.
– Required packing height = NTU × HTU. For 95% HCl removal with standard PP pall ring packing, NTU ≈ 3, HTU ≈ 0.5 m, packing height ≈ 1.5 m. Add 20% safety margin for design.
– L/G ratio is the master variable — increasing L/G from 2 to 5 L/m³ reduces HTU (improves mass transfer) but increases pumping cost and wastewater volume.
Removal Rate Formula — The Quick Sizing Model
The removal rate is the simplest scrubber efficiency formula and the one most commonly used in early-stage system sizing. It defines efficiency as the fraction of inlet pollutant mass that the scrubber captures:
η = (Cin − Cout) / Cin × 100%
Where η is removal efficiency (%), Cin is inlet pollutant concentration (mg/Nm³), and Cout is outlet concentration (mg/Nm³).
This formula answers the question: “What removal efficiency must the scrubber achieve to meet the emission limit?” — which is then used to select packing height and L/G ratio from empirical tables.
Worked Example: HCl Scrubbing
Given: Electroplating pickling exhaust, inlet HCl = 150 mg/Nm³, local emission limit = 10 mg/Nm³ (CPCB standard).
Required removal rate:
η = (150 − 10) / 150 × 100% = 93.3%
Design target: 95% minimum (add 2% margin above regulatory minimum to account for measurement uncertainty and operating drift). For EU BAT-AEL compliance (3 mg/Nm³), the required efficiency jumps to 98%, which demands a taller packing bed.
Removal Rate by Pollutant
| Pollutant | Typical Inlet | Common Outlet Target | Required η | Packing Height (PP pall rings) |
|---|---|---|---|---|
| HCl | 50–2,000 mg/Nm³ | 5–10 mg/Nm³ | 90–99% | 1.5–3.0 m |
| H₂S | 50–1,000 ppm | 1–5 ppm | 95–99% | 2.0–3.5 m |
| SO₂ | 500–3,000 mg/Nm³ | 35–200 mg/Nm³ | 90–98% | 2.5–4.0 m |
| NH₃ | 100–2,000 ppm | 1–5 ppm | 95–99% | 1.5–3.0 m |
| Chrome mist (CrO₃) | 0.05–0.5 mg/Nm³ | 0.005 mg/Nm³ | 90–99% | 2.0–3.0 m + mist eliminator |
Limitations of the removal rate model: The removal rate does not account for the specific packing type, L/G ratio, gas velocity, or temperature — all of which affect actual performance. A 95% efficient scrubber at L/G = 2 L/m³ with 2 meters of structured packing is not the same system as a 95% efficient scrubber at L/G = 5 L/m³ with 1.5 meters of random packing. The NTU/HTU model provides the engineering rigor to distinguish these designs.
NTU/HTU Model — The Mass Transfer Approach
The NTU/HTU model is the standard engineering scrubber efficiency formula for sizing packed bed scrubbers from first principles — documented in the EPA wet scrubber design guidelines and widely used in industrial practice. It accounts for the specific packing type, liquid and gas flow rates, and pollutant-specific mass transfer characteristics.
Key Definitions
NTU (Number of Transfer Units) — a dimensionless number representing how many “ideal stages” of gas-liquid contact the scrubber must provide. Higher inlet/outlet ratios require more NTUs. For a dilute system (pollutant concentration < 2% by volume), the simplifying assumption of linear equilibrium applies:
NTU = ln(Cin / Cout) / (1 − 1/A)
Where A is the absorption factor:
A = L / (G × m)
Where L is liquid flow rate (mol/s), G is gas flow rate (mol/s), and m is the dimensionless Henry’s law equilibrium constant for the specific pollutant-solvent system at the operating temperature.
HTU (Height of a Transfer Unit) — the packing height required to achieve one NTU of mass transfer. Lower HTU means the packing is more efficient (more contact area per meter):
HTU = G / (Ka × a × Ω)
Where G is gas molar flow rate (mol/s), Ka is the overall gas-phase mass transfer coefficient (mol/m²·s), a is the specific surface area of the packing (m²/m³), and Ω is the scrubber cross-sectional area (m²).
Required packing height:
Z = NTU × HTU
Worked Example: H₂S Scrubbing at a Biogas Plant
Given:
– Biogas exhaust: 5,000 CFM (2,360 L/s at operating conditions)
– Inlet H₂S: 300 ppm (target outlet: 2 ppm)
– Scrubbing liquid: NaOH solution at pH 9, L/G = 3 L/m³
– Packing: 25mm PP pall rings, specific surface area a = 210 m²/m³
– Henry’s law constant for H₂S at 30°C: m = 0.4
– Ka for H₂S in NaOH: 1.8 × 10⁻³ mol/m²·s
Step 1 — Absorption factor:
A = L / (G × m) = 3.0 / (1.0 × 0.4) = 7.5
(High A means caustic is in excess — favorable for removal)
Step 2 — NTU:
NTU = ln(300/2) / (1 − 1/7.5) = ln(150) / 0.867 = 5.01 / 0.867 = 5.8
Step 3 — HTU (using scrubber diameter 1.4 m, Ω = 1.54 m²):
HTU = 2,360 / (1.8×10⁻³ × 210 × 1.54) = 2,360 / 0.581 = 0.58 m
Step 4 — Packing height:
Z = 5.8 × 0.58 = 3.36 m → add 20% safety margin → 4.0 m
Design: two packed beds of 2.0 m each, with an intermediate liquid redistribution tray between them.
For a simpler sizing approach using standard model selection charts, see our PP wet scrubber sizing guide.
L/G Ratio — The Master Variable
The liquid-to-gas ratio (L/G) is the single most influential parameter in any scrubber efficiency formula. It determines the HTU (packing efficiency), the caustic consumption, the pumping energy, and the wastewater volume — all at once.
L/G is defined as:
L/G = Liquid flow rate (L/min) / Gas flow rate (m³/min) → units: L/m³
L/G Ratios by Pollutant
| Pollutant | Recommended L/G (L/m³) | Why |
|---|---|---|
| HCl | 1.5–3.0 | Highly water-soluble, fast reaction with NaOH. Low L/G sufficient. |
| H₂S | 2.0–5.0 | Moderate solubility, higher L/G needed for complete absorption. |
| SO₂ | 3.0–8.0 | Lower solubility than HCl; needs more liquid contact. |
| NH₃ | 1.5–3.0 | Highly water-soluble, rapid reaction with H₂SO₄. |
| Chrome mist | 2.0–4.0 | Aerosol capture requires liquid droplets, not just film. |
The trade-off: Increasing L/G from 2 to 5 L/m³ reduces HTU by approximately 40% (shorter packing height for the same removal) but increases pumping energy by 2.5× and wastewater volume by 2.5×. The optimal L/G is the one that achieves the target removal efficiency with the minimum total cost (capital + operating).
For detailed operating cost projections by L/G ratio, see our gas scrubber operating cost analysis.
Pressure Drop and Gas Velocity — The Flooding Limit
The empty tower gas velocity (v) and pressure drop (ΔP) through the packed bed are the operational boundaries of any scrubber efficiency formula:
v = Q / (A × 3600)
Where v is empty tower velocity (m/s), Q is gas flow rate (m³/h), and A is cross-sectional area (m²).
Operating Envelope
| Parameter | Minimum | Optimal | Maximum (Flooding) |
|---|---|---|---|
| Empty tower velocity | 0.8 m/s | 1.2–2.0 m/s | 2.5–3.0 m/s |
| Pressure drop (random packing) | 200 Pa/m | 400–600 Pa/m | >1,000 Pa/m |
| Pressure drop (structured packing) | 100 Pa/m | 200–400 Pa/m | >600 Pa/m |
Below the minimum velocity, liquid channeling occurs — the scrubbing liquid preferentially flows down the wall rather than through the packing, and the gas bypasses through dry channels in the center of the bed. This reduces actual removal efficiency below the calculated value by 20–40%.
Above the flooding velocity, the packing cannot drain the liquid fast enough — the bed fills with liquid, pressure drop rises sharply, and the scrubber operates as a bubble column rather than a packed bed. Flooding destroys removal efficiency and can damage the scrubber internals.
The optimal operating point is approximately 60–70% of the flooding velocity — high enough for effective mass transfer, low enough for stable operation with margin for flow variations.
For scrubber model selection charts covering the full 3,000–45,000 m³/h range with pre-calculated velocities and pressure drops, see our PP wet scrubber sizing guide.
Frequently Asked Questions
What is the difference between removal efficiency and NTU?
Removal efficiency (η) is a single number describing what percentage of the inlet pollutant the scrubber removes — easy to understand but does not tell you how to design the scrubber. NTU is a dimensionless design parameter that tells you how many “stages” of mass transfer are needed for a given inlet/outlet concentration ratio. NTU is used with HTU to calculate the required packing height, which is the physical dimension that drives scrubber sizing.
How do I calculate HTU for a specific packing type?
HTU depends on the packing’s specific surface area (a), the overall mass transfer coefficient (Ka), and the gas flow rate. For 25mm PP pall rings at L/G = 3 L/m³, HTU is approximately 0.4–0.7 m for soluble gases (HCl, NH₃) and 0.6–1.0 m for moderately soluble gases (H₂S, SO₂). The packing manufacturer’s datasheet provides Ka values for specific pollutant-solvent systems. For a simpler approach, the worked example above shows the full calculation.
Can I use the same formula for all pollutant gases?
The formulas are the same, but the parameters differ by pollutant: Henry’s law constant (m), mass transfer coefficient (Ka), and recommended L/G ratio are all pollutant-specific. A scrubber sized for HCl at L/G = 2 L/m³ will underperform for SO₂ at the same L/G because SO₂ is less water-soluble. The pollutant comparison table above provides the L/G and packing height ranges.
What packing height achieves 99% removal?
For a highly soluble gas like HCl at L/G = 3 L/m³ with 25mm PP pall rings: NTU ≈ 4.6, HTU ≈ 0.5 m, packing height ≈ 2.3 m. Add 20% safety → 2.8 m total. For a moderately soluble gas like H₂S at the same conditions: NTU ≈ 6.9, HTU ≈ 0.7 m, packing height ≈ 4.8 m → 5.8 m total. The difference illustrates why SO₂ and H₂S require significantly taller scrubbers than HCl for the same removal efficiency.
What Ka value should I use for my scrubber design?
Ka depends on the packing type, L/G ratio, gas velocity, and pollutant-solvent system. Published values for PP pall rings: HCl/NaOH: 1.5–2.5 × 10⁻³ mol/m²·s; H₂S/NaOH: 1.0–2.0 × 10⁻³ mol/m²·s; SO₂/NaOH: 0.8–1.5 × 10⁻³ mol/m²·s. Structured packing has 20–40% higher Ka than random packing at equivalent L/G. If Ka data is unavailable for your specific system, the empirical removal rate model with safety margins provides a workable design basis.
Conclusion
The scrubber efficiency formula you use depends on your design stage: the removal rate model (η = (Cin − Cout) / Cin) for initial sizing and vendor discussions, and the NTU/HTU model (Z = NTU × HTU) for detailed engineering design where packing type, L/G ratio, and gas velocity must be specified precisely. The L/G ratio is the master variable that determines mass transfer efficiency, caustic consumption, and operating cost — optimizing L/G is where the most engineering value is created. For the complete scrubber sizing methodology using standard model selection charts, see our PP wet scrubber sizing guide. Send us your exhaust composition and emission targets, and we will calculate the packing height, tower diameter, and operating cost for your specific application — at factory-direct pricing.
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Written by Corbin, a senior process engineer whose career has spanned over a decade designing and sizing wet scrubbers for HCl, H₂S, SO₂, NH₃, and chrome mist across three continents. Every formula, parameter range, and worked example in this article is drawn from documented outcomes of our 500+ completed installations.
