Formula
Verhoff and Banchero (1974), partial pressures in mmHg:
\(\frac{1000}{T_{dp}} = 2.276 - 0.02943\,\ln p_{H_2O} - 0.0858\,\ln p_{SO_3} + 0.0062\,\ln p_{H_2O}\,\ln p_{SO_3}\)
\(p_{H_2O} = y_{H_2O}\,p \qquad p_{SO_3} = y_{SO_3}\,p\)
SO₃ estimated from the fuel: sulphur burns to SO₂ one mole per mole, a fraction \(f_{SO_3}\) oxidises further:
\(y_{SO_2} = \frac{S / M_S \cdot V_m}{V_g} \qquad y_{SO_3} = f_{SO_3}\, y_{SO_2}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(T_{dp}\) | sulphuric acid dew point | K |
| \(y_{H_2O}\) | water vapour in wet flue gas, volume fraction | – |
| \(p\) | absolute flue gas pressure | Pa |
| \(\text{mode}\) | SO₃ estimated from fuel sulphur, or entered | – |
| \(S\) | sulphur in the fuel as fired, mass fraction | – |
| \(M_S\) | molar mass of sulphur, 32.06 | kg/kmol |
| \(V_m\) | molar volume at 0 °C and 101.325 kPa, 22.414 | Nm³/kmol |
| \(V_g\) | wet flue gas volume per kg fuel | Nm³/kg |
| \(f_{SO_3}\) | fraction of SO₂ converted to SO₃ | – |
| \(y_{SO_2}\) | SO₂ in wet flue gas, volume fraction | – |
| \(y_{SO_3,in}\) | SO₃ entered directly, volume fraction | – |
| \(y_{SO_3}\) | SO₃ used in the correlation | – |
| \(p_{H_2O}\) | partial pressure of water vapour (converted to mmHg in the correlation) | Pa |
| \(p_{SO_3}\) | partial pressure of SO₃ (converted to mmHg in the correlation) | Pa |
Method and standards
The Verhoff–Banchero correlation is the form used in ASME PTC 4.3 and most boiler design practice. It was fitted to measured dew points with partial pressures in mmHg; the calculator converts the SI partial pressures to mmHg (1 mmHg = 133.322 Pa) before taking the logarithms. Entering the pressures in atmospheres instead, a common mistake, gives dew points about 125 K too low.
Assumptions and limits
- Fitted range roughly 5–15 % H₂O and 1–100 ppm SO₃; outside it the result is indicative.
- The SO₂ estimate assumes all fuel sulphur reaches the gas (no sulphur retained in ash or sorbent). For fluidised beds with limestone, enter the measured SO₂ or SO₃ directly.
- A separate water dew point governs when SO₃ is nil.
References
- Verhoff & Banchero (1974)
- ASME PTC 4.3 air heaters
Questions and answers
Why does the dew point depend so weakly on water but strongly on SO₃?
In the correlation the SO₃ term has a coefficient three times that of water, and SO₃ varies over orders of magnitude (1 to 50 ppm) while water varies by a factor of two. Doubling SO₃ raises the dew point about 8 K; doubling water raises it about 3 K.
How much SO₂ converts to SO₃?
Typically 1–3 % in coal-fired boilers, more with vanadium-bearing heavy fuel oil (2–5 %) and across SCR catalysts (0.5–1.5 % additional). It is the least certain input; try the range.
What metal temperature should I design for?
Keep the cold-end minimum metal temperature at or above the acid dew point plus a margin (commonly 10–15 K). Corrosion rate peaks 20–40 K below the dew point, not at it.