Boiler Efficiency
Calculate the thermal efficiency of a boiler by the direct method, η = (m_steam × Δh) ÷ (m_fuel × LHV) × 100%, comparing the useful heat absorbed by the water/steam (steam flow × enthalpy gain) with the energy released by burning the fuel (fuel flow × lower heating value). The result, in %, shows how much fuel energy actually reached the steam; the rest is lost in flue gases, blowdown, radiation and unburnt fuel. Well-run industrial boilers reach 80–90%. Enter the steam flow, enthalpy gain, fuel flow and LHV.
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Boiler efficiency
The boiler is the heart of a steam power plant: inside it the chemical energy of the fuel becomes heat that turns water into high-pressure steam. Efficiency measures how much of that energy actually reaches the steam. The direct method compares input and output: η = (m_steam × Δh) ÷ (m_fuel × LHV) × 100%. The numerator is the useful heat — the steam flow multiplied by the enthalpy gain of the water (from the feedwater state up to the steam produced). The denominator is the fuel energy — the fuel flow times its lower heating value (LHV), the heat released on burning once the energy carried away by the water formed has been discounted. The gap between 100% and the efficiency corresponds to the losses: hot flue gases (by far the largest share), blowdown, radiation through the walls and unburned fuel. Well-tuned industrial boilers run at 80–90%; economizers and air preheaters recover heat from the flue gas to push that figure up. Enter the steam flow, the enthalpy gain, the fuel flow and the LHV.
Related Tools
Stack Heat Loss (Siegert)
Calculate the heat loss through the exhaust gases by the Siegert formula, loss = K × (T_gas − T_air) ÷ CO₂, from the fuel factor K (~0.5 for natural gas, ~0.6 for oil), the gas and combustion air temperatures (°C) and the CO₂ percentage in the gases. The result, in %, is the largest energy loss of a boiler or furnace — the heat escaping hot through the stack. Lowering the gas temperature (with economizers and preheaters) and adjusting the excess air (which dilutes CO₂) minimizes this loss. The combustion efficiency is approximately 100% minus this loss. Enter the K factor, the temperatures and the CO₂.
Adiabatic Flame Temperature
Estimate the adiabatic flame temperature, T_ad = T_initial + LHV ÷ (m × cp), from the lower heating value LHV (kJ/kg fuel), the mass of combustion products per kg fuel m, the average specific heat of the gases cp (kJ/kg·K) and the initial temperature. The result, in °C, is the maximum theoretical temperature the gases would reach if all the combustion energy heated the products, with no heat loss. It is an upper bound: real flames are cooler (radiation losses, dissociation, excess air). It sets the thermal severity on materials and NOx formation. Enter the LHV, the gas mass, the cp and the initial temperature.
Steam Loss Through a Trap or Orifice (Napier)
Computes the saturated steam flow escaping through a trap stuck open or a leak hole, using the Napier formula for critical flow: ṁ = C_d · 0.5244 · A · P_abs, with the orifice area in mm² and the absolute line pressure in bar, giving kg/h. Above roughly 1.9 bar absolute the flow is choked, and from there on the rate depends only on the UPSTREAM pressure, not on downstream back pressure — which is why the loss grows linearly with line pressure and with the square of the hole diameter, and why a high-pressure line loses disproportionately more through the same defect. The constant 0.5244 kg/(h·mm²·bar) is the exact conversion of the published imperial form, ṁ[lb/h] = 51.43 · A[in²] · P[psia], and with C_d = 1 it reproduces the isentropic choked flow to within 1 %. A hole of just 3 mm at 8 bar, with a discharge coefficient of 0.7, lets 20.8 kg/h escape — over 180 tonnes of steam per year of continuous operation, the central economic argument of any steam trap maintenance programme. Enter the discharge coefficient, the orifice diameter and the absolute line pressure.
Excess Air (from Flue Gas)
Calculate the excess air of a combustion from the oxygen in dry flue gas, EA = O₂ ÷ (20.9 − O₂) × 100%, from the measured O₂ percentage in the stack. The result, in %, shows how much air was supplied beyond stoichiometric — measured by the leftover oxygen in the exhaust gases. Some excess air (10-30%) is needed to ensure complete combustion (avoid CO and soot), but too much wastes energy heating useless air that leaves hot through the stack. Gas analyzers measure O₂ and compute the excess air to optimize combustion efficiency. Enter the O₂ percentage in the gases.
Combined Cycle Efficiency
Calculate the efficiency of a gas-steam combined cycle, η_cc = η_gas + η_steam − (η_gas × η_steam ÷ 100), combining the gas turbine efficiency (Brayton, topping) with the steam cycle (Rankine, bottoming) that recovers heat from the exhaust gases. The result, in %, exceeds either cycle alone because the heat rejected by the gas turbine, instead of being wasted, raises steam for a second turbine. This is why modern combined-cycle plants top 60% efficiency, the highest in thermal generation. Enter the gas-cycle and steam-cycle efficiencies (in %).
Acid Dew Point of Flue Gas
Computes the temperature at which sulphuric acid starts to condense on the cold surfaces of a boiler, using the Verhoff and Banchero correlation: the reciprocal of the absolute dew point temperature is a combination of the logarithms of the partial pressures of water vapour and sulphur trioxide in the flue gas, plus the product of those two logarithms. The result is the thermal floor of the design — keeping the stack, the economiser and the air preheater above it is what prevents the acid corrosion that eats steel in a few weeks, and it is why heavy fuel oil boilers throw away up the stack heat they could otherwise recover. SO₃ is what rules here, not humidity, and the reason is the range each one spans: water vapour barely leaves the 5% to 15% band in a flue gas, which accounts for 11 °C end to end, while SO₃ varies by orders of magnitude with the sulphur in the fuel — going from 1 to 10 ppm alone raises the dew point by almost 22 °C. The Verhoff and Banchero correlation was adopted, with partial pressures in millimetres of mercury at atmospheric pressure, as it is the one most used in boiler design, in its original form with the interaction term between the two logarithms; the later Okkes correlation returns 1 to 8 °C lower for the same composition, so treat the value as a reference and not as an exact limit. Enter the water vapour content and the SO₃ content of the flue gas.
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