COMBUSTION ENGINEERING / ENGINEERING GUIDE

How to Calculate Flue Gas Volume from Fuel Composition

Reviewed by WattCostLab Editorial Team · Updated September 2, 2026

Flue-gas volume can be built from the major species terms calculated from ultimate analysis, air humidity and excess air, then summed to obtain stoichiometric or real gas volume.

Build flue gas from its calculated components

The WattCostLab solid-fuel model calculates major gas-volume terms separately and then sums them. At the stoichiometric baseline, the total is:

Each component is linked to the corresponding ultimate-analysis input and, for water and nitrogen, to the combustion-air terms.

Carbon dioxide term

In the numerical implementation, C is converted from percent to mass fraction by division by 100. This term represents the carbon-dioxide volume associated with the model's carbon conversion assumption.

Water-vapor term

Water vapor contains contributions from fuel hydrogen, fuel moisture W and moisture carried with the combustion air. This is why the total gas volume is a wet-gas result rather than a dry-gas-only result.

Sulfur dioxide term

The source model includes sulfur as sulfur dioxide in this major-species volume calculation.

Nitrogen term

This includes both fuel nitrogen and the nitrogen brought in with theoretical dry air.

Real flue gas with excess air

For λ different from 1, the model scales the air-derived nitrogen and humid-air water terms and includes residual oxygen:

Worked baseline example

Using the default WattCostLab input set and λ = 1, the component sum produces 9.30597815625 m³N/kg fuel. Because λ = 1, the real-flue-gas and stoichiometric-flue-gas totals coincide in this example.

If the fuel flow B is 1 kg/h, the calculated flue-gas flow is 9.30597815625 m³N/h. If B is doubled while all composition and air inputs stay constant, the flow doubles.

Why composition matters

Different fuels produce different gas volumes because carbon, hydrogen, oxygen, sulfur, nitrogen and moisture enter different parts of the equations. A fuel name by itself is not enough. The calculator does not apply a hidden “coal factor” or “biomass factor”; it calculates from the entered ultimate analysis.

What is outside this flue-gas model

The calculation does not perform equilibrium chemistry and does not predict NOx, CO, hydrocarbons, particulate matter, acid-gas chemistry beyond the listed SO₂ term or species formed by incomplete combustion. It is a transparent volume model for the species included in the cited source.

Scientific basis

The full species equations and gas-volume sequence follow Paraschiv, Serban and Paraschiv, Energy Reports 6(Suppl. 3), 36–45 (2020). DOI: 10.1016/j.egyr.2019.10.016.

Component-by-component calculation is easier to audit

Rather than jumping directly to total flue gas, calculate each species term and keep the units beside it. This makes it possible to identify which input caused a change. If carbon changes, V_CO₂ should respond. If W changes in a normalized analysis, the water term responds directly and other terms may respond because the other mass fractions must also change. If λ changes, the real-gas air terms respond while the stoichiometric species equations remain the baseline.

Stoichiometric total versus real total

V°_ga uses the stoichiometric air-derived N₂ and water terms. V_ga introduces λ and residual oxygen. At λ = 1, these totals should match for the same input set in the implemented model. That equality is a strong regression check and is used in WattCostLab testing.

How fuel flow changes the result

The per-kilogram gas volume describes composition-driven behavior. The volumetric flow rate is B·V_ga. Therefore, changing B does not alter the calculated composition terms per kilogram, but it scales the stack-gas flow rate linearly. When comparing two operating cases, distinguish a composition change from a throughput change.

Normal cubic metres and actual stack volume are different concepts

The calculator reports normal-volume quantities using the constants of the cited model. A hot stack gas occupies a different actual volume at stack temperature and pressure. Converting normal volume to actual volumetric flow requires the appropriate gas-state assumptions, which are outside this page's current calculation.

Dry-gas analysis requires another step

Because H₂O is explicitly included, the total is a wet-gas volume. If you need dry-basis fractions, the water term would have to be excluded from the denominator consistently and the relevant species fractions recalculated. WattCostLab currently reports the source-model volumes directly rather than adding an unstated dry-basis conversion.

Use the species table to diagnose inputs

Unexpected results are easier to trace by looking at CO₂, H₂O, SO₂ and N₂ separately before looking at the total. This is one reason the calculator exposes all intermediate species volumes and not only the final V_ga.

From component volumes to approximate volume fractions

The calculator reports component volumes directly. For an exploratory wet-basis composition, a component volume can be divided by the consistent total volume from the same model and scenario. Any such fraction must use the same basis and species set throughout. Do not mix a wet total with dry component fractions.

Because the model intentionally omits several possible combustion products, these simple fractions describe only the included source-model species. They should not be presented as a complete stack-gas chemical analysis when additional species are relevant.

For traceability, save the ultimate-analysis sum and λ with every exported result. Those two values make it much easier to reproduce the same total later and to distinguish a composition error from a different excess-air scenario.