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MEASUR-Tools-Suite v1.0.11
The MEASUR Tools Suite is a collection of industrial efficiency calculations written in C++ and with bindings for compilation to WebAssembly.
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This calculator estimates the benefit of enriching combustion air with oxygen to improve combustion efficiency and reduce fuel consumption. The calculation uses combustion air properties, flue gas temperatures, oxygen concentrations, and fuel consumption data. The method is based on standard industrial practice for oxygen enrichment in process heating systems.
The calculation follows a top-down approach:
Relevant formulas and symbol definitions are documented below.
The formula provides a quick estimate of excess air based on measured flue gas oxygen content. For more complex fuel compositions, iterative refinement may be applied (as in solid_liquid_flue_gas_material::calculateExcessAirFromFlueGasO2).
\begin{equation}\label{eq:process-heat-excess-air} EA = \frac{k_1 \cdot O_{2,flue}}{2 - k_2 \cdot O_{2,flue}}\end{equation}
| \(EA\) | Excess air \([\unit{ \unitless}]\) |
| \(O_{2,flue}\) | Oxygen in flue gas \([\unit{ \unitless}]\) |
| \(k_1\) | Stoichiometric air factor (8.52381) \([\unit{ \unitless}]\) |
| \(k_2\) | Oxygen flue gas factor (9.52381) \([\unit{ \unitless}]\) |
Heat input calculated based on flue gas temperature.
The heat input is estimated from the flue gas temperature using an empirical linear relationship. Higher flue gas temperatures indicate greater heat losses, resulting in lower available heat for the process. The relationship is based on typical industrial furnace operating conditions.
\begin{equation}\label{eq:o2-enrichment-heat-input} Q_{in} = 95 - 0.025 \cdot T_{flue}\end{equation}
| \(Q_{in}\) | Heat input \([\unit{ \percent}]\) |
| \(T_{flue}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(95\) | Heat input intercept constant \([\unit{ \percent}]\) |
| \(0.025\) | Heat input slope constant \([\unit{ \percent\per\degreeFahrenheit}]\) |
Specific heat of combustion air calculated based on preheat temperature.
The specific heat of air varies with temperature according to an empirical linear relationship. This accounts for the temperature-dependent thermodynamic properties of air. The base specific heat and temperature coefficient are referenced from physics::us::kSpecificHeatAirBase and physics::us::kSpecificHeatAirCoeff.
\begin{equation}\label{eq:o2-enrichment-air-specific-heat} C_{p,air} = C_{p,base} + k_{temp} \cdot T_{air}\end{equation}
| \(C_{p,air}\) | Air specific heat \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\) |
| \(C_{p,base}\) | Base specific heat of air (0.017828518) - see physics::us::kSpecificHeatAirBase \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\) |
| \(k_{temp}\) | Temperature coefficient (0.000002556) - see physics::us::kSpecificHeatAirCoeff \([\unit{ \btu\per\pound\per\degreeFahrenheit\per\degreeFahrenheit}]\) |
| \(T_{air}\) | Combustion air preheat temperature \([\unit{ \degreeFahrenheit}]\) |
Correction factor for excess air heat losses.
The air correction accounts for heat losses due to excess air being heated and discharged with the flue gas. The correction is proportional to the excess air fraction, flue gas temperature, and air specific heat. The base constant is referenced from physics::us::kAirCorrectionBase.
\begin{equation}\label{eq:o2-enrichment-air-correction} AC = -(k_{base} + C_{p,air} \cdot T_{flue}) \cdot EA\end{equation}
| \(AC\) | Air correction \([\unit{ \percent}]\) |
| \(k_{base}\) | Air correction base constant (-1.078913827) - see physics::us::kAirCorrectionBase \([\unit{ \btu\per\pound}]\) |
| \(C_{p,air}\) | Air specific heat \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\) |
| \(T_{flue}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(EA\) | Excess air \([\unit{ \unitless}]\) |
Correction factor for combustion air preheat.
The combustion air correction accounts for the heat credit from preheating combustion air. Higher preheat temperatures reduce fuel consumption by providing sensible heat to the combustion process. The correction is applied to both stoichiometric and excess air. The base constant is the same as the air correction base.
\begin{equation}\label{eq:o2-enrichment-combustion-air-correction} CAC = (k_{base} + C_{p,air} \cdot T_{air}) \cdot (1 + EA)\end{equation}
| \(CAC\) | Combustion air correction \([\unit{ \percent}]\) |
| \(k_{base}\) | Combustion air correction base constant (-1.078913827) \([\unit{ \btu\per\pound}]\) |
| \(C_{p,air}\) | Air specific heat \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\) |
| \(T_{air}\) | Combustion air preheat temperature \([\unit{ \degreeFahrenheit}]\) |
| \(EA\) | Excess air \([\unit{ \unitless}]\) |
Standard available heat from heat input and correction factors.
The standard available heat represents the net heat available for the process after accounting for flue gas losses and combustion air preheat. It is the sum of the heat input, air correction (negative for losses), and combustion air correction (positive for preheat credit).
\begin{equation}\label{eq:o2-enrichment-standard-available-heat} AH_{std} = Q_{in} + AC + CAC\end{equation}
| \(AH_{std}\) | Standard available heat \([\unit{ \percent}]\) |
| \(Q_{in}\) | Heat input \([\unit{ \percent}]\) |
| \(AC\) | Air correction \([\unit{ \percent}]\) |
| \(CAC\) | Combustion air correction \([\unit{ \percent}]\) |
Available heat accounting for oxygen enrichment effects.
The available heat is adjusted from the standard available heat to account for the benefits of oxygen enrichment. Enriching the combustion air with oxygen reduces the nitrogen content, which decreases sensible heat losses in the flue gas. The correction is proportional to the oxygen enrichment level, flue gas temperature, and the difference from ambient conditions.
\begin{equation}\label{eq:o2-enrichment-available-heat} AH = AH_{std} + 100 \cdot k_O \cdot \frac{O_{2,air} - 0.21}{O_{2,air}} \cdot 0.02 \cdot \frac{T_{flue} - 60}{980}\end{equation}
| \(AH\) | Available heat with enrichment \([\unit{ \percent}]\) |
| \(AH_{std}\) | Standard available heat \([\unit{ \percent}]\) |
| \(k_O\) | Oxygen enrichment factor (9.38) \([\unit{ \unitless}]\) |
| \(O_{2,air}\) | Oxygen in combustion air \([\unit{ \unitless}]\) |
| \(0.21\) | Reference oxygen fraction in air \([\unit{ \unitless}]\) |
| \(0.02\) | Available heat fraction factor \([\unit{ \unitless}]\) |
| \(T_{flue}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(60\) | Ambient reference temperature \([\unit{ \degreeFahrenheit}]\) |
| \(980\) | Available heat temperature divisor \([\unit{ \degreeFahrenheit}]\) |
| \(100\) | Conversion factor to percentage \([\unit{ \unitless}]\) |
Fuel consumption with oxygen enrichment.
The fuel consumption with oxygen enrichment is calculated by adjusting the baseline fuel consumption based on the ratio of standard available heat to the available heat with enrichment. As the available heat increases with enrichment, less fuel is required to deliver the same process heat.
\begin{equation}\label{eq:o2-enrichment-fuel-consumption} FC_{enriched} = FC_{base} \cdot \frac{AH_{std}}{AH_{enriched}}\end{equation}
| \(FC_{enriched}\) | Fuel consumption with O2 enrichment \([\unit{ \mega\btu\per\hour}]\) |
| \(FC_{base}\) | Baseline fuel consumption \([\unit{ \mega\btu\per\hour}]\) |
| \(AH_{std}\) | Standard available heat (baseline) \([\unit{ \percent}]\) |
| \(AH_{enriched}\) | Available heat with O2 enrichment \([\unit{ \percent}]\) |
Fuel savings with oxygen enrichment as a percentage.
The fuel savings represents the percentage reduction in fuel consumption achieved through oxygen enrichment. It is calculated as the difference between baseline and enriched fuel consumption divided by the baseline, expressed as a percentage.
\begin{equation}\label{eq:o2-enrichment-fuel-savings} FS = \frac{FC_{base} - FC_{enriched}}{FC_{base}} \cdot 100\end{equation}
| \(FS\) | Fuel savings with O2 enrichment \([\unit{ \percent}]\) |
| \(FC_{base}\) | Baseline fuel consumption \([\unit{ \mega\btu\per\hour}]\) |
| \(FC_{enriched}\) | Fuel consumption with O2 enrichment \([\unit{ \mega\btu\per\hour}]\) |
| \(100\) | Conversion factor to percentage \([\unit{ \unitless}]\) |
Modules | |
| Excess Air Formula | |
| Heat Input Formula | |
| Heat input calculated based on flue gas temperature. | |
| Air Specific Heat Formula | |
| Specific heat of combustion air calculated based on preheat temperature. | |
| Air Correction Formula | |
| Correction factor for excess air heat losses. | |
| Combustion Air Correction Formula | |
| Correction factor for combustion air preheat. | |
| Standard Available Heat Formula | |
| Standard available heat from heat input and correction factors. | |
| Available Heat Formula | |
| Available heat accounting for oxygen enrichment effects. | |
| Fuel Consumption with O2 Enrichment Formula | |
| Fuel consumption with oxygen enrichment. | |
| Fuel Savings with O2 Enrichment Formula | |
| Fuel savings with oxygen enrichment as a percentage. | |
1.9.8