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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 using waste heat from exhaust gas to preheat incoming combustion air through a heat exchanger. The calculation uses fuel properties, flue gas temperature, excess air, firing rate, airflow, and heat exchanger efficiency. The method is based on standard industrial practice for waste heat recovery in process heating systems.
The calculation follows a top-down approach:
Relevant formulas and symbol definitions are documented below.
Heat capacity of exhaust flue gas based on fuel properties and combustion parameters.
The heat capacity of flue gas is calculated based on the firing rate, stoichiometric air requirement, excess air, flue gas temperature, and fuel heating value. An empirical factor of 0.021 is applied to account for the specific heat properties of typical flue gas compositions.
\begin{equation}\label{eq:air-heating-exhaust-heat-capacity-flue} C_{flue} = \frac{Q_{fire} \cdot 10^6 \cdot \left(\frac{(1 + EA) \cdot A_{stoich}}{32} + 1\right) \cdot T_{flue}}{HV_{fuel} \cdot 1000} \cdot 0.021\end{equation}
| \(C_{flue}\) | Heat capacity of flue gas \([\unit{ \btu\per\degreeFahrenheit}]\) |
| \(Q_{fire}\) | Firing rate \([\unit{ \mega\btu\per\hour}]\) |
| \(EA\) | Excess air fraction \([\unit{ \unitless}]\) |
| \(A_{stoich}\) | Stoichiometric air requirement (gas) \([\unit{ \cubicFoot\per\cubicFoot}]\) |
| \(A_{stoich}\) | Stoichiometric air requirement (solid/liquid) \([\unit{ \pound\per\pound}]\) |
| \(T_{flue}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(HV_{fuel}\) | Fuel heating value (gas) \([\unit{ \btu\per\cubicFoot}]\) |
| \(HV_{fuel}\) | Fuel heating value (solid/liquid) \([\unit{ \btu\per\pound}]\) |
| \(0.021\) | Empirical factor for flue gas heat capacity \([\unit{ \unitless}]\) |
| \(32\) | Empirical divisor for stoichiometric air calculation \([\unit{ \unitless}]\) |
Heat capacity of incoming air to be preheated.
The heat capacity of air is calculated from the volumetric airflow rate converted to an hourly basis. An empirical factor of 0.0186 is applied to account for the specific heat of air at typical combustion conditions.
\begin{equation}\label{eq:air-heating-exhaust-heat-capacity-air} C_{air} = 0.0186 \cdot \dot{V}_{air} \cdot 60\end{equation}
| \(C_{air}\) | Heat capacity of air \([\unit{ \btu\per\degreeFahrenheit}]\) |
| \(\dot{V}_{air}\) | Air flow rate \([\unit{ \standardCubicFeet\per\minute}]\) |
| \(0.0186\) | Empirical factor for air heat capacity \([\unit{ \unitless}]\) |
| \(60\) | Conversion factor from minutes to hours - see physics::conversions::kMinutesPerHour \([\unit{ \minute\per\hour}]\) |
Heat transferred from exhaust to cold air through the heat exchanger.
The heat recovered is determined by the limiting heat capacity (minimum of air or flue gas), the heat exchanger efficiency, and the temperature difference between the flue gas and inlet air. The limiting capacity ensures the calculation respects thermodynamic constraints.
\begin{equation}\label{eq:air-heating-exhaust-heat-recovered} Q_{recovered} = \eta_{hx} \cdot \min(C_{air}, C_{flue}) \cdot (T_{flue} - T_{inlet})\end{equation}
| \(Q_{recovered}\) | Heat recovered by cold air \([\unit{ \btu\per\hour}]\) |
| \(\eta_{hx}\) | Heat exchanger efficiency \([\unit{ \unitless}]\) |
| \(C_{air}\) | Heat capacity of air \([\unit{ \btu\per\degreeFahrenheit}]\) |
| \(C_{flue}\) | Heat capacity of flue gas \([\unit{ \btu\per\degreeFahrenheit}]\) |
| \(T_{flue}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(T_{inlet}\) | Inlet air temperature \([\unit{ \degreeFahrenheit}]\) |
Exhaust gas temperature after heat recovery.
The outlet exhaust temperature is calculated by subtracting the temperature drop in the flue gas from the inlet flue gas temperature. The temperature drop is the ratio of heat recovered to the heat capacity of the flue gas.
\begin{equation}\label{eq:air-heating-exhaust-outlet-temperature} T_{outlet} = T_{flue} - \frac{Q_{recovered}}{C_{flue}}\end{equation}
| \(T_{outlet}\) | Outlet exhaust temperature \([\unit{ \degreeFahrenheit}]\) |
| \(T_{flue}\) | Flue gas temperature \([\unit{ \degreeFahrenheit}]\) |
| \(Q_{recovered}\) | Heat recovered by cold air \([\unit{ \btu\per\hour}]\) |
| \(C_{flue}\) | Heat capacity of flue gas \([\unit{ \btu\per\degreeFahrenheit}]\) |
Total energy savings over the operating period.
The annual energy savings is calculated by multiplying the operating hours by the heat recovered, then dividing by the heater efficiency and converting from Btu to MMBtu. The heater efficiency accounts for the fact that the recovered heat reduces the fuel input needed by the heating system.
\begin{equation}\label{eq:air-heating-exhaust-energy-savings} E_{savings} = \frac{t_{op} \cdot Q_{recovered}}{\eta_{heater} \cdot 10^6}\end{equation}
| \(E_{savings}\) | Annual energy savings \([\unit{ \mega\btu\per\year}]\) |
| \(t_{op}\) | Annual operating hours \([\unit{ \hour\per\year}]\) |
| \(Q_{recovered}\) | Heat recovered by cold air \([\unit{ \btu\per\hour}]\) |
| \(\eta_{heater}\) | Heater efficiency \([\unit{ \unitless}]\) |
| \(10^6\) | Conversion factor from Btu to MMBtu - see physics::conversions::kMMBtuToBtu \([\unit{ \btu\per\mega\btu}]\) |
Modules | |
| Heat Capacity of Flue Gas Formula | |
| Heat capacity of exhaust flue gas based on fuel properties and combustion parameters. | |
| Heat Capacity of Air Formula | |
| Heat capacity of incoming air to be preheated. | |
| Heat Recovered by Cold Air Formula | |
| Heat transferred from exhaust to cold air through the heat exchanger. | |
| Outlet Exhaust Temperature Formula | |
| Exhaust gas temperature after heat recovery. | |
| Annual Energy Savings Formula | |
| Total energy savings over the operating period. | |
Files | |
| file | air_heating_using_exhaust.h |
| Air heating using exhaust calculations for process heating systems. | |
Namespaces | |
| namespace | air_heating_using_exhaust |
| Air heating using exhaust calculations for process heating systems. | |
Classes | |
| struct | air_heating_using_exhaust::AirHeatingUsingExhaustResults |
| Results of the air heating using exhaust calculation. More... | |
Functions | |
| AirHeatingUsingExhaustResults | air_heating_using_exhaust::airHeatingUsingExhaustWithGasComposition (const gas_composition::GasComposition &gas_composition, double flue_temperature, double excess_air, double fire_rate, double airflow, double inlet_temperature, double heater_efficiency, double hx_efficiency, double operating_hours) |
| Calculates air heating using exhaust for gaseous fuels. | |
| AirHeatingUsingExhaustResults | air_heating_using_exhaust::airHeatingUsingExhaustWithSolidLiquidFlueGasMaterial (const solid_liquid_flue_gas_material_data::SolidLiquidFlueGasMaterial &material, double flue_temperature, double excess_air, double fire_rate, double airflow, double inlet_temperature, double heater_efficiency, double hx_efficiency, double operating_hours) |
| Calculates air heating using exhaust for solid/liquid fuels. | |
| AirHeatingUsingExhaustResults air_heating_using_exhaust::airHeatingUsingExhaustWithGasComposition | ( | const gas_composition::GasComposition & | gas_composition, |
| double | flue_temperature, | ||
| double | excess_air, | ||
| double | fire_rate, | ||
| double | airflow, | ||
| double | inlet_temperature, | ||
| double | heater_efficiency, | ||
| double | hx_efficiency, | ||
| double | operating_hours | ||
| ) |
Uses gas composition to determine fuel heating value and stoichiometric air, then estimates heat recovery.
| gas_composition | GasComposition object with fuel properties |
| flue_temperature | Flue gas temperature \([\unit{\degreeFahrenheit}]\) |
| excess_air | Excess air (fraction) |
| fire_rate | Firing rate \([\unit{MMBtu/hr}]\) |
| airflow | Air flow \([\unit{scfm}]\) |
| inlet_temperature | Inlet air temperature \([\unit{\degreeFahrenheit}]\) |
| heater_efficiency | Heater efficiency (fraction) |
| hx_efficiency | Heat exchanger efficiency (fraction) |
| operating_hours | Annual operating hours \([\unit{hr}]\) |
| AirHeatingUsingExhaustResults air_heating_using_exhaust::airHeatingUsingExhaustWithSolidLiquidFlueGasMaterial | ( | const solid_liquid_flue_gas_material_data::SolidLiquidFlueGasMaterial & | material, |
| double | flue_temperature, | ||
| double | excess_air, | ||
| double | fire_rate, | ||
| double | airflow, | ||
| double | inlet_temperature, | ||
| double | heater_efficiency, | ||
| double | hx_efficiency, | ||
| double | operating_hours | ||
| ) |
Uses the provided SolidLiquidFlueGasMaterial to determine fuel heating value and stoichiometric air, then estimates heat recovery.
| material | SolidLiquidFlueGasMaterial object with fuel composition and properties |
| flue_temperature | Flue gas temperature \([\unit{\degreeFahrenheit}]\) |
| excess_air | Excess air (fraction) |
| fire_rate | Firing rate \([\unit{MMBtu/hr}]\) |
| airflow | Air flow \([\unit{scfm}]\) |
| inlet_temperature | Inlet air temperature \([\unit{\degreeFahrenheit}]\) |
| heater_efficiency | Heater efficiency (fraction) |
| hx_efficiency | Heat exchanger efficiency (fraction) |
| operating_hours | Annual operating hours \([\unit{hr}]\) |
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