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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 heat recovery from flue gas through a condensing heat exchanger, accounting for both sensible and latent heat recovery. The calculation uses gas composition, combustion parameters, and operating temperatures to determine recoverable heat from the flue gas stream. The method is based on standard industrial practice for waste heat recovery with condensation, particularly relevant for low-temperature heat recovery applications where moisture condensation can occur.
The calculation follows a top-down approach:
Relevant formulas and symbol definitions are documented below.
Flue gas properties from combustion analysis.
The flue gas properties (excess air, specific heat, and available heat) are calculated using the gas_flue_gas_material::processHeatProperties function. This function analyzes the fuel gas composition and operating conditions to determine key combustion parameters needed for heat recovery calculations.
| \(EA\) | Excess air fraction \([\unit{ \unitless}]\) |
| \(C_{p,flue}\) | Specific heat of flue gas \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(AH\) | Available heat fraction (sensible only) \([\unit{ \unitless}]\) |
| \(SA_{req}\) | Stoichiometric air required \([\unit{ \standardCubicFeet\per\standardCubicFeet}]\) |
| \(HHV_{fuel}\) | Higher heating value of fuel \([\unit{ \btu\per\standardCubicFeet}]\) |
Flue gas mass flow rate based on fuel properties and heat input.
The flue gas mass flow rate is calculated using the heat input, stoichiometric air requirement, excess air, and fuel heating value. The empirical coefficient 0.0763 represents the density relationship, and 0.6 is a base flow factor. The result is converted from MMBtu/hr to Btu/hr by multiplying by 1,000,000.
\begin{equation}\label{eq:air-water-cooling-flue-gas-flow} \dot{m}_{flue} = \frac{Q_{in} \cdot 0.0763 \cdot (0.6 + SA_{req} \cdot (1 + EA)) \cdot 10^{6}}{HHV_{fuel}}\end{equation}
| \(\dot{m}_{flue}\) | Flue gas mass flow rate \([\unit{ \pound\per\hour}]\) |
| \(Q_{in}\) | Heat input \([\unit{ \mega\btu\per\hour}]\) |
| \(SA_{req}\) | Stoichiometric air required \([\unit{ \standardCubicFeet\per\standardCubicFeet}]\) |
| \(EA\) | Excess air fraction \([\unit{ \unitless}]\) |
| \(HHV_{fuel}\) | Higher heating value of fuel \([\unit{ \btu\per\standardCubicFeet}]\) |
Fraction of water vapor condensed in the heat exchanger.
The fraction condensed is calculated using an empirical correlation based on the outlet flue gas temperature and oxygen content. The correlation accounts for the saturation characteristics of water vapor at different temperatures and oxygen concentrations. This represents the fraction of water vapor in the flue gas that condenses as the gas is cooled.
\begin{equation}\label{eq:air-water-cooling-flue-fraction-condensed} f_{cond} = 1 - \frac{0.0000009 \cdot T_{out}^{3.0136}}{2.8082 - 0.1168 \cdot O_{2}}\end{equation}
| \(f_{cond}\) | Fraction of water vapor condensed \([\unit{ \unitless}]\) |
| \(T_{out}\) | Flue gas outlet temperature \([\unit{ \degreeFahrenheit}]\) |
| \(O_{2}\) | Oxygen content in flue gas (as fraction, e.g., 0.03 for 3%) \([\unit{ \unitless}]\) |
Fraction of heat available from water vapor condensation.
The latent heat fraction is calculated by multiplying the fraction condensed by the moisture content factor (0.00935) and the latent heat of vaporization of water (1087 Btu/lb), then converting to a percentage by dividing by 100. The moisture content factor 0.00935 represents the typical water vapor content per unit fuel combusted, and 1087 Btu/lb is the approximate latent heat of vaporization at typical flue gas dewpoint conditions.
\begin{equation}\label{eq:air-water-cooling-flue-latent-heat-fraction} f_{latent} = \frac{f_{cond} \cdot 0.00935 \cdot 1087}{100}\end{equation}
| \(f_{latent}\) | Latent heat fraction \([\unit{ \unitless}]\) |
| \(f_{cond}\) | Fraction of water vapor condensed \([\unit{ \unitless}]\) |
| \(0.00935\) | Moisture content factor (typical water vapor per fuel unit) \([\unit{ \pound\per\pound}]\) |
| \(1087\) | Latent heat of vaporization at dewpoint \([\unit{ \btu\per\pound}]\) |
Sensible heat recovered from cooling the flue gas.
The sensible heat recovery is calculated by multiplying the specific heat of the flue gas by the temperature difference (inlet minus outlet) and the mass flow rate. The result is divided by 1,000,000 to convert from Btu/hr to MMBtu/hr. This represents the heat recovered by cooling the flue gas without phase change.
\begin{equation}\label{eq:air-water-cooling-flue-sensible-heat-recovery} Q_{sensible} = \frac{C_{p,flue} \cdot (T_{in} - T_{out}) \cdot \dot{m}_{flue}}{10^{6}}\end{equation}
| \(Q_{sensible}\) | Sensible heat recovery \([\unit{ \mega\btu\per\hour}]\) |
| \(C_{p,flue}\) | Specific heat of flue gas \([\unit{ \btu\per\pound\degreeFahrenheit}]\) |
| \(T_{in}\) | Flue gas inlet temperature \([\unit{ \degreeFahrenheit}]\) |
| \(T_{out}\) | Flue gas outlet temperature \([\unit{ \degreeFahrenheit}]\) |
| \(\dot{m}_{flue}\) | Flue gas mass flow rate \([\unit{ \pound\per\hour}]\) |
Latent heat recovered from water vapor condensation.
The latent heat recovery is calculated by multiplying the heat input by the latent heat fraction. This represents the additional heat recovered when water vapor in the flue gas condenses to liquid water, releasing its latent heat of vaporization.
\begin{equation}\label{eq:air-water-cooling-flue-latent-heat-recovery} Q_{latent} = Q_{in} \cdot f_{latent}\end{equation}
| \(Q_{latent}\) | Latent heat recovery \([\unit{ \mega\btu\per\hour}]\) |
| \(Q_{in}\) | Heat input \([\unit{ \mega\btu\per\hour}]\) |
| \(f_{latent}\) | Latent heat fraction \([\unit{ \unitless}]\) |
Total fraction of heat available including sensible and latent components.
The total available heat fraction is calculated by adding the available heat fraction (sensible only) to the latent heat fraction. This represents the total fraction of input heat that can be recovered through the condensing heat exchanger, accounting for both cooling the flue gas and condensing water vapor.
\begin{equation}\label{eq:air-water-cooling-flue-total-available-heat} AH_{total} = AH + f_{latent}\end{equation}
| \(AH_{total}\) | Total available heat fraction (sensible + latent) \([\unit{ \unitless}]\) |
| \(AH\) | Available heat fraction (sensible only) \([\unit{ \unitless}]\) |
| \(f_{latent}\) | Latent heat fraction \([\unit{ \unitless}]\) |
Modules | |
| Flue Gas Properties | |
| Flue gas properties from combustion analysis. | |
| Flue Gas Flow Formula | |
| Flue gas mass flow rate based on fuel properties and heat input. | |
| Fraction Condensed Formula | |
| Fraction of water vapor condensed in the heat exchanger. | |
| Latent Heat Fraction Formula | |
| Fraction of heat available from water vapor condensation. | |
| Sensible Heat Recovery Formula | |
| Sensible heat recovered from cooling the flue gas. | |
| Latent Heat Recovery Formula | |
| Latent heat recovered from water vapor condensation. | |
| Total Available Heat Fraction Formula | |
| Total fraction of heat available including sensible and latent components. | |
Files | |
| file | air_water_cooling_using_flue.h |
| Air/water cooling using flue gas calculations for condensing heat exchangers. | |
Namespaces | |
| namespace | air_water_cooling_using_flue |
| Air/water cooling using flue gas calculations for condensing heat exchangers. | |
Classes | |
| struct | air_water_cooling_using_flue::AirWaterCoolingUsingFlueResults |
| Results of the air/water cooling using flue calculation. More... | |
Functions | |
| AirWaterCoolingUsingFlueResults | air_water_cooling_using_flue::airWaterCoolingUsingFlue (const gas_composition::GasComposition &gas_compositions, double heat_input, double temp_flue_gas_in, double temp_flue_gas_out, double temp_comb_air, double fuel_temp, double perc_o2, double ambient_air_temp=60, double moist_comb_air=0) |
| Calculates heat recovery using flue gas and condensing heat exchanger. | |
| AirWaterCoolingUsingFlueResults air_water_cooling_using_flue::airWaterCoolingUsingFlue | ( | const gas_composition::GasComposition & | gas_compositions, |
| double | heat_input, | ||
| double | temp_flue_gas_in, | ||
| double | temp_flue_gas_out, | ||
| double | temp_comb_air, | ||
| double | fuel_temp, | ||
| double | perc_o2, | ||
| double | ambient_air_temp = 60, |
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| double | moist_comb_air = 0 |
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| ) |
Uses gas composition and process parameters to estimate heat recovery, available heat, and latent heat effects.
| gas_compositions | GasComposition object with fuel properties |
| heat_input | Heat input \([\unit{\mega\btu\per\hour}]\) |
| temp_flue_gas_in | Flue gas inlet temperature \([\unit{\degreeFahrenheit}]\) |
| temp_flue_gas_out | Flue gas outlet temperature \([\unit{\degreeFahrenheit}]\) |
| temp_comb_air | Combustion air temperature \([\unit{\degreeFahrenheit}]\) |
| fuel_temp | Fuel temperature \([\unit{\degreeFahrenheit}]\) |
| perc_o2 | Percent O2 in flue gas (fraction) |
| ambient_air_temp | Ambient air temperature \([\unit{\degreeFahrenheit}]\) (default: 60) |
| moist_comb_air | Moisture in combustion air (fraction, default: 0) |
1.9.8