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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 flue gas to preheat boiler feedwater through a heat exchanger. The calculation uses flue gas properties, steam system parameters, heat exchanger efficiency, and operating costs. The method is based on standard industrial practice for waste heat recovery in boiler systems utilizing the effectiveness-NTU heat exchanger method.
The calculation follows a top-down approach:
Relevant formulas and symbol definitions are documented below.
Flue gas mass flow rate based on boiler rating and fuel properties.
The flue gas mass flow rate is calculated using the total generated flue gas (from gas composition and combustion analysis), boiler rating, and fuel higher heating value. The density conversion factor physics::conversions::kLbPerFt3ToKgPerM3 (16.018463 kg/m³ per lb/ft³) is applied.
\begin{equation}\label{eq:water-heating-flue-gas-mass-flow} \dot{m}_{flue} = \rho_{conv} \cdot Q_{gen} \cdot R_{boiler} \cdot \frac{10^{6}}{HHV_{fuel}}\end{equation}
| \(\dot{m}_{flue}\) | Flue gas mass flow rate \([\unit{ \kilogram\per\hour}]\) |
| \(\rho_{conv}\) | Density conversion factor - see physics::conversions::kLbPerFt3ToKgPerM3 \([\unit{ \kilogram\per\meter\cubed\per\pound\per\foot\cubed}]\) |
| \(Q_{gen}\) | Total generated flue gas from combustion \([\unit{ \pound\per\foot\cubed}]\) |
| \(R_{boiler}\) | Boiler rating \([\unit{ \giga\joule\per\hour}]\) |
| \(HHV_{fuel}\) | Fuel higher heating value \([\unit{ \kilo\joule\per\normalCubicMeter}]\) |
Steam mass flow rate based on boiler rating and enthalpy difference.
The steam mass flow rate is calculated using the boiler rating, available heat fraction, blowdown percentage, and the enthalpy difference between steam and feedwater. Available heat accounts for losses in the combustion process.
\begin{equation}\label{eq:water-heating-flue-steam-mass-flow} \dot{m}_{steam} = \frac{R_{boiler} \cdot 10^{6} \cdot AH \cdot (1 - BD)}{h_{steam} - h_{fw}}\end{equation}
| \(\dot{m}_{steam}\) | Steam mass flow rate \([\unit{ \kilogram\per\hour}]\) |
| \(R_{boiler}\) | Boiler rating \([\unit{ \giga\joule\per\hour}]\) |
| \(AH\) | Available heat fraction \([\unit{ \unitless}]\) |
| \(BD\) | Blowdown percentage (fraction) \([\unit{ \unitless}]\) |
| \(h_{steam}\) | Steam specific enthalpy \([\unit{ \kilo\joule\per\kilogram}]\) |
| \(h_{fw}\) | Feedwater specific enthalpy \([\unit{ \kilo\joule\per\kilogram}]\) |
Feedwater mass flow rate accounting for steam production and blowdown.
The feedwater mass flow rate is calculated by adding the blowdown fraction to the steam mass flow. Blowdown is the water deliberately discharged from the boiler to control dissolved solids concentration.
\begin{equation}\label{eq:water-heating-flue-feedwater-mass-flow} \dot{m}_{fw} = \dot{m}_{steam} \cdot (1 + BD)\end{equation}
| \(\dot{m}_{fw}\) | Feedwater mass flow rate \([\unit{ \kilogram\per\hour}]\) |
| \(\dot{m}_{steam}\) | Steam mass flow rate \([\unit{ \kilogram\per\hour}]\) |
| \(BD\) | Blowdown percentage (fraction) \([\unit{ \unitless}]\) |
Heat capacity rate of the flue gas stream.
The flue gas heat capacity rate is the product of the mass flow rate and specific heat. This represents the thermal capacity of the flue gas stream to transfer heat.
\begin{equation}\label{eq:water-heating-flue-gas-heat-capacity} \dot{C}_{flue} = C_{p,flue} \cdot \dot{m}_{flue}\end{equation}
| \(\dot{C}_{flue}\) | Flue gas heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
| \(C_{p,flue}\) | Flue gas specific heat \([\unit{ \kilo\joule\per\kilogram\kelvin}]\) |
| \(\dot{m}_{flue}\) | Flue gas mass flow rate \([\unit{ \kilogram\per\hour}]\) |
Heat capacity rate of the feedwater stream.
The feedwater heat capacity rate is the product of the mass flow rate and specific heat. The feedwater specific heat is calculated using an empirical polynomial fit in gas_constants::specificHeatFeedwater.
\begin{equation}\label{eq:water-heating-flue-feedwater-heat-capacity} \dot{C}_{fw} = C_{p,fw} \cdot \dot{m}_{fw}\end{equation}
| \(\dot{C}_{fw}\) | Feedwater heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
| \(C_{p,fw}\) | Feedwater specific heat \([\unit{ \kilo\joule\per\kilogram\kelvin}]\) |
| \(\dot{m}_{fw}\) | Feedwater mass flow rate \([\unit{ \kilogram\per\hour}]\) |
Minimum heat capacity rate between the two streams.
The minimum heat capacity rate determines the maximum possible heat transfer in a heat exchanger. It is the smaller of the flue gas and feedwater heat capacity rates.
\begin{equation}\label{eq:water-heating-flue-min-heat-capacity} \dot{C}_{min} = \min(\dot{C}_{flue}, \dot{C}_{fw})\end{equation}
| \(\dot{C}_{min}\) | Minimum heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
| \(\dot{C}_{flue}\) | Flue gas heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
| \(\dot{C}_{fw}\) | Feedwater heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
Heat recovered through the heat exchanger using effectiveness-NTU method.
The recovered heat is calculated using the heat exchanger efficiency (effectiveness), minimum heat capacity rate, and temperature difference between the flue gas inlet and feedwater inlet. This represents the actual heat transferred from the flue gas to the feedwater.
\begin{equation}\label{eq:water-heating-flue-recovered-heat} Q_{rec} = \eta_{hx} \cdot \dot{C}_{min} \cdot (T_{flue,in} - T_{fw,in})\end{equation}
| \(Q_{rec}\) | Recovered heat \([\unit{ \kilo\joule\per\hour}]\) |
| \(\eta_{hx}\) | Heat exchanger efficiency (effectiveness) \([\unit{ \unitless}]\) |
| \(\dot{C}_{min}\) | Minimum heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
| \(T_{flue,in}\) | Flue gas inlet temperature \([\unit{ \kelvin}]\) |
| \(T_{fw,in}\) | Feedwater inlet temperature \([\unit{ \kelvin}]\) |
Exit temperature of flue gas after heat exchanger.
The flue gas exit temperature is calculated by subtracting the heat lost (recovered heat) divided by the flue gas heat capacity rate from the inlet temperature. This represents the cooled flue gas temperature leaving the heat exchanger.
\begin{equation}\label{eq:water-heating-flue-gas-exit-temp} T_{flue,out} = T_{flue,in} - \frac{Q_{rec}}{\dot{C}_{flue}}\end{equation}
| \(T_{flue,out}\) | Flue gas exit temperature \([\unit{ \kelvin}]\) |
| \(T_{flue,in}\) | Flue gas inlet temperature \([\unit{ \kelvin}]\) |
| \(Q_{rec}\) | Recovered heat \([\unit{ \kilo\joule\per\hour}]\) |
| \(\dot{C}_{flue}\) | Flue gas heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
Exit temperature of feedwater after heat exchanger.
The feedwater exit temperature is calculated by adding the heat gained (recovered heat) divided by the feedwater heat capacity rate to the inlet temperature. This represents the preheated feedwater temperature leaving the heat exchanger.
\begin{equation}\label{eq:water-heating-flue-feedwater-exit-temp} T_{fw,out} = T_{fw,in} + \frac{Q_{rec}}{\dot{C}_{fw}}\end{equation}
| \(T_{fw,out}\) | Feedwater exit temperature \([\unit{ \kelvin}]\) |
| \(T_{fw,in}\) | Feedwater inlet temperature \([\unit{ \kelvin}]\) |
| \(Q_{rec}\) | Recovered heat \([\unit{ \kilo\joule\per\hour}]\) |
| \(\dot{C}_{fw}\) | Feedwater heat capacity rate \([\unit{ \kilo\joule\per\hour\kelvin}]\) |
Annual energy savings from using waste heat recovery.
The annual energy savings is calculated by dividing the recovered heat by the available heat fraction and multiplying by the operating hours. This is then converted to GJ/yr by dividing by 1,000,000. The division by available heat fraction accounts for the boiler efficiency to determine the fuel energy savings.
\begin{equation}\label{eq:water-heating-flue-annual-energy-savings} E_{annual} = \frac{Q_{rec}}{AH} \cdot t_{op} \cdot \frac{1}{10^{6}}\end{equation}
| \(E_{annual}\) | Annual energy savings \([\unit{ \giga\joule\per\year}]\) |
| \(Q_{rec}\) | Recovered heat \([\unit{ \kilo\joule\per\hour}]\) |
| \(AH\) | Available heat fraction \([\unit{ \unitless}]\) |
| \(t_{op}\) | Operating hours \([\unit{ \hour\per\year}]\) |
Annual cost savings from using waste heat recovery.
The annual cost savings is calculated by multiplying the annual energy savings by the fuel cost. This represents the monetary benefit of implementing the waste heat recovery system.
\begin{equation}\label{eq:water-heating-flue-annual-cost-savings} C_{annual} = E_{annual} \cdot C_{fuel}\end{equation}
| \(C_{annual}\) | Annual cost savings \([\unit{ \dollar\per\year}]\) |
| \(E_{annual}\) | Annual energy savings \([\unit{ \giga\joule\per\year}]\) |
| \(C_{fuel}\) | Fuel cost \([\unit{ \dollar\per\giga\joule}]\) |
Modules | |
| Flue Gas Mass Flow Formula | |
| Flue gas mass flow rate based on boiler rating and fuel properties. | |
| Steam Mass Flow Formula | |
| Steam mass flow rate based on boiler rating and enthalpy difference. | |
| Feedwater Mass Flow Formula | |
| Feedwater mass flow rate accounting for steam production and blowdown. | |
| Flue Gas Heat Capacity Formula | |
| Heat capacity rate of the flue gas stream. | |
| Feedwater Heat Capacity Formula | |
| Heat capacity rate of the feedwater stream. | |
| Minimum Heat Capacity Formula | |
| Minimum heat capacity rate between the two streams. | |
| Recovered Heat Formula | |
| Heat recovered through the heat exchanger using effectiveness-NTU method. | |
| Flue Gas Exit Temperature Formula | |
| Exit temperature of flue gas after heat exchanger. | |
| Feedwater Exit Temperature Formula | |
| Exit temperature of feedwater after heat exchanger. | |
| Annual Energy Savings Formula | |
| Annual energy savings from using waste heat recovery. | |
| Annual Cost Savings Formula | |
| Annual cost savings from using waste heat recovery. | |
Namespaces | |
| namespace | water_heating_using_flue |
| Water heating using flue calculations for process heating systems. | |
Classes | |
| struct | water_heating_using_flue::WaterHeatingUsingFlueResults |
| Results of the water heating using flue calculation. More... | |
Functions | |
| WaterHeatingUsingFlueResults | water_heating_using_flue::waterHeatingUsingFlue (const gas_composition::GasComposition &gas_compositions, double temp_flue_gas_f, double perc_o2, double temp_comb_air_f, double moist_comb_air, double rating_boiler, double pr_steam, double temp_ambient_air_f, double temp_steam_f, double temp_fw, double perc_blow_down, double eff_hx, double op_hours, double cost_fuel, double hhv_fuel, SteamCondition cond_steam=SteamCondition::Superheated, double fuel_temp_f=60) |
| Calculates energy and cost savings from using flue gas (waste) heat to heat boiler feed water using a non-condensing heat exchanger. | |
| WaterHeatingUsingFlueResults water_heating_using_flue::waterHeatingUsingFlue | ( | const gas_composition::GasComposition & | gas_compositions, |
| double | temp_flue_gas_f, | ||
| double | perc_o2, | ||
| double | temp_comb_air_f, | ||
| double | moist_comb_air, | ||
| double | rating_boiler, | ||
| double | pr_steam, | ||
| double | temp_ambient_air_f, | ||
| double | temp_steam_f, | ||
| double | temp_fw, | ||
| double | perc_blow_down, | ||
| double | eff_hx, | ||
| double | op_hours, | ||
| double | cost_fuel, | ||
| double | hhv_fuel, | ||
| SteamCondition | cond_steam = SteamCondition::Superheated, |
||
| double | fuel_temp_f = 60 |
||
| ) |
Uses process parameters to estimate the benefit of using waste heat for water heating and boiler operation.
| [in] | gas_compositions | Fuel gas composition for flue gas calculations. |
| [in] | temp_flue_gas_f | Flue gas temperature \([\unit{\degreeFahrenheit}]\) |
| [in] | perc_o2 | Oxygen percentage in flue gas (fraction) |
| [in] | temp_comb_air_f | Combustion air temperature \([\unit{\degreeFahrenheit}]\) |
| [in] | moist_comb_air | Combustion air moisture (fraction) |
| [in] | rating_boiler | Boiler rating \([\unit{GJ/hr}]\) |
| [in] | pr_steam | Steam pressure \([\unit{MPa}]\) |
| [in] | temp_ambient_air_f | Ambient air temperature \([\unit{\degreeFahrenheit}]\) |
| [in] | temp_steam_f | Steam temperature \([\unit{\degreeFahrenheit}]\) |
| [in] | temp_fw | Feedwater temperature \([\unit{\degreeFahrenheit}]\) |
| [in] | perc_blow_down | Blowdown percentage (fraction) |
| [in] | eff_hx | Heat exchanger efficiency (fraction) |
| [in] | op_hours | Operating hours \([\unit{hr}]\) |
| [in] | cost_fuel | Fuel cost \([\unit{dollar/GJ}]\) |
| [in] | hhv_fuel | Fuel higher heating value \([\unit{kJ/Nm3}]\) |
| [in] | cond_steam | Steam condition (Superheated or Saturated) |
| [in] | fuel_temp_f | Fuel temperature \([\unit{\degreeFahrenheit}]\) (default: 60) |
1.9.8