Detailed Description

This calculator estimates the benefit of efficiency improvements in a fuel-fired furnace by computing excess air, heat input, air properties, available heat, fuel savings, and new energy input. The calculation is based on standard thermodynamic relationships and is implemented in the processHeatEfficiencyImprovement function.

The calculation follows a top-down approach:

Excess Air Calculation: Compute current and new excess air from flue gas oxygen and air multipliers.
Heat Input Calculation: Compute current and new heat input from flue gas temperature and coefficients.
Air Specific Heat Calculation: Compute current and new air specific heat from combustion air temperature and coefficients.
Air Correction Calculation: Compute current and new air correction using air specific heat, flue gas temperature, and excess air.
Combustion Air Correction Calculation: Compute current and new combustion air correction using air specific heat, combustion air temperature, and excess air.
Available Heat Calculation: Compute current and new available heat as the sum of heat input, air correction, and combustion air correction.
Fuel Savings Calculation: Compute new fuel savings as the percent improvement in available heat.
New Energy Input Calculation: Compute new energy input based on current energy input and fuel savings.

Excess Air Calculation

Calculates current and new excess air.

Computes the excess air percentage for both current and improved conditions based on measured flue gas oxygen and process-specific multipliers. Excess air is a key indicator of combustion efficiency and impacts fuel usage.

\begin{equation}\label{eq:pheic-excess-air} EA = \frac{100 \cdot S_A \cdot (\frac{O_2}{100})}{D_B - O_2M \cdot (\frac{O_2}{100})}\end{equation}

\(EA\)	Excess air \([\unit{ \percent}]\)
\(S_A\)	Stoichiometric air multiplier (8.52381) \([\unit{ \unitless}]\)
\(O_2\)	Flue gas oxygen (dry) \([\unit{ \percent}]\)
\(D_B\)	Denominator base (2.0) \([\unit{ \unitless}]\)
\(O_2M\)	O2 denominator multiplier (9.52381) \([\unit{ \unitless}]\)

Heat Input Calculation

Calculates current and new heat input.

Calculates the effective heat input to the process for both current and improved conditions, using flue gas temperature and empirical coefficients. Heat input reflects the energy delivered to the system.

\begin{equation}\label{eq:pheic-heat-input} HI = H_B + H_C \cdot T_{FG}\end{equation}

\(HI\)	Heat input \([\unit{ \percent}]\)
\(H_B\)	Heat input base (95.0) \([\unit{ \percent}]\)
\(H_C\)	Heat input temp coeff (-0.025) \([\unit{ \percent\per\degreeFahrenheit}]\)
\(T_{FG}\)	Flue gas temperature \([\unit{ \degreeFahrenheit}]\)

Air Specific Heat Calculation

Calculates current and new air specific heat.

Determines the specific heat capacity of combustion air for both current and improved conditions, as a function of air temperature. This value is important for quantifying the energy required to heat the combustion air.

\begin{equation}\label{eq:pheic-air-specific-heat} C_{p,air} = C_B + C_C \cdot T_{CA}\end{equation}

\(C_{p,air}\)	Air specific heat \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\)
\(C_B\)	Air specific heat base (0.017828518) \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\)
\(C_C\)	Air specific heat temp coeff (0.000002556) \([\unit{ \btu\per\pound\per\degreeFahrenheit}]\)
\(T_{CA}\)	Combustion air temperature \([\unit{ \degreeFahrenheit}]\)

Air Correction Calculation

Calculates current and new air correction.

Calculates the energy correction associated with heating excess air, for both current and improved conditions. This correction accounts for the energy lost to heating air that does not participate in combustion.

\begin{equation}\label{eq:pheic-air-correction} AC = -\left(A_B + C_{p,air} \cdot T_{FG}\right) \cdot \frac{EA}{100}\end{equation}

\(AC\)	Air correction \([\unit{ \percent}]\)
\(A_B\)	Air correction base (-1.07891327) \([\unit{ \unitless}]\)
\(C_{p,air}\)	Air specific heat \([\unit{ \btu\per\pound\degreeFahrenheit}]\)
\(T_{FG}\)	Flue gas temperature \([\unit{ \degreeFahrenheit}]\)
\(EA\)	Excess air \([\unit{ \percent}]\)

Combustion Air Correction Calculation

Calculates current and new combustion air correction.

Computes the energy correction for heating the total combustion air (including excess air), for both current and improved conditions. This step quantifies the energy required to bring all combustion air to the desired temperature.

\begin{equation}\label{eq:pheic-combustion-air-correction} CAC = \left(CA_B + C_{p,air} \cdot T_{CA}\right) \cdot \left(1 + \frac{EA}{100}\right)\end{equation}

\(CAC\)	Combustion air correction \([\unit{ \percent}]\)
\(CA_B\)	Combustion air correction base (-1.078913827) \([\unit{ \unitless}]\)
\(C_{p,air}\)	Air specific heat \([\unit{ \btu\per\pound\degreeFahrenheit}]\)
\(T_{CA}\)	Combustion air temperature \([\unit{ \degreeFahrenheit}]\)
\(EA\)	Excess air \([\unit{ \percent}]\)

Available Heat Calculation

Calculates current and new available heat.

Sums the heat input and both air corrections to determine the available heat for the process, for both current and improved conditions. Available heat represents the fraction of input energy that is actually usable for the process.

\begin{equation}\label{eq:pheic-available-heat} AH = HI + AC + CAC\end{equation}

\(AH\)	Available heat \([\unit{ \percent}]\)
\(HI\)	Heat input \([\unit{ \percent}]\)
\(AC\)	Air correction \([\unit{ \btu}]\)
\(CAC\)	Combustion air correction \([\unit{ \btu}]\)

Fuel Savings Calculation

Calculates new fuel savings.

Calculates the percentage of fuel saved by implementing the efficiency improvement, based on the increase in available heat. This value quantifies the benefit of the improvement in terms of reduced fuel consumption.

\begin{equation}\label{eq:pheic-fuel-savings} FS = \frac{AH_{new} - AH_{current}}{AH_{new}} \cdot 100\end{equation}

\(FS\)	Fuel savings \([\unit{ \percent}]\)
\(AH_{new}\)	New available heat \([\unit{ \percent}]\)
\(AH_{current}\)	Current available heat \([\unit{ \percent}]\)

New Energy Input Calculation

Calculates new energy input.

Determines the new required energy input to the process after efficiency improvements, accounting for the calculated fuel savings. This step provides the expected reduction in energy demand.

\begin{equation}\label{eq:pheic-new-energy-input} EI_{new} = EI_{current} \cdot \left(1 - \frac{FS}{100}\right)\end{equation}

\(EI_{new}\)	New energy input \([\unit{ \MMBtu\per\hour}]\)
\(EI_{current}\)	Current energy input \([\unit{ \MMBtu\per\hour}]\)
\(FS\)	Fuel savings \([\unit{ \percent}]\)

Modules
	Excess Air Calculation
	Calculates current and new excess air.

	Heat Input Calculation
	Calculates current and new heat input.

	Air Specific Heat Calculation
	Calculates current and new air specific heat.

	Air Correction Calculation
	Calculates current and new air correction.

	Combustion Air Correction Calculation
	Calculates current and new combustion air correction.

	Available Heat Calculation
	Calculates current and new available heat.

	Fuel Savings Calculation
	Calculates new fuel savings.

	New Energy Input Calculation
	Calculates new energy input.

Files
file	process_heat_efficiency_improvement.h
	Efficiency improvement calculations for process heating systems.

Namespaces
namespace	process_heat_efficiency_improvement
	Efficiency improvement calculations for process heating systems.

Classes
struct	process_heat_efficiency_improvement::ProcessHeatEfficiencyImprovementResults
	Results of the process heat efficiency improvement calculation. More...

Functions
ProcessHeatEfficiencyImprovementResults	process_heat_efficiency_improvement::processHeatEfficiencyImprovement (double current_flue_gas_oxygen, double new_flue_gas_oxygen, double current_flue_gas_temp, double new_flue_gas_temp, double current_combustion_air_temp, double new_combustion_air_temp, double current_energy_input)
	Calculates the efficiency improvement for a fuel fired furnace.

double	process_heat_efficiency_improvement::calculateExcessAir (double flue_gas_oxygen, double stoich_air_multiplier, double excess_air_denominator_base, double excess_air_o2_multiplier)
	Calculates excess air percentage.

double	process_heat_efficiency_improvement::calculateHeatInput (double flue_gas_temp, double heat_input_base, double heat_input_temp_coeff)
	Calculates heat input.

double	process_heat_efficiency_improvement::calculateAirSpecificHeat (double combustion_air_temp, double air_specific_heat_base, double air_specific_heat_coeff)
	Calculates air specific heat.

double	process_heat_efficiency_improvement::calculateAirCorrection (double air_correction_base, double air_specific_heat, double flue_gas_temp, double excess_air)
	Calculates air correction.

double	process_heat_efficiency_improvement::calculateCombustionAirCorrection (double combustion_air_correction_base, double air_specific_heat, double combustion_air_temp, double excess_air)
	Calculates combustion air correction.

double	process_heat_efficiency_improvement::calculateAvailableHeat (double heat_input, double air_correction, double combustion_air_correction)
	Calculates available heat.

double	process_heat_efficiency_improvement::calculateFuelSavings (double new_available_heat, double current_available_heat)
	Calculates new fuel savings.

double	process_heat_efficiency_improvement::calculateNewEnergyInput (double current_energy_input, double new_fuel_savings)
	Calculates new energy input.

Function Documentation

◆ calculateAirCorrection()

double process_heat_efficiency_improvement::calculateAirCorrection	(	double	air_correction_base,
		double	air_specific_heat,
		double	flue_gas_temp,
		double	excess_air
	)

Parameters

[in]	air_correction_base	Base for air correction \([\unit{\btu\per\pound}]\).
[in]	air_specific_heat	Air specific heat \([\unit{\btu\per\pound\per\degreeFahrenheit}]\).
[in]	flue_gas_temp	Flue gas temperature \([\unit{\degreeFahrenheit}]\).
[in]	excess_air	Excess air \([\unit{\percent}]\).

Returns: Air correction as \([\unit{\percent}]\) of HHV.

◆ calculateAirSpecificHeat()

double process_heat_efficiency_improvement::calculateAirSpecificHeat	(	double	combustion_air_temp,
		double	air_specific_heat_base,
		double	air_specific_heat_coeff
	)

Parameters

[in]	combustion_air_temp	Combustion air temperature \([\unit{\degreeFahrenheit}]\).
[in]	air_specific_heat_base	Base specific heat of air \([\unit{\btu\per\pound\per\degreeFahrenheit}]\).
[in]	air_specific_heat_coeff	Temperature coefficient for specific heat of air \([\unit{\btu\per\pound\per\degreeFahrenheit}]\).

Returns: Air specific heat \([\unit{\btu\per\pound\per\degreeFahrenheit}]\).

◆ calculateAvailableHeat()

double process_heat_efficiency_improvement::calculateAvailableHeat	(	double	heat_input,
		double	air_correction,
		double	combustion_air_correction
	)

Parameters

[in]	heat_input	Heat input \([\unit{\percent}]\).
[in]	air_correction	Air correction \([\unit{\percent}]\) of HHV.
[in]	combustion_air_correction	Combustion air correction \([\unit{\percent}]\) of HHV.

Returns: Available heat \([\unit{\percent}]\) of HHV.

◆ calculateCombustionAirCorrection()

double process_heat_efficiency_improvement::calculateCombustionAirCorrection	(	double	combustion_air_correction_base,
		double	air_specific_heat,
		double	combustion_air_temp,
		double	excess_air
	)

Parameters

[in]	combustion_air_correction_base	Base for combustion air correction \([\unit{\btu\per\pound}]\).
[in]	air_specific_heat	Air specific heat \([\unit{\btu\per\pound\per\degreeFahrenheit}]\).
[in]	combustion_air_temp	Combustion air temperature \([\unit{\degreeFahrenheit}]\).
[in]	excess_air	Excess air \([\unit{\percent}]\).

Returns: Combustion air correction as \([\unit{\percent}]\) of HHV.

◆ calculateExcessAir()

double process_heat_efficiency_improvement::calculateExcessAir	(	double	flue_gas_oxygen,
		double	stoich_air_multiplier,
		double	excess_air_denominator_base,
		double	excess_air_o2_multiplier
	)

Parameters

[in]	flue_gas_oxygen	Flue gas oxygen percentage (dry basis) \([\unit{\percent}]\).
[in]	stoich_air_multiplier	Stoichiometric air multiplier.
[in]	excess_air_denominator_base	Base value in denominator.
[in]	excess_air_o2_multiplier	O2 multiplier in denominator.

Returns: Excess air \([\unit{\percent}]\).

◆ calculateFuelSavings()

double process_heat_efficiency_improvement::calculateFuelSavings	(	double	new_available_heat,
		double	current_available_heat
	)

Parameters

[in]	new_available_heat	New available heat \([\unit{\percent}]\) of HHV.
[in]	current_available_heat	Current available heat \([\unit{\percent}]\) of HHV.

Returns: New fuel savings \([\unit{\percent}]\).

◆ calculateHeatInput()

double process_heat_efficiency_improvement::calculateHeatInput	(	double	flue_gas_temp,
		double	heat_input_base,
		double	heat_input_temp_coeff
	)

Parameters

[in]	flue_gas_temp	Flue gas temperature \([\unit{\degreeFahrenheit}]\).
[in]	heat_input_base	Base value for heat input \([\unit{\percent}]\).
[in]	heat_input_temp_coeff	Temperature coefficient for heat input \([\unit{\percent\per\degreeFahrenheit}]\).

Returns: Heat input \([\unit{\percent}]\).

◆ calculateNewEnergyInput()

double process_heat_efficiency_improvement::calculateNewEnergyInput	(	double	current_energy_input,
		double	new_fuel_savings
	)

Parameters

[in]	current_energy_input	Current energy input \([\unit{\mega\btu\per\hour}]\).
[in]	new_fuel_savings	New fuel savings \([\unit{\percent}]\).

Returns: New energy input \([\unit{\mega\btu\per\hour}]\).

◆ processHeatEfficiencyImprovement()

ProcessHeatEfficiencyImprovementResults process_heat_efficiency_improvement::processHeatEfficiencyImprovement	(	double	current_flue_gas_oxygen,
		double	new_flue_gas_oxygen,
		double	current_flue_gas_temp,
		double	new_flue_gas_temp,
		double	current_combustion_air_temp,
		double	new_combustion_air_temp,
		double	current_energy_input
	)

Uses process parameters to estimate the benefit of efficiency improvements.

Parameters

[in]	current_flue_gas_oxygen	Current % dry of flue gas oxygen.
[in]	new_flue_gas_oxygen	New % dry of flue gas oxygen.
[in]	current_flue_gas_temp	Current temperature of flue gas \([\unit{\degreeFahrenheit}]\).
[in]	new_flue_gas_temp	New temperature of flue gas \([\unit{\degreeFahrenheit}]\).
[in]	current_combustion_air_temp	Current temperature of combustion air \([\unit{\degreeFahrenheit}]\).
[in]	new_combustion_air_temp	New temperature of combustion air \([\unit{\degreeFahrenheit}]\).
[in]	current_energy_input	Current energy input \([\unit{\mega\btu\per\hour}]\).

Returns: ProcessHeatEfficiencyImprovementResults struct with all calculated outputs.

Detailed Description

Excess Air Calculation

Heat Input Calculation

Air Specific Heat Calculation

Air Correction Calculation

Combustion Air Correction Calculation

Available Heat Calculation

Fuel Savings Calculation

New Energy Input Calculation

Modules

Files

Namespaces

Classes

Functions

Function Documentation

◆ calculateAirCorrection()

◆ calculateAirSpecificHeat()

◆ calculateAvailableHeat()

◆ calculateCombustionAirCorrection()

◆ calculateExcessAir()

◆ calculateFuelSavings()

◆ calculateHeatInput()

◆ calculateNewEnergyInput()

◆ processHeatEfficiencyImprovement()