Compressed Air Pressure Reduction Calculator

Detailed Description

This calculator can be used to quantify the electricity saved from reducing compressed air system pressure. The benefits of lowering system pressure are twofold:

1. Reduced compressor work — Lower pressure reduces compressor work and therefore reduces electrical demand.
2. Reduced airflow losses — Lower pressure reduces delivered airflow and therefore reduces losses from artificial demand and air leaks.

This calculator only estimates electricity savings at compressors. These savings are not applicable when compressed air is supplied from an external source.

Note

This calculator is not valid for centrifugal compressors.

The calculation estimates annual electrical energy use and annual energy cost for compressed-air systems evaluated during treasure hunt activities. It supports a baseline mode and a modification mode, and the baseline mode includes two power-entry options:

1. Baseline (Measured Power) — Uses measured compressor power and annual operating hours directly.
2. Baseline (Rated Power) — Uses rated (or otherwise estimated) compressor power and annual operating hours directly.
3. Modification — Uses proposed pressure, atmospheric pressure, and rated pressure to estimate adjusted power.

For each measure, the selected mode computes annual energy use and annual energy cost, then totals are accumulated across all measures.

Baseline Energy Use

---

Annual energy use for baseline compressed-air operation using measured or rated power.

The baseline calculation accepts compressor power as a direct input and applies the same equation for both baseline options:

1. Measured Power baseline — \(P_{comp}\) is measured compressor power.
2. Rated Power baseline — \(P_{comp}\) is rated compressor power.

In both cases, annual energy use is compressor power multiplied by annual operating hours.

\begin{equation}\label{eq:compressed-air-pressure-reduction-baseline-energy} E_{use} = P_{comp} \cdot t_{op}\end{equation}

Symbols

\(E_{use}\)	Annual energy use \([\unit{ \kWh\per\year}]\)
\(P_{comp}\)	Compressor power \([\unit{ \kW}]\)
\(t_{op}\)	Annual operating hours \([\unit{ \hour\per\year}]\)

Modification Energy Use

---

Annual energy use for pressure-reduction modification.

First estimate modification power from pressure terms, then multiply by annual operating hours. The ratio \(x\) converts the proposed pressure from gauge (psig) to absolute (psia) using the user-supplied atmospheric pressure \(P_{atm}\). The ratio \(r\) converts the rated compressor pressure from psig to psia using an assumed standard atmospheric pressure of \(14.7\) \([\unit{\psi}]\). The exponent \(c = (k-1)/k\) is the isentropic exponent derived from the heat capacity ratio \(k = 1.395\) for air (ratio of specific heats \(c_p/c_v\)).

\begin{equation}\label{eq:compressed-air-pressure-reduction-modification-power} P_{mod} = P_{comp} \cdot \frac{x^c - 1}{r^c - 1}\end{equation}

\begin{equation}\label{eq:compressed-air-pressure-reduction-modification-ratio-x} x = \frac{P_{proposed} + P_{atm}}{P_{atm}}\end{equation}

\begin{equation}\label{eq:compressed-air-pressure-reduction-modification-ratio-r} r = \frac{P_{rated} + 14.7}{14.7}\end{equation}

\begin{equation}\label{eq:compressed-air-pressure-reduction-modification-c} c = \frac{k-1}{k}\end{equation}

\begin{equation}\label{eq:compressed-air-pressure-reduction-modification-energy} E_{use} = P_{mod} \cdot t_{op}\end{equation}

Symbols

\(E_{use}\)	Annual energy use \([\unit{ \kWh\per\year}]\)
\(P_{mod}\)	Modification compressor power estimate \([\unit{ \kW}]\)
\(P_{comp}\)	Compressor power \([\unit{ \kW}]\)
\(P_{proposed}\)	Proposed compressor discharge pressure (psig) \([\unit{ \psi}]\)
\(P_{atm}\)	Atmospheric pressure (user-supplied, converts psig to psia) \([\unit{ \psi}]\)
\(P_{rated}\)	Rated compressor discharge pressure (psig) \([\unit{ \psi}]\)
\(14.7\)	Assumed standard atmospheric pressure (converts \(P_{rated}\) from psig to psia) \([\unit{ \psi}]\)
\(x\)	Proposed absolute pressure ratio \([\unit{ \unitless}]\)
\(r\)	Rated absolute pressure ratio \([\unit{ \unitless}]\)
\(c\)	Isentropic exponent, (k-1)/k \([\unit{ \unitless}]\)
\(k\)	Heat capacity ratio of air, c_p/c_v (1.395) \([\unit{ \unitless}]\)
\(t_{op}\)	Annual operating hours \([\unit{ \hour\per\year}]\)

Energy Cost

---

Annual energy cost from annual energy use and electricity rate.

\begin{equation}\label{eq:compressed-air-pressure-reduction-energy-cost} C_{energy} = E_{use} \cdot r_{elec}\end{equation}

Symbols

\(C_{energy}\)	Annual energy cost \([\unit{ \dollar\per\year}]\)
\(E_{use}\)	Annual energy use \([\unit{ \kWh\per\year}]\)
\(r_{elec}\)	Electricity cost rate \([\unit{ \dollar\per\kWh}]\)

Modules
	Baseline Energy Use Formula
	Annual energy use for baseline compressed-air operation using measured or rated power.
	Modification Energy Use Formula
	Annual energy use for pressure-reduction modification.
	Energy Cost Formula
	Annual energy cost from annual energy use and electricity rate.

Files
file	compressed_air_pressure_reduction.h
	Declares structs and functions for the Compressed Air Pressure Reduction Calculator.Quantifies electricity savings from reducing compressed air system pressure.

Namespaces
namespace	compressed_air_pressure_reduction
	Compressed-air pressure reduction calculations for treasure hunt measures.

Classes
struct	compressed_air_pressure_reduction::CompressedAirPressureReductionInput
	Input data for a single compressed-air pressure reduction measure. More...
struct	compressed_air_pressure_reduction::CompressedAirPressureReductionOutput
	Output data for compressed-air pressure reduction calculations. More...

Functions
CompressedAirPressureReductionOutput	compressed_air_pressure_reduction::compressedAirPressureReduction (const std::vector< CompressedAirPressureReductionInput > &input_vec)
	Calculates total annual energy use and cost for compressed-air pressure reduction measures.
CompressedAirPressureReductionOutput	compressed_air_pressure_reduction::baselineReduction (int hours_per_year, double electricity_cost, double compressor_power)
	Calculates annual energy use and cost for a baseline compressed-air case.
CompressedAirPressureReductionOutput	compressed_air_pressure_reduction::modificationReduction (int hours_per_year, double electricity_cost, double compressor_power, double proposed_pressure, double atmospheric_pressure, double pressure_rated)
	Calculates annual energy use and cost for a compressed-air pressure-reduction modification.

Function Documentation

baselineReduction()

CompressedAirPressureReductionOutput compressed_air_pressure_reduction::baselineReduction	(	int	hours_per_year,
		double	electricity_cost,
		double	compressor_power
	)

Parameters

[in]	hours_per_year	Annual operating hours \([\unit{\hour\per\year}]\).
[in]	electricity_cost	Electricity cost rate \([\unit{\dollar\per\kWh}]\).
[in]	compressor_power	Compressor power \([\unit{\kW}]\).

Returns

CompressedAirPressureReductionOutput with annual energy use and cost.

compressedAirPressureReduction()

CompressedAirPressureReductionOutput compressed_air_pressure_reduction::compressedAirPressureReduction

(

const std::vector< CompressedAirPressureReductionInput > &

input_vec

)

Parameters

[in]

input_vec

Vector of CompressedAirPressureReductionInput structs.

Returns

CompressedAirPressureReductionOutput containing accumulated annual energy use and cost.

modificationReduction()

CompressedAirPressureReductionOutput compressed_air_pressure_reduction::modificationReduction	(	int	hours_per_year,
		double	electricity_cost,
		double	compressor_power,
		double	proposed_pressure,
		double	atmospheric_pressure,
		double	pressure_rated
	)

Parameters

[in]	hours_per_year	Annual operating hours \([\unit{\hour\per\year}]\).
[in]	electricity_cost	Electricity cost rate \([\unit{\dollar\per\kWh}]\).
[in]	compressor_power	Compressor power \([\unit{\kW}]\).
[in]	proposed_pressure	Proposed compressor discharge pressure \([\unit{\psi}]\).
[in]	atmospheric_pressure	Local atmospheric pressure \([\unit{\psi}]\).
[in]	pressure_rated	Rated compressor pressure \([\unit{\psi}]\).

Returns

CompressedAirPressureReductionOutput with annual energy use and cost.