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BULLETIN BCTB-302 GAS COMPRESSIBILITY

INTRODUCTIONDeviations from the Ideal Gas Laws are known as compressibility factors. These must be

accounted for at both suction and discharge conditions. This bulletin presents a briefreview of the ideal gas laws and the deviations which must be considered when dealingwith gas compression applications. The information presented herein is believed to be themost accurate at the time of publication.

IDEAL GAS LAWPressure, temperature and volume are the three variables that influence the status of thegas. A change in one variable affects either or both of the other two variables. Boyleobserved that a change in the absolute pressure of a gas resulted in an inverse change inthe volume when held at a constant temperature.Charles observed that when the volumeis held constant, the absolute pressure will vary in proportion to the change in absolutetemperature. The order of influence of these variables and the gas constant is established

in the so-called "Ideal Gas Law" or "Perfect Gas Law":

(P1V1) / T1 = (P2V2) / T2 = constant R, for each gas at standard conditions

The standard specific volume and specific weight of a pound mole of any gas can beexpressed as:

Vs= cu.ft. / lb, or 379.5 cu.ft. / mole

= 0.002635m lb / cu.ft.

Boyle's law gives the change of state for the ideal condition where there is no change in

temperature and the PV relationship is equal to a constant:

P1V1= P2V2= constant

This is the theoretical supposition known as an isothermal change of state. Such aphenomenon does not occur in nature or in fact. When a gas is compressed or expanded,it has been established that the pressure will vary to an exponential power of the volume:

P1V1k = P2V2

k = constant

This relationship for the ideal change of state, wherein no heat is lost or friction is incurred,is known as the adiabatic state. When an adiabatic process is reversible, it is known as anisentropic process. In as much as all adiabatic processes herein concerned are reversible,the terms "adiabatic" and "isentropic" are considered synonymous.

True adiabatic compression can only be attained under ideal research conditions.Industrial compressors reject heat, have valve leakage (ring leakage on piston

379.5 m

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BCTB-302, GAS COMPRESSIBILITY

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compressors), and generate frictional heat. The effect of these losses and the departurefrom the ideal adiabatic slope illustrates the phenomenon known as a polytropic process.

It is defined as an internally reversible change of state where:

P1V1n = P2V2

n = constant

A polytropic process differs from an adiabatic process in that the change of state does nottake place at constant entropy. Heat is either rejected from or added to the gas in apolytropic process. The polytropic exponent n that governs the change of state becomesa function of the compressor design. When heat is extracted from the gas by the cooling

media, and in the case of diaphragm compressors by both the cooling and hydraulicmedia, the n value is less than the adiabatic k value. Values for n are determined fromactual performance data for each type of compressor.

VAN DER WAALS' GAS EQUATIONSThis is an equation of state that extends the application and accuracy of the ideal gas law

by including corrections for the volume occupied by the molecules at elevated pressures

and temperatures and for the mutual attraction that exists between the molecules. Whena gas is confined under elevated pressure and temperature, the molecular behaviorbecomes abnormal and turbulent, requiring corrections to the ideal gas law condition ofstate.

The van der Waals gas equations account for much of the extraordinary behavior of realgas. The transitional processes indicated by van der Waals charts are comparable to theprocess of evaporation and condensation of a real fluid. In environs where transition doesnot occur, the gas characteristics correspond to the critical pressures and temperatures ofreal gases. The behavior can be expressed in terms of reduced critical pressure andreduced critical temperature, thereby establishing a common equation of state for most

gases. Commonly called Reduced Pressure-Reduced Temperature Charts or Generalized

Compressibility Charts, they are widely used to determine compressor performance.

Z = (PV)/(PcVc)

The compressibility factor Z is applied to the ideal gas law and produces what is commonlycalled the real gas law:

(P1V1)/(Z1T1) = (P2V2)/(Z2T2) = constant

GAS PROPERTIESOn the following pages we have provided a table listing basic properties of selected gases,vapor pressure curves, and compressibility curves for many of those gases. If a

compressibility curve does not exist for a specific gas, the use of the GeneralizedCompressibility Curves is recommended. The compressibility curves presented have beendrawn from a collection of the best data available.

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