Perfect Gas Equation and Compressibility

Equation 100-1 defines the behavior of a “perfect” gas in terms of variables listed: pressure, temperature, volume, etc. This is a helpful starting point, although few gases actually are “perfect”:

equ 1 - Perfect Gas Equation and Compressibility

where:
p = absolute pressure in pounds per square foot
V = volume in cubic feet
W = weight in pounds
R = Ro /M = constant for specific gas
Ro = universal gas constant = 1545.3 (ft.-lb./lb mol °R)
T = absolute temperature in degrees Rankine (°R)
M = molecular weight

For a continuous flow process, Equation 100-1 is modified as follows

equ 2 - Perfect Gas Equation and Compressibility

where:
Q = actual volumetric flow rate in cubic feet per minute (ACFM)
w = weight flow, pounds per minute and,
P is now in psia

To correct for deviations from a “perfect” gas, a compressibility factor, Z, is added
to Equation 100-2. Z is an empirical factor to correct the equation for actual, real
gases which deviate from “perfect.”

equ 3 - Perfect Gas Equation and Compressibility

For example:
At standard conditions (14.7 psia, 60°F) the factor (Z) of most gases is generally assumed to be 1.0. However, some gases deviate appreciably even at standard conditions. For example, normal butane has a Zo value of 0.975 (Zo denotes the factor at standard conditions).

Values for Z are available in charts for the gas being compressed. If a chart is not available, or if the gas is a mixture, generalized compressibility charts may be used. To use these charts, it is necessary to compute the so-called reduced pressure and temperature as follows[v]

equ 4 - Perfect Gas Equation and Compressibility

Pr = Reduced pressure
P = Actual absolute pressure, psia
Pc = Critical pressure of the gas, psia
Tr = Reduced temperature
T = Actual absolute temperature, °R
Tc = Critical temperature of the gas, °R

The compressibility of some pure gases, notably steam and ammonia, cannot be accurately predicted using the generalized charts. However, steam tables and an individual chart for pure ammonia are available. When the water vapor or ammonia content of a mixture is small (5% or less), the generalized charts may be used for the mixture with relatively good accuracy.

For gas mixtures containing hydrogen or helium, effective values of critical pressure and temperature for helium and hydrogen must be used to derive acceptable accuracy from the generalized charts.


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