BULLETIN BCTB-302
GAS COMPRESSIBILITY
INTRODUCTION Deviations 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 brief review of the ideal gas laws and the deviations which must be considered when dealing with gas compression applications. The information presented herein is believed to be the most accurate at the time of publication. IDEAL GAS LAW Pressure, temperature and volume are the three variables that influence the status of the gas. A change in one variable affects either or both of the other two variables. Boyle observed that a change in the absolute pressure of a gas resulted in an inverse change in the volume when held at a constant temperature.Charles observed that when the volume is held constant, the absolute pressure will vary in proportion to the change in absolute temperature. 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) / T 2 = constant R, for each each gas at standard conditions The standard specific volume and specific weight of a pound mole of any gas can be expressed as: Vs =
δ =
379.5 m
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 a phenomenon 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: P1V1 k = P2V2 k = constant This relationship for the ideal change of state, wherein no heat is lost los t or friction is incurred, is known as the adiabatic state. st ate. When an adiabatic process is reversible, rever sible, it is known as an isentropic 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
BCTB-302, GAS COMPRESSIBILITY
compressors), and generate frictional heat. The effect of these losses and the departure from the ideal adiabatic slope illustrates the phenomenon known as a polytropic process. It is defined as an internally reversible change of state where: P1V1 n = P2V2 n = constant A polytropic process differs from an adiabatic process in that the change of state does not take place at constant entropy. Heat is either rejected from or added to the gas in a polytropic process. The polytropic exponent n that governs the change of state becomes a 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 hydraulic media, the n value is less than the adiabatic k value. Values for n are determined from actual performance data for each type of compressor. VAN DER WAALS' GAS EQUATIONS This 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. When a gas is confined under elevated pressure and temperature, the molecular behavior becomes abnormal and turbulent, requiring corrections to the ideal gas law condition of state. The van der Waals gas equations account for much of the extraordinary behavior of real gas. The transitional processes indicated by van der Waals charts are comparable to the process of evaporation and condensation of a real fluid. In environs where transition does not occur, the gas characteristics correspond to the critical pressures and temperatures of real gases. The behavior can be expressed in terms of reduced critical pressure and reduced 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 commonly called the real gas law: (P1V1)/(Z1T1) = (P 2V2)/(Z2T2) = constant GAS PROPERTIES On 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 Generalized Compressibility Curves is recommended. The compressibility curves presented have been drawn from a collection of the best data available.
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BCTB-302, GAS COMPRESSIBILITY
CONTENTS OF DATA SECTION TITLE
Page No.(s)
Table 1, Properties of Selected Gases Vapor Pressure Curves Air Ammonia Butane (N-Butane) Carbon Dioxide Ethane Ethylene lsobutane Helium Hydrogen Methane Nitrogen Propane Propylene Synthetic Ammonia Feed Gas (5 component) Synthetic Ammonia Mixture (76/24) Procedure for Using Generalized Curves
4 5 6 7 8, 9 10, 11 12, 13 14, 15 16, 17 18 19 20 21 22, 23 24 25, 26 27, 28 29, 30
Generalized Compressibility Curves: Number 1 Number 2 Number 3 Number 4
31 32 33 34
Natural Gas Supercompressibility
35
Natural Gas Compressibility Curves: 0.60 Specific Gravity 0.65 Specific Gravity 0.70 Specific Gravity 0.75 Specific Gravity 0.80 Specific Gravity 0.90 Specific Gravity 1.0 Specific Gravity
36 37 38 39 40 41 42
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