Ideal Gas

Key Takeaways

• The gas compressibility factor (Z-factor) quantifies the deviation of real natural gas from ideal behavior by expressing the ratio of the actual molar volume of the gas to the ideal molar volume predicted by the ideal gas law at the same temperature and pressure, with Z = Vactual / Videal: at low pressures (below approximately 500 psia for most natural gases), Z is close to 1 and the ideal gas law is an excellent approximation; at intermediate pressures (1,000 to 3,000 psia), attractive forces between gas molecules dominate and Z decreases below 1 (the gas occupies less volume than the ideal gas law predicts, meaning it is more compressible than ideal); at very high pressures (above approximately 5,000 to 8,000 psia), repulsive forces at close molecular separations dominate and Z increases above 1 (the gas is less compressible than ideal because the finite molecular volume reduces the available compressible space); the Standing-Katz Z-factor chart (developed from experimental data for natural gas mixtures in 1942 and still the most widely used industry reference) plots Z as a function of pseudo-reduced pressure and pseudo-reduced temperature for natural gas mixtures using the principle of corresponding states.
• Standard conditions for natural gas measurement (the reference state at which gas volumes are reported and custody transfer occurs) are based on the ideal gas law framework: in the United States, standard conditions are typically 14.696 psia and 60 degrees Fahrenheit (519.67 degrees Rankine), at which one pound-mole of ideal gas occupies 379.4 standard cubic feet (scf); gas volumes measured at elevated reservoir pressure and temperature must be converted to standard conditions for reporting, surface facility sizing, and sales metering using the real gas equation P1V1/Z1T1 = P2V2/Z2T2 (where subscripts 1 and 2 refer to reservoir and standard conditions respectively); the concept of reservoir gas in place (GIP) in standard cubic feet (Mcf, MMscf, or Bcf) requires converting the physical volume of gas in the reservoir pore space (at reservoir pressure and temperature) to the equivalent volume at standard conditions, using the formation volume factor Bg = (T/Tsc)(Psc/P)(Zsc/Z) as the conversion factor between reservoir and standard volumes; different countries and contracts use different standard conditions (15 degrees Celsius and 101.325 kPa in SI and Canadian usage), requiring careful attention to which standard conditions are being used in international gas volume comparisons and contracts.
• Material balance equations for gas reservoirs are derived directly from the ideal gas law and its real gas modification, using the PV = ZnRT framework to relate the decline in reservoir pressure over time to the volume of gas produced (the Havlena-Odeh material balance for gas): as gas is produced from a reservoir, the pressure declines proportionally to the fraction of original gas in place that has been removed (adjusted for Z-factor changes with pressure), providing the basis for the p/Z plot that plots (pressure divided by Z-factor) versus cumulative gas production on a graph where a straight-line plot indicates volumetric depletion behavior (no water influx) and the x-intercept of the straight line (at p/Z = 0) gives the original gas in place; the deviation of actual p/Z plots from a straight line indicates water influx or other pressure support mechanisms; this simple application of the ideal gas law framework (modified by Z) provides one of the most powerful tools in reservoir engineering for estimating gas reserve size and forecasting future pressure and production rate.
• Gas processing and pipeline design calculations rely on the ideal gas law and Dalton's law of partial pressures (which states that the total pressure of a mixture of ideal gases equals the sum of the partial pressures each gas would exert alone in the same volume at the same temperature) for compressor sizing, separator design, and flow line hydraulics: a compressor that must move gas from 100 psia to 1,000 psia increases the pressure by a factor of 10, and if the gas were ideal, the volume would decrease by a factor of 10 at the same temperature; in practice the temperature rises during adiabatic compression (the isentropic compression path is calculated using the ideal gas adiabatic exponent gamma = Cp/Cv), and the real gas Z-factor changes with pressure, so the actual compression work differs from the ideal isothermal minimum by the adiabatic efficiency of the compressor; all multi-stage compression calculations in gas processing use the real gas law (with appropriate equation of state models for Z) rather than the ideal gas law directly, but the ideal gas law provides the conceptual framework and the limiting case that simplifies the analysis of the direction and magnitude of the pressure-volume-temperature changes during processing.
• Equations of state (EOS) used in petroleum reservoir and process simulation are sophisticated extensions of the ideal gas law that incorporate molecular interaction terms to accurately represent real gas and liquid behavior over the full range of pressures and temperatures encountered in reservoirs and processing facilities: the van der Waals equation (the first modification of the ideal gas law, adding a molecular volume correction (b) and an intermolecular attraction correction (a)) provides the conceptual basis for all subsequent EOS development; the Peng-Robinson and Soave-Redlich-Kwong (SRK) cubic equations of state, which add temperature-dependent attraction terms to improve liquid property predictions, are the industry-standard EOS for natural gas and oil reservoir simulation and PVT (pressure-volume-temperature) analysis; these complex EOS models converge to ideal gas behavior (Z approaches 1) at low pressures and high temperatures, confirming that the ideal gas law is the correct asymptotic limit of all accurate gas behavior models and the appropriate simplification when pressures are low enough that molecular interaction effects are negligible.