OpenSpecEngineering

Finds the density of a gas at a given pressure and temperature from the real-gas law, along with its molar volume, specific volume, its density at standard conditions and the ratio of actual to standard volume. Process and pipeline engineers use it to turn a standard flow rate into an actual one, to size lines and vessels, and to find the mass of gas held in a volume.

Equations

ρ = P·M/(Z·R·T)     V_m = Z·R·T/P     v = 1/ρ

ρ_std = P_std·M/(R·T_std)

ρ is the gas density and v the specific volume. P is the absolute pressure and T the absolute temperature (the page converts °C or °F to kelvin). M is the molecular weight in g/mol, and R = 8.314462618 J/(mol·K) is the universal gas constant. Z is the compressibility factor: the ratio of the real molar volume V_m to the ideal one [1], [2]. Standard conditions are 15 °C and 101.325 kPa, where the gas is taken as ideal (Z = 1). The last result, ρ_std/ρ, is the actual volume that one standard volume of gas fills at P and T.

Inputs

• Choosing a Gas fills in its molecular weight [3]. For a mixture, choose Custom and enter the mole-weighted average M.
• The page does not find Z. Use 1 for an ideal gas, read it from a generalized chart [1], [2], or get it from the Peng–Robinson calculator.

Limits and common mistakes

• Enter absolute pressure. A gauge reading of 500 kPa is about 601 kPa absolute at sea level.
• Z must match the same P and T. A Z found at one condition does not carry over to another.
• Standard conditions vary: 15 °C here, but 0 °C for “normal” volumes and 60 °F in US gas practice. Check which one your flow figure uses.
• The law applies to a single gas phase. Near the dew point or the critical point, Z changes fast and needs a careful source.

Worked example

A natural gas line, taken as pure methane, runs at 7000 kPa absolute and 15 °C. What is the gas density in the line, and how much does the gas shrink from standard volume?

1. Find Z on the Peng–Robinson calculator for methane at 15 °C and 7000 kPa. It gives Z = 0.849247; round it to 0.849.
2. Enter Pressure 7000 kPa and Temperature 15 °C.
3. Choose Gas Methane (CH₄). The molecular weight fills in as 16.043 g/mol.
4. Enter Compressibility Factor 0.849 and press Solve. The Solution shows: Gas density ρ: 55.2107 kg/m³
   Molar volume: 0.290578 L/mol
   Specific volume: 0.0181124 m³/kg
   Standard density (15 °C, 101.325 kPa): 0.678499 kg/m³
   Actual volume / standard volume: 0.0122893

Check by hand: at the same temperature, the volume ratio is just Z·P_std/P = 0.849 × 101.325/7000 = 0.01229, so the density is 0.6785/0.01229 = 55.2 kg/m³. As an ideal gas (Z = 1) it would be about 15 % lighter, which is why Z matters at pipeline pressures.