How is CNG Calculated?

CNG (Compressed Natural Gas) volume in standard cubic feet (scf) is calculated using pressure, temperature, total volume, and NIST (National Institute of Standards and Technology) data. The calculation relies on the principles of thermodynamics and gas laws, specifically accounting for the compressibility of natural gas at high pressures.

Here's a breakdown of the calculation process:

Understanding the Variables

• Pressure (P): The pressure of the CNG in the container, typically measured in pounds per square inch (psi) or bar.
• Temperature (T): The temperature of the CNG in the container, typically measured in degrees Fahrenheit (°F) or Celsius (°C). This needs to be converted to an absolute temperature scale (Rankine or Kelvin) for calculations.
• Volume (V): The total volume of the CNG container, typically measured in cubic feet or liters.
• Standard Pressure (P_std): A defined standard pressure, usually 14.7 psi (1 atm).
• Standard Temperature (T_std): A defined standard temperature, usually 60°F (520°R) or 15°C (288.15 K).
• Compressibility Factor (Z): A factor that accounts for the deviation of real gases from ideal gas behavior, especially at high pressures. This factor depends on the gas composition, pressure, and temperature, and is often obtained from NIST data or empirical equations.

The Calculation Process

The core principle involves converting the volume of CNG at the actual pressure and temperature to an equivalent volume at standard conditions. The ideal gas law (PV = nRT) is often used as a starting point, but it needs to be corrected for the non-ideal behavior of natural gas at high pressures. The compressibility factor (Z) is used to account for this.

1. Determine the Compressibility Factor (Z): This is the most complex part. The compressibility factor can be found using:

   • NIST Data: The NIST REFPROP database provides accurate values for Z based on the specific composition of the natural gas, pressure, and temperature.
   • Equations of State: Various equations of state (e.g., Peng-Robinson, Benedict-Webb-Rubin) can be used to estimate Z based on the gas composition, pressure, and temperature.

2. Apply the Real Gas Law: The real gas law is a modified version of the ideal gas law that includes the compressibility factor:

   PV = Z n R T

   Where:

   • P = Pressure
   • V = Volume
   • Z = Compressibility Factor
   • n = Number of moles of gas
   • R = Ideal gas constant
   • T = Temperature

3. Calculate the Equivalent Volume at Standard Conditions (V_std): This is done by relating the real gas law at actual conditions to the real gas law at standard conditions. Assuming the number of moles of gas (n) remains constant:

   (P V) / (Z T) = (P<sub>std</sub> V<sub>std</sub>) / (Z<sub>std</sub> T<sub>std</sub>)

   Solving for V_std (the volume at standard conditions, which is the CNG volume in scf):

   V<sub>std</sub> = (P V Z<sub>std</sub> T<sub>std</sub>) / (Z T P<sub>std</sub>)

   Where:

   • Z_std is the compressibility factor at standard conditions (often close to 1 for natural gas).

Simplified Formula (Assuming Z_std = 1)

If we assume that the compressibility factor at standard conditions (Z_std) is approximately 1, the equation simplifies to:

V<sub>std</sub> = (P V T<sub>std</sub>) / (Z T P<sub>std</sub>)

This simplified formula is often used when Z_std is close to 1 and the compressibility factor (Z) at the actual pressure and temperature is known or can be accurately estimated.

Example

Let's say you have a CNG cylinder with the following parameters:

• Volume (V) = 10 cubic feet
• Pressure (P) = 3000 psi
• Temperature (T) = 80°F (540°R)
• Compressibility Factor (Z) = 0.9 (obtained from NIST data or an equation of state)
• Standard Pressure (P_std) = 14.7 psi
• Standard Temperature (T_std) = 60°F (520°R)

Using the simplified formula:

V<sub>std</sub> = (3000 psi * 10 cubic feet * 520°R) / (0.9 * 540°R * 14.7 psi) ≈ 2188 scf

Therefore, the CNG cylinder contains approximately 2188 standard cubic feet of natural gas.

Conclusion

Calculating CNG volume accurately requires considering the compressibility of natural gas at high pressures. By using the real gas law and incorporating the compressibility factor (obtained from NIST data or appropriate equations of state), a more precise determination of CNG volume in standard cubic feet can be achieved.