The compressibility of natural gas is typically calculated using the gas's critical temperature and pressure, along with its actual temperature and pressure. This calculation often relies on determining the gas's reduced temperature and reduced pressure.
Calculating Compressibility Using Reduced Temperature and Pressure
One common method involves using the concept of corresponding states, where the compressibility factor (Z) is related to the reduced temperature (Tr) and reduced pressure (Pr).
1. Determine Critical Temperature (Tc) and Critical Pressure (Pc)
First, you need to know the critical temperature (Tc) and critical pressure (Pc) of the natural gas mixture. These values can be found in reference tables or calculated based on the composition of the gas. If the gas is a mixture, appropriate mixing rules (like Kay's rule) must be applied to calculate the pseudo-critical temperature and pseudo-critical pressure.
2. Calculate Reduced Temperature (Tr) and Reduced Pressure (Pr)
Next, you calculate the reduced temperature (Tr) and reduced pressure (Pr) using the following formulas:
- Reduced Temperature (Tr): Tr = T / Tc
- Reduced Pressure (Pr): Pr = P / Pc
Where:
- T = Actual temperature of the gas
- P = Actual pressure of the gas
- Tc = Critical temperature of the gas
- Pc = Critical pressure of the gas
3. Determine Compressibility Factor (Z)
Using the calculated Tr and Pr, you can determine the compressibility factor (Z) using one of the following methods:
-
Compressibility Charts: Generalized compressibility charts (like the Standing and Katz chart) plot Z against Pr for various values of Tr. You can read the value of Z from the chart based on your calculated Tr and Pr.
-
Equations of State: Use an equation of state, such as the Peng-Robinson equation or the Soave-Redlich-Kwong (SRK) equation, to calculate Z. These equations relate pressure, volume, temperature, and composition to the compressibility factor.
- Peng-Robinson Equation of State (example): This is a cubic equation of state, which generally has to be solved iteratively to find the Z-factor.
4. Why is Compressibility Important?
The compressibility factor (Z) represents the deviation of a real gas from ideal gas behavior. Ideal gases have a Z-factor of 1. Real gases, including natural gas, have Z-factors that deviate from 1, especially at high pressures and low temperatures. It is critical for accurate calculations of gas volume, density, and flow rates in pipelines and processing equipment.
Example Scenario
Let's say you have natural gas at a temperature of 150 °F (65.6 °C or 338.8 K) and a pressure of 1000 psia (6895 kPa). Assume its critical temperature is 360 °R (200 K) and its critical pressure is 670 psia (4620 kPa).
- Convert temperature to consistent units: T = 338.8 K
- Convert pressure to consistent units: P = 6895 kPa
- Critical Temperature: Tc = 200 K
- Critical Pressure: Pc = 4620 kPa
Now, calculate Tr and Pr:
- Tr = 338.8 K / 200 K = 1.694
- Pr = 6895 kPa / 4620 kPa = 1.492
Using these values, you would consult a compressibility chart or use an equation of state to find the Z-factor. Note that the answer here would depend on chart resolution, reading accuracy and selected EOS equation.
