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Phase Behavior and ThermodynamicsGas Properties

Real Gas Isothermal Compressibility with Z-Factor Derivative Formula

cg=1P1z(dzdP)Tc_g=\frac{1}{P}-\frac{1}{z}\left(\frac{dz}{dP}\right)_T

Real Gas Isothermal Compressibility with Z-Factor Derivative calculates real gas isothermal compressibility for gas properties workflows in phase behavior and thermodynamics.

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How engineers use this formula

Use this formula when the listed inputs (P, z, dz_dP) are known and the assumptions behind the cited gas properties relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, c_g equals 0.000357 1/psi.

Ppsia

3000

zdimensionless

0.85

dz_dP1/psi

-0.00002

Inputs

P

psia

Pressure

z

dimensionless

Gas Compressibility Factor

dz_dP

1/psi

Isothermal Derivative of Z Factor with Respect to Pressure

Outputs

c_g

1/psi

Real Gas Isothermal Compressibility

dz_dP

1/psi

Isothermal Derivative of Z Factor with Respect to Pressure

Source and review

reviewed

Penn State PNG 301. Natural Gas Properties, Equations 3.69 through 3.70.

Source

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