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Synonyms: Compressibility factor = Z-factor

Disclaimer: Not to be confused with Compressibility 

Dimensionless multiplier describing Dimensionless multiplier in real gas equation of state which describes the deviation of a real gas from  ideal gas behavior fluid density from ideal gas estimate under the same pressure & temperature conditions:

Z = \frac{p  \, V_m}{R \, T} = \frac{p}{\rho} \nu Rcdot \frac{M}{R \, T}

where

Alternatively Z-factor can be expressed through the dynamic fluid properties at reference conditions as:

Z(T, p) = Z^{\circ} \cdot \frac{\rho^{\circ} \, T^{\circ}}{p^{\circ}} \cdot \frac{p}{\rho(T, p) \, T} 

where 

Z-factor can be used to calculate fluid density 

\rho(T, p) = \rho^{\circ} \cdot \frac{Z^{\circ} \, T^{\circ}}{p^{\circ}} \cdot \frac{p}{Z(T, p) \, T} 

B(T, p) = \frac{\rho^{\circ}}{\rho(T, p)} =  \frac{p^{\circ} }{Z^{\circ} \, T^{\circ}} \cdot \frac{Z(T, p) \, T}{p} 

Z-factor is related to fluid It is related to gas compressibility 

c_g(p) = \frac{1}{p} - \frac{p1}{Z} \frac{dZ}{dp}

Z(p) = Z_0 \cdot \frac{Z_0p}{p_0} \cdot p \cdot \exp \left[ - \int_{p_0}^p c(p) dp  \right]

c

 = 

\frac{1}{\rho} \frac{

d\rho}{

dp}  = \frac{

d \ln \rho}{dp} = 

 \frac{d }{dp} \left(  \ln

  \left(\frac{p}{Z} \right)  \right) = \frac{Z}{p} \cdot \frac{d }{dp} \left(\frac{p}{Z} \right) = \frac{Z}{p} \cdot \left( \frac{1}{Z} + p \cdot \frac{d }{dp} \left( \frac{1}{Z} \right)   \right) = \frac{1}{p}  - \frac{1}{Z} \frac{dZ}{dp}

\frac{d \ln Z}{dp} = \frac{1}{p} - c(p) \rightarrow \ln \frac{

Z}{

Z_0} = \ln \frac{p}{p_0} - \int_{p_0}^p c(p) 

\, dp

The Z-factor value for Ideal Gas is strictly unit: 

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For many real gases (particularly for the most compositions of natural gases) the Z-factoris trending towards unit value (

For incompressible fluids  the Z-factor is trending to linear pressure dependence (

Modelling Z-factor 

There is also a good number of explicit Z-factor Correlations @models.

See also

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Natural Science / Physics / Thermodynamics / Equation of State

[ Compressibility ][ Fluid Compressibility ][ Gas compressibility ]

References

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