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Synonyms: Compressibility factor = Z-factor

Disclaimer: Not to be confused with Compressibility 

Dimensionless multiplier describing the deviation of a fluid density from ideal gas estimate under the same pressure & temperature conditions:

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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 is related to  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) = 

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\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 compressibility 

c(p) = \frac{1}{p} - \frac{1}{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: 

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  for incompressible fluids and linear pressure dependence (

Modelling Z-factor 

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Natural Science / Physics / Thermodynamics / Equation of State

[ Compressibility ][ Fluid Compressibility ][ Gas compressibility ]

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