@wikipedia
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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Z = \frac{p \, V_m}{R \, T} = \frac{p}{\rho} \cdot \frac{M}{R \, T} |
where
Alternatively Z-factor can be expressed through the dynamic fluid properties at reference conditions as:
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Z(T, p) = Z^{\circ} \cdot \frac{\rho^{\circ} \, T^{\circ}}{p^{\circ}} \cdot \frac{p}{\rho(T, p) \, T} |
where
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| body | --uriencoded--()%5e%7B\circ%7D |
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means reference conditions, usually
Standard Conditions (STP).
Z-factor can be used to calculate fluid density
and
Formation Volume Factor (FVF) as:
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| \rho(T, p) = \rho^{\circ} \cdot \frac{Z^{\circ} \, T^{\circ}}{p^{\circ}} \cdot \frac{p}{Z(T, p) \, T} |
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| B(T, p) = \frac{\rho^{\circ}}{\rho(T, p)} = \frac{p^{\circ} }{Z^{\circ} \, T^{\circ}} \cdot \frac{Z(T, p) \, T}{p} |
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Z-factor is related to fluid compressibility
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| c(p) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp} |
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| Z(p) = Z_0 \cdot \frac{p}{p_0} \cdot \exp \left[ - \int_{p_0}^p c(p) dp \right] |
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| 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} |
Rewriting | LaTeX Math Block Reference |
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| \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 |
which arrives to | LaTeX Math Block Reference |
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The Z-factor value is trending towards unit value (
)
for incompressible fluids and linear pressure dependence (| LaTeX Math Inline |
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| body | Z \rightarrow a \cdot p |
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)
for strongly compressible fluids.
Modelling Z-factor as a function of fluidpressure and temperature is based on Equation of State.
There is also a good number of explicit Z-factor Correlations @models.
See also
Natural Science / Physics / Thermodynamics / Equation of State
[ Compressibility ][ Fluid Compressibility ][ Gas compressibility ]
References
