Synonyms: Compressibility Z-factor = Z-factor

Dimensionless multiplier in real gas equation of state which describes the deviation of a real gas from ideal gas behaviour:

(1)	$\begin{array}{l}\displaystyle Z = \frac{p V}{\nu \, R \, T} = \frac{p}{\rho} \cdot \frac{M}{R \, T}\end{array}$

where

It is related to fluid compressibility $\begin{array}{l}c\end{array}$ as:

(2)	$\begin{array}{l}\displaystyle c(p) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp}\end{array}$

(3)	$\begin{array}{l}\displaystyle Z(p) = \frac{Z_0}{p_0} \cdot p \cdot \exp \left[ - \int_{p_0}^p c(p) dp \right]\end{array}$

Derivation

(4)	$\begin{array}{l}\displaystyle c = - \frac{1}{V} \frac{dV}{dp} = - \frac{d}{dp} \left( \ln V \right) \rightarrow \ln \frac{V}{V_0} = - \int_{p_0}^p c(p) dp\end{array}$

Substituting $\begin{array}{l}V\end{array}$ from (1) into (4) one arrives to (2).

The Z-factor value is trending towards $\begin{array}{l}Z \rightarrow 1\end{array}$ for incompressible fluids and $\begin{array}{l}Z \rightarrow a \cdot p\end{array}$ for strongly compressible Fluids.

Modelling Z-factor $\begin{array}{l}Z(T,p)\end{array}$ as a function of fluid pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ is based on Equation of State.

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

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References