Compressibility = β = c

Disclaimer: Not to be confused with Compressibility factor $\begin{array}{l}Z\end{array}$ .

A measure of relative change in density $\begin{array}{l}\rho\end{array}$ or molar volume $\begin{array}{l}V_m\end{array}$ under a unit pressure $\begin{array}{l}p\end{array}$ variation:

(1)	$\begin{array}{l}\displaystyle \beta = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right) = - \frac{1}{V_m} \left( \frac{\partial V_m}{\partial p} \right)\end{array}$

Symbol	Dimension	SI units	Oil metric units	Oil field units
$\begin{array}{l}\beta\end{array}$ or $\begin{array}{l}c\end{array}$	M^-1 L¹T²	Pa^-1	kPa^-1	psi^-1

Compressibility measures resistance of Continuum body to compression/decompression and is inverse to Bulk modulus $\begin{array}{l}K\end{array}$ :

(2)	$\begin{array}{l}\displaystyle c = \frac{1}{K}\end{array}$

Compressibility depends on the thermodynamic conditions at which it is measured and as such is not a material property.

The two major medium compression/decompression processes are isothermal and isentropic which result in different values of compressibility:

Isothermal Compressibility

Isentropic Compressibility

$\begin{array}{l}T = \rm const\end{array}$

$\begin{array}{l}S = \rm const\end{array}$

(3)	$\begin{array}{l}\displaystyle \beta_T = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right)_T\end{array}$

(4)	$\begin{array}{l}\displaystyle \beta_S = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right)_S\end{array}$

Both $\begin{array}{l}\beta_T\end{array}$ and $\begin{array}{l}\beta_S\end{array}$ are not dependent on the amount of chemical substance and defined under specific conditions of thermodynamic process and as such are the material properties and properly tabulated for the vast majority of materials.

In engineering practise, when the term Compressibility is used as material property it normally means Isothermal Compressibility: $\begin{array}{l}\beta=\beta_T\end{array}$ .

Compressibility is related to Z-factor $\begin{array}{l}Z\end{array}$ and Formation Volume Factor (FVF) $\begin{array}{l}B\end{array}$ as:

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

(6)	$\begin{array}{l}\displaystyle \beta(p) = - \frac{1}{B} \frac{dB}{dp}\end{array}$

Disclaimer

In Thermodynamics the compressibility is denoted by $\begin{array}{l}\beta\end{array}$ while intensive heat capacities are denoted by $\begin{array}{l}c\end{array}$ with corresponding subscript.

On the other hand Petroleum Industry is traditionally using $\begin{array}{l}c\end{array}$ symbol to denote compressibility which often lead to confusion with heat capacity.

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Compressibility = β = c