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

A measure of resistance of a Continuum body to compression/decompression.

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

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

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

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

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

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

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

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

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

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

Page tree

See also