# 18.7: Isothermal Compressibilities

The isothermal compressibility of a fluid is defined as follows:

,(18.15)

This expression can be also given in term of fluid density, as follows:

(18.16)

**For liquids****,** the value of isothermal compressibility is very small because a unitary change in pressure causes a very small change in volume for a liquid. In fact, for slightly compressible liquid, the value of compressibility (c_{o}) is usually assumed independent of pressure. Therefore, for small ranges of pressure across which c_{o} is nearly constant, Equation (18.16) can be integrated to get:

(18.17)

In such a case, the following expression can be derived to relate two different liquid densities (,ob) at two different pressures (p, p_{b}):

(18.18)

The Vasquez-Beggs correlation is the most commonly used relationship for c_{o}.

**For natural**** gases,** isothermal compressibility varies significantly with pressure. By introducing the real gas law into Equation (18.16), it is easy to prove that, for gases:

(18.19)

Note that for an ideal gas, c_{g} is just the reciprocal of the pressure. “c_{g}” can be readily calculated by graphical means (chart of Z versus P) or by introducing an equation of state into Equation (18.19).

### Contributors

Prof. Michael Adewumi (The Pennsylvania State University). Some or all of the content of this module was taken from Penn State's College of Earth and Mineral Sciences' OER Initiative.