Isothermal Compressibilities

The isothermal compressibility of a fluid is defined as follows:

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

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:

In such a case, the following expression can be derived to relate two different liquid densities $({\rho }_o\text{, }\rho \text{ob)}$ at two different pressures (p, p_b):

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:

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).