Fluid Compressibility is a function of temperature and pressure :

c = c(T, p)

The multi-phase fluid compressibility is a linear sum of compressibilities of its phases (see multi-phase fluid compressibility @ model).

There is no universal analytical model for Fluid Compressibility but there is a good number of approximations which can be effectively used in engineering practice.

Approximations

Incompressible fluid

Compressible fluid

Full-Range Compressibility Proxy Model

Slightly compressible fluid

Strongly Compressible Fluid

Ideal Gas

c(T, p) = 0

c(T, p) = c_0 = \rm const

c(T, p) = \frac{1}{p}

c(T, p) = \frac{c_0(T)}{1+c_0(T) \cdot p}

\rho(T, p) = \rho_0(T)

\rho(T, p) = \rho_0 \cdot \exp \left[ c_0 \cdot (p-p_0) \right]

\rho(T, p) = \frac{\rho_0(T)}{p_0} \cdot p

\rho(T, p) = \rho_0(T) \cdot \frac{1+c_0 \, p}{1+c_0 \, p_0}

Z(T, p) = \frac{p}{p_0}

Z(T, p) =\frac{p}{p_0}\cdot \exp \left[ - c_0 \cdot (p-p_0) \right]

Z(T, p) = 1

Z(T, p) = \frac{p}{p_0} \cdot \frac{1+c_0 \, p_0}{1 + c_0 \, p}