@wikipedia


Compressibility of the fluid with density  and molar volume  as a function of temperature  and pressure :

c(T,p) = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right)_T = - \frac{1}{V_m} \left( \frac{\partial V_m}{\partial p} \right)_T


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

Approximations

Incompressible fluidCompressible fluid


Full-Range Proxy Model


Slightly compressible fluidStrongly Compressible Fluid

Real GasIdeal 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,p)}{1+c_0(T,p) \cdot p}



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



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



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



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



...


Z(T, p) = 1



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


where

fluid compressibility

fluid density

Z-factor



Mathematical models of Fluid Compressibility are reviewed in Fluid Compressibility @model.


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


See also

Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics

[Compressibility]  [ Z-factor ]

[Multi-phase compressibility @model] [ Fluid Compressibility @model ]

[ Incompressible fluid ] [ Slightly Compressible Fluid ] [ Strongly Compressible Fluid ] [ Ideal Gas ]