Page tree

Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.

@wikipedia


One of the cubic equations of real gas state defining the Compressibility factor 

LaTeX Math Inline
bodyZ(p, T)
 as a function of Gas pressure 
LaTeX Math Inline
bodyp
and Gas temperature 
LaTeX Math Inline
bodyT
:


LaTeX Math Block
anchorEOSIG
alignmentleft
Z^3 - (1-B) \, Z^2 +(A-2B-3B^2) \, Z -(AB-B^2-B^3) = 0



LaTeX Math Block
anchorWRWJ4
alignmentleft
A=\frac{a \, \alpha \, p}{ R^2 \, T^2}



LaTeX Math Block
anchorWRWJ4
alignmentleft
B=\frac{b \, p}{ R \, T}



LaTeX Math Block
anchorWRWJ4
alignmentleft
a = 0.45724 \cdot \frac{R^2 \, T_c^2}{p_c}



LaTeX Math Block
anchorWRWJ4
alignmentleft
b = 0.07780 \cdot \frac{R \, T_c}{p_c}



LaTeX Math Block
anchorWRWJ4
alignmentleft
\alpha = \left( 1 + \kappa \, (1-T_r^{0.5}) \right)^2



LaTeX Math Block
anchorWRWJ4
alignmentleft
\kappa = 0.37464 + 1.54226 \, \omega -0.26992 \, \omega^2


where

LaTeX Math Inline
bodyZ

Compressibility factor

LaTeX Math Inline
bodyp_c

critical pressure

LaTeX Math Inline
bodyp

Gas pressure

LaTeX Math Inline
bodyT_c

critical temperature

LaTeX Math Inline
bodyT

Gas temperature

LaTeX Math Inline
bodyT_r = T/T_c

reduced temperature

LaTeX Math Inline
bodyR

Gas constant

LaTeX Math Inline
body\omega

accentric factor



Once compressibility Z-factor

LaTeX Math Inline
bodyZ(p, T)
 is known the gas density 
LaTeX Math Inline
body\rho
can be calculated as:

LaTeX Math Block
anchorUKHVN
alignmentleft
\rho(p, T) = \frac{1}{Z(p,T)} \cdot \frac{M}{R} \cdot \frac{p}{T}

where

LaTeX Math Inline
bodyM

Gas molar mass


See also


Natural Science / Physics / Thermodynamics / Real Gas / Real Gas EOS @model