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It is related to
gas compressibility 

LaTeX Math Inline
bodyc_g
as:


LaTeX Math Block
anchorZ_c
alignmentleft
c_g(p) = \frac{1}{p} - \frac{p}{Z} \frac{dZ}{dp}



LaTeX Math Block
anchorZ_c
alignmentleft
Z(p) = \frac{Z_0}{p_0} \cdot p \cdot \exp \left[ - \int_{p_0}^p c(p) dp  \right]




Expand
titleDerivation


LaTeX Math Block
anchorcg1
alignmentleft
c_g = - \frac{1}{V} \frac{dV}{dp} = - \frac{d}{dp} \left( \ln V \right) \rightarrow \ln \frac{V}{V_0} = - \int_{p_0}^p c(p) dp 


Substituting

LaTeX Math Inline
bodyV
from
LaTeX Math Block Reference
anchorZ
into
LaTeX Math Block Reference
anchorcg1
one arrives to
LaTeX Math Block Reference
anchorZ_c
.

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Fluid Compressibility ][ Gas compressibility ]


References

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grouparax


Panel
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titleARAX

Lateef A. Kareem, New explicit correlation for the compressibility factor of natural gas, 2016



https://www.dropbox.com/s/s0tf280d28rw82p/Kareem2016_Article_NewExplicitCorrelationForTheCo.pdf?dl=0