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titleDerivation
LaTeX Math Block
anchorcg1
alignmentleft
c_g = - \frac{1}{V} \frac{dV}{dp} = - \frac{d}{dp} \left( \ln V \right)


Substituting

LaTeX Math Inline
bodyV
from
LaTeX Math Block Reference
anchorZ
pageCompressibility factor
into
LaTeX Math Block Reference
anchorcg1
one arrives to:

LaTeX Math Block
anchor1
alignmentleft
c_g = - \frac{d}{dp} \left( \ln \left( \frac{Z}{p} + \ln (\nu R T) \right) \right) = - \frac{p}{Z} \frac{d}{dp} \left( \frac{Z}{p} \right) = 


- \frac{p}{Z} \left( \frac{1}{p} \frac{dZ}{dp}  - \frac{Z}{p^2} \right) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp}


See Also

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Natural Science / Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics / Fluid compressibility

Natural Science / Physics / Chemistry / Chemical Substance / Natural Gas (chemical substance)

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Fluid (PVT) Analysis / Fluid (PVT) modelling

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