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| c = \frac{1}{\rho} \frac{d\rho}{dp} = \frac{d \ln \rho}{dp} = \frac{d }{dp} \left( \ln \left(\frac{p}{Z} \right) \right) = \frac{Z}{p} \cdot \frac{d }{dp} \left(\frac{p}{Z} \right) = \frac{Z}{p} \cdot \left( \frac{1}{Z} + p \cdot \frac{d }{dp} \left( \frac{1}{Z} \right) \right) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp} |
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| \frac{d \ln Z}{dp} = \frac{1}{p} - c(p) \rightarrow \ln \frac{Z}{Z_0} = \ln \frac{p}{p_0} - \int_{p_0}^p c(p) \, dp |
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The Z-factor value for Ideal Gas is strictly unit: .
For many real gases (particularly for the most compositions of natural gases) the Z-factoris trending towards unit value (
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while approaching the STP.For incompressible fluids the Z-factor is trending to for strongly compressible fluids and linear pressure dependence (
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| body | Z \rightarrow a \cdot p |
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for incompressible fluidswith pressure growth.
Modelling Z-factor as a function of fluidpressure and temperature is based on Equation of State.
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