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Alternatively Z-factor can be expressed through the dynamic fluid properties at reference conditions as:
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Z(T, p) = Z^{\circ} \cdot \frac{\rho^{\circ} \, T^{\circ}}{p^{\circ}} \cdot \frac{p}{\rho(T, p) \, T} |
where
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means reference conditions, usually Standard Conditions (STP).
Z-factor can be used to calculate Z-factor is related to fluid density
and
Formation Volume Factor (FVF) as:
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| \rho(T, p) = \rho^{\circ} \cdot \frac{p}{Z(T, p)Z^{\circ} \, T^{\circ}}{p^{\circ}} \cdot \frac{Mp}{RZ(T, p) \, T} |
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| ZB(T, p) = B\frac{\rho^{\circ}}{\rho(T, p)} = \cdot \frac{p}{T{p^{\circ} }{Z^{\circ} \, T^{\circ}} \cdot \frac{M}{RZ(T, p) \, \rho_{ref}}T}{p} |
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Z-factor is related to fluid compressibility
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| c(p) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp} |
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| Z(p) = Z_0 \cdot \frac{Z_0p}{p_0} \cdot p \cdot \exp \left[ - \int_{p_0}^p c(p) dp \right] |
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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 |
which arrives to LaTeX Math Block Reference |
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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 incompressible fluids and linear pressure dependence (
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body | Z \rightarrow a \cdot p |
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for strongly compressible Fluidswith pressure growth.
Modelling Z-factor as a function of fluidpressure and temperature is based on Equation of State.
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