ZFactor
The Zfactor is a main variable in the generalized equation of state model defined by
where \(v\) is the molar volume (\(v=V/n\)).
There is a unique Zfactor for each fluid phase in the system. For real gas the Zfactor can be thought of as the gas correction or deviation factor. Some of the most common Zfactor models are given in the following sections.
Real Gases
Note
The main article on real gases is: Real Gas Law
Real gas behavior is defined by its deviation from the ideal gas law. There are several approaches to describe the nonideal behavior, but the most common is by estimating the Zfactor correction (sometimes called the gas correction factor for real gases). Other approaches involve applying an EOS to describe the phase behavior of the gas. An Example of this is the BenedictWebbRubin EOS models.
Some of the most common methods for estimating the Zfactor for hydrocarbon real gases behavior are given below.
StandingKatz Zfactor Chart
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For more information see the real gas page section on the StandingKatz chart
The StandingKatz charts are a set of empirically derived plots made by Standing and Katz in 1944^{1}. The general approach of the chart is to first find the gas pseudoreduced conditions by dividing the current conditions by the pseudocritical conditions , i.e. yielding the pseudoreduced pressure (\(p_{pr}=p/p_{pc}\)) and pseudoreduced temperature (\(T_{pr}=T/T_{pc}\)). The pseudocritical conditions can be calculated by correlation (e.g. the Sutton correlation) or by applying Kay's mixing rule if compositions are available. Once the pseudoreduced conditions are found, then the StandingKatz chart can be used to look up the associated Zfactor value.
HallYarbrough Estimation of Gas ZFactor
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For more information see the real gas page section on the HallYarbrough gas Zfactor
The HallYarbrough Zfactor approach is an iterative method to calculate the Zfactor for real gases. This approach uses the CarnahanStanding hardsphere EOS to iteratively estimate the Zfactor. Similar to the StandingKatz chart the HallYarbrough approach uses the pseudoreduced conditions and the molecular weight (\(MW\)), critical temperature (\(T_c\)), critical pressure (\(p_c\)) and accentric factor (\(\omega\)).
TwoPhase ZFactors
The most common approach for twophase EOS modeling involves the Zfactor as the main variable. The industry standard has become using cubic EOS models to describe the variation in Zfactor as a cubic polynomial. A general description of cubic EOS models as well as some specific models are given in the following sections.
Cubic Equation of States
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The main article on cubic EOS models is: Cubic Equation of State Models
A cubic EOS is any fluid model that can be written of the following form
For the most common cubic EOS models used in the industry (i.e. the PengRobinson and SoaveRedlichKwong EOS models) the general structure of the coefficients and parameters of the model are the same. The main bulk parameters are given by
where the coefficients \(\Omega_a\) and \(\Omega_b\) are different for the different EOS models, the function for the \(m(\omega)\) term is different for the different EOS models and the coefficients of equation \eqref{eq:ceos} are different for the different EOS models. In the following sections, the specific structure of the coefficients in equation \eqref{eq:ceos} are given for the van der Waals, PengRobinson and SoaveRedlichKwong EOS models are given.
van der Waals EOS
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The main article on the van der Waals EOS models is: van der Waals Equation of State
Note that the \(\alpha(T)\) term was not introduced until Soave's modification of the original RedlichKwong EOS, so the van der Waals EOS model has \(\alpha(T)=1\) for all temperatures.
PengRobinson EOS
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The main article on the PengRobinson EOS models is: PengRobinson Equation of State
SoaveRedlichKwong EOS
Note
The main article on the SoaveRedlichKwong EOS models is: SoaveRedlichKwong Equation of State

M.B. Standing and D.L. Katz. Vaporliquid equilibria of natural gascrude oil systems. Transactions of the AIME, 155:paper SPE–944232–G, 1944. ↩