Explicit Z-factor correlation @model for the natural gas in the wide range of pseudo-reduced temperature $\begin{array}{l}1.05 \leq T_{pr} \leq 3\end{array}$ and pseudo-reduced pressure $\begin{array}{l}0.2 \leq P_{pr} \leq 15\end{array}$ :

(1)	$\begin{array}{l}\displaystyle Z = \frac{D \cdot P_{pr} \cdot (1+ y + y^2 - y^3)}{(D \cdot P_{pr} + E \cdot y^2 - F \cdot y^G)(1-y)^3}\end{array}$

(2)	$\begin{array}{l}\displaystyle y = \frac{D \cdot P_{pr} }{Z^*}\end{array}$

(3)	$\begin{array}{l}\displaystyle Z^* = \frac{1+A^2}{C} - \frac{A^2 B}{C^3}\end{array}$

(4)	$\begin{array}{l}\displaystyle A=a_1 \, t \, \exp \left[ a_2 \, (1-t)^2 \right] \, p_{pr}\end{array}$

(5)	$\begin{array}{l}\displaystyle B=a_3 \, t + a_4 \, t^2 + a_5\, t^6 \, p^6_{pr}\end{array}$

(6)	$\begin{array}{l}\displaystyle C= a_9 + a_8 \, t \, p_{pr} + a_7 \, t^2 \, p^2_{pr} + a_6 \, t^3 \, p^3_{pr}\end{array}$

(7)	$\begin{array}{l}\displaystyle D=a_{10} \, t \, \exp \left[ a_{11} (1-t)^2 \right]\end{array}$

(8)	$\begin{array}{l}\displaystyle E=a_{12}\,t +a_{13}\,t^2 + a_{14}\,t^3\end{array}$

(9)	$\begin{array}{l}\displaystyle F= a_{15}\,t +a_{16}\,t^2 + a_{17}\,t^3\end{array}$

(10)	$\begin{array}{l}\displaystyle G=a_{18} + a_{19} t\end{array}$

(11)	$\begin{array}{l}\displaystyle t= \frac{1}{T_{pr}}\end{array}$

where

$\begin{array}{l}Z\end{array}$	Z-factor
$\begin{array}{l}T\end{array}$	fluid temperature	$\begin{array}{l}T_{pr} = T/T_{pc}\end{array}$	pseudo-reduced temperature (or reduced temperature $\begin{array}{l}T_{r}\end{array}$ in case of pure substances)	$\begin{array}{l}T_{pc}\end{array}$	pseudo-critical temperature (or critical temperature $\begin{array}{l}T_{c}\end{array}$ in case of pure substances)
$\begin{array}{l}P\end{array}$	fluid pressure	$\begin{array}{l}P_{pr} = P/P_{pc}\end{array}$	pseudo-reduced pressure (or reduced pressure $\begin{array}{l}P_{r}\end{array}$ in case of pure substances)	$\begin{array}{l}P_{pc}\end{array}$	pseudo-critical pressure (or critical pressure $\begin{array}{l}P_{c}\end{array}$ in case of pure substances)

and

$\begin{array}{l}a_1=0.317842\end{array}$	$\begin{array}{l}a_2=0.382216\end{array}$	$\begin{array}{l}a_3=-7.768354\end{array}$	$\begin{array}{l}a_4=14.290531\end{array}$	$\begin{array}{l}a_5=0.000002\end{array}$	$\begin{array}{l}a_6=-0.004693\end{array}$	$\begin{array}{l}a_7=0.096254\end{array}$
$\begin{array}{l}a_8=0.166720\end{array}$	$\begin{array}{l}a_9=0.966910\end{array}$	$\begin{array}{l}a_{10}=0.063069\end{array}$	$\begin{array}{l}a_{11}=-1.966847\end{array}$	$\begin{array}{l}a_{12}=21.0581\end{array}$	$\begin{array}{l}a_{13}=-27.0246\end{array}$	$\begin{array}{l}a_{14}=16.23\end{array}$
$\begin{array}{l}a_{15}=207.783\end{array}$	$\begin{array}{l}a_{16}=-488.161\end{array}$	$\begin{array}{l}a_{17}=176.29\end{array}$	$\begin{array}{l}a_{18}=1.88453\end{array}$	$\begin{array}{l}a_{19}=3.05921\end{array}$

The accuracy of the Kareem Z-factor Correlation @model within the stated above temperature-pressure range is given below:

Maximum Absolute Error

0.0270

0.99972

Maximum Percentage Error

5.9976 %

Average Percentage Error

0.4379 %

Reference

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