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Implicit Implicit Z-factor Correlations correlation @model for the natural gas in the wide range of pseudo-reduced temperature 

LaTeX Math Inline
body--uriencoded--1.05 \leq 0 < T_%7Bpr%7D \leq 3.0
 and pseudo-reduced pressure 
LaTeX Math Inline
body--uriencoded--0.2 \leq P_%7Bpr%7D \leq 1530

and also a specific range of

LaTeX Math Inline
body--uriencoded--0.7 < T_%7Bpr%7D \leq 1.0
 and
LaTeX Math Inline
body--uriencoded--P_%7Bpr%7D < 1.0
:

LaTeX Math Block
anchorz
alignmentleft
Z = \frac{0.27 \, P_{pr}}{y \, T_{pr}}
LaTeX Math Block
anchory
alignmentleft
R_5
1 + T_1 \, y + T_2 \, y^2 + T_3 \, y^5  + T_4 \, y^2 \, (1+ A_{11} \, y^2) \
cdot
, \exp
\left
(
- A_{11} \, y^2
\right
)
+ R_1
\, y 
- \frac{
R
T_
2
5}{y}
+R_3 \, y^2 - R_4 \,
y^5 +1 
= 0

LaTeX Math Block
anchor
A
z
alignmentleft
R
T_1 = A_1 + \frac{A_2
\, t + A_3 \, t^3 + A_4 \, t^4 + A_5 \, t^5 LaTeX Math Block
anchorB
alignmentleft
R_2 = \frac{0.27 \, P_{pr}}
}{T_{pr}} +  \frac{A_3}{T_{pr}^3}  +  \frac{A_4}{T_{pr}^4}  +  \frac{A_5}{T_{pr}^5}
LaTeX Math Block
anchor
D
z
alignmentleft
R
T_
3
2 = A_6 + \frac{A_7
\, t + A_8 \, t^2
}{T_{pr}} +  \frac{A_8}{T_{pr}^2}
LaTeX Math Block
anchor
E
z
alignmentleft
R
T_
4
3 = - A_9 \
, ( 
cdot \left[
 \frac{A_7
\, t + A_8 \, t^2) 
}{T_{pr}} +  \frac{A_8}{T_{pr}^2}  
\right]
LaTeX Math Block
anchor
t
z
alignmentleft
R
T_
5
4 =
\frac{A_
10 \, t^3
{10}}{T_{pr}^3}
LaTeX Math Block
anchor
t
NDRCA
alignmentleft
t
T_5 = \frac{
1
0.27 \, P_{pr} }{T_{pr}}

where

LaTeX Math Inline
bodyZ

Z-factor

LaTeX Math Inline
bodyT

fluid temperature 

LaTeX Math Inline
body--uriencoded--T_%7Bpr%7D = T/T_%7Bpc%7D

pseudo-reduced temperature 
(or reduced temperature 

LaTeX Math Inline
body--uriencoded--T_%7Br%7D
 in case of pure substances)

LaTeX Math Inline
body--uriencoded--T_%7Bpc%7D

 pseudo-critical temperature 
(or critical temperature 

LaTeX Math Inline
body--uriencoded--T_%7Bc%7D
 in case of pure substances)

LaTeX Math Inline
bodyP

fluid pressure

LaTeX Math Inline
body--uriencoded--P_%7Bpr%7D = P/P_%7Bpc%7D

pseudo-reduced pressure 
(or reduced pressure 

LaTeX Math Inline
body--uriencoded--P_%7Br%7D
 in case of pure substances)

LaTeX Math Inline
body--uriencoded--P_%7Bpc%7D

 pseudo-critical pressure 
(or critical pressure 

LaTeX Math Inline
body--uriencoded--P_%7Bc%7D
 in case of pure substances)

and

LaTeX Math Inline
bodyA_1 = 0.3265

LaTeX Math Inline
bodyA_2 = -1.070

LaTeX Math Inline
bodyA_3 = - 0.5339

LaTeX Math Inline
bodyA_4 = 0.01569

LaTeX Math Inline
bodyA_5 = - 0.05165

LaTeX Math Inline
bodyA_6 = 0.5475

LaTeX Math Inline
bodyA_7 = -0.7361

LaTeX Math Inline
bodyA_8 = 0.1844

LaTeX Math Inline
bodyA_9 = 0.1056

LaTeX Math Inline
body--uriencoded--A_%7B10%7D = 0.6134

LaTeX Math Inline
body--uriencoded--A_%7B11%7D = 0.7210


See also

...

Natural Science / Physics /Thermodynamics / Z-factor / Z-factor Correlations @model

Reference

...

Dranchuk, P.M., and H. Abou-Kassem. "Calculation of Z Factors For Natural Gases Using Equations of State." J Can Pet Technol 14 (1975): doi.org/10.2118/75-03-03Lateef A. Kareem, et al, New explicit correlation for the compressibility factor of natural gas: linearized z-factor isotherms, J Petrol Explor Prod Technol (2016) 6:481–492, DOI 10.1007/s13202-015-0209-3