View source for Dranchuk correlation

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=== Brief ===

[[Dranchuk correlation]] is the fitting function of the classic Standing and Katz <ref name=Standing and Katz /> gas compressibility factor correlation.

=== Math & Physics ===
equation on gas compressibility factor z<br/>
A1 = 0.3265<br/>
A2 = –1.0700<br/>
A3 = –0.5339<br/>
A4 = 0.01569<br/>
A5 = –0.05165<br/>
A6 = 0.5475<br/>
A7 = –0.7361<br/>
A8 = 0.1844<br/>
A9 = 0.1056<br/>
A10 = 0.6134<br/>
A11 = 0.7210<br/>
:<math> z =  1-z+
\left(A_1
 +\frac{A_2}{T_{pr}}
 +\frac{A_3}{T^3_{pr}}
 +\frac{A_4}{T^4_{pr}}
 +\frac{A_5}{T^5_{pr}}
\right)\  \rho_r+
\left(A_6
 +\frac{A_7}{T_{pr}}
 +\frac{A_8}{T^2_{pr}}
\right)\ \rho^2_r
-A_9\ \left(\frac{A_7}{T_{pr}}+\frac{A_8}{T^2_{pr}}\right)
+A_{10}\ \left(1+A_{11}\ \rho^2_r\right)\ \frac{\rho^2_r}{T^3_{pr}}
\ e^{-A_{11}\ \rho^2_r}
</math><ref name=Turner/>
where 
:<math>  T_{pc} =  99.3+180\ SG_g-6.94\ SG^2_g</math>

:<math>  P_{pc} =  4.6+0.1\ SG_g-0.258\ SG^2_g</math>

:<math>  T_{pr} =  \frac{T}{T_{pc}}</math>

:<math>  P_{pr} =  \frac{P}{P_{pc}}</math>

:<math>  \rho_r = \frac{0.27\ P_{pr}}{({z\ T_{pr}})}  </math>

=== Discussion  ===
To avoid the [[Liquid loading]] the gas velocity should be above the [[Liquid loading]] velocity.

The higher the gas rate the higher the gas velocity.

The lower the wellhead flowing pressure the higher the gas rate.

The bigger the tubing ID the higher the gas rate.

In case when the gas rate is limited by the [[Reservoirs|Reservoir]] deliverability smaller tubing ID will increase the gas velocity.

=== Nomenclature ===
:<math> z </math> = gas compressibility factor, dimensionless
:<math> P </math> = Pressure, psia
:<math> T </math> = Temperature, °R
:<math> P_{pc} </math> = Pseudo critical pressure, psia
:<math> T_{pc} </math> = Pseudo critical temperature, °R
:<math> SG_g </math> = gas specific density 

=== References ===
<references>

<ref name=Turner>{{cite journal
 |last1= Turner |first1=R. G.
 |last2= Hubbard |first2=M. G.
 |last3= Dukler |first2=A. E.
 |title=Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells
 |journal=Journal of Petroleum Technology
 |number=SPE-2198-PA
 |date=Nov 1969
 |pages=1475–1482
 |url=https://www.scribd.com/doc/269398353/Friction-Factors-for-Pipe-Flow-MoodyLFpaper1944
 |url-access=registration 
}}</ref>

</references>

[[Category:pengtools]]
[[Category:PVT]]