Dranchuk correlation

From wiki.pengtools.com
Revision as of 11:43, 25 April 2017 by MishaT (talk | contribs) (References)
Jump to: navigation, search

Brief

Dranchuk correlation is the fitting function of the classic Standing and Katz [1] gas compressibility factor correlation.

Math & Physics

equation on gas compressibility factor z
A1 = 0.3265
A2 = –1.0700
A3 = –0.5339
A4 = 0.01569
A5 = –0.05165
A6 = 0.5475
A7 = –0.7361
A8 = 0.1844
A9 = 0.1056
A10 = 0.6134
A11 = 0.7210

 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}
[2]

where

  T_{pc} =  99.3+180\ SG_g-6.94\ SG^2_g
  P_{pc} =  4.6+0.1\ SG_g-0.258\ SG^2_g
  T_{pr} =  \frac{T}{T_{pc}}
  P_{pr} =  \frac{P}{P_{pc}}
  \rho_r = \frac{0.27\ P_{pr}}{({z\ T_{pr}})}

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 Reservoir deliverability smaller tubing ID will increase the gas velocity.

Nomenclature

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

References

  1. Standing, M. B.; Katz, D. L. (Nov 1969). "Density of Natural Gases"Free registration required. Journal of Petroleum Technology (SPE-2198-PA): 1475–1482. 
  2. Turner, R. G.; Hubbard, A. E.; Dukler (Nov 1969). "Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells"Free registration required. Journal of Petroleum Technology (SPE-2198-PA): 1475–1482.