Difference between revisions of "Dranchuk correlation"

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<ref name=Turner>{{cite journal
 
<ref name=Turner>{{cite journal
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  |last1= Turner |first1=R. G.
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  |last1= Dranchuk |first1=P. M.
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  |last2= Hubbard |first2=M. G.
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  |last2= Abou-Kassem |first2=H.
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|last3= Dukler |first2=A. E.
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  |title=Calculation of Z Factors For Natural Gases Using Equations of State
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  |title=Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells
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  |journal=The Journal of Canadian Petroleum
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  |journal=Journal of Petroleum Technology
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  |number=PETSOC-75-03-03
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  |number=SPE-2198-PA
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  |date=July 1975
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  |date=Nov 1969
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|volume=14
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  |pages=1475–1482
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  |issue=03
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  |url=https://www.scribd.com/doc/269398353/Friction-Factors-for-Pipe-Flow-MoodyLFpaper1944
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  |url=https://www.onepetro.org/journal-paper/PETSOC-75-03-03
 
  |url-access=registration  
 
  |url-access=registration  
 
}}</ref>
 
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Revision as of 11:52, 25 April 2017

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. (December 1942). "Density of Natural Gases"Free registration required. Transactions of the AIME. Society of Petroleum Engineers. 146 (SPE-942140-G). 
  2. ↑ Dranchuk, P. M.; Abou-Kassem, H. (July 1975). "Calculation of Z Factors For Natural Gases Using Equations of State"Free registration required. The Journal of Canadian Petroleum. 14 (03).  More than one of |number= and |issue= specified (help)
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