Difference between revisions of "Dranchuk correlation"

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=== Discussion  ===
 
=== 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.
+
Application range:
 
 
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 ===
 
=== Nomenclature ===

Revision as of 13:25, 25 April 2017

Brief

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

Math & Physics

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

  \rho_r = \frac{0.27\ P_{pr}}{{z\ T_{pr}}}
  P_{pr} =  \frac{P}{P_{pc}}
  T_{pr} =  \frac{T}{T_{pc}}

Workflow

To solve the Dranchuk equation use the iterative secant method.

To find the pseudo critical properties given the gas specific gravity[1]:

  P_{pc} =  4.6+0.1\ SG_g-0.258\ SG^2_g
  T_{pc} =  99.3+180\ SG_g-6.94\ SG^2_g

Discussion

Application range:

Nomenclature

 A_1..A_{11} coefficients
 \rho_r = reduced density, dimensionless
 P = Pressure, psia
 P_{pc} = pseudo critical pressure, psia
 P_{pr} = pseudoreduced pressure, dimensionless
 SG_g = gas specific gravity, dimensionless
 T = temperature, °R
 T_{pc} = pseudo critical temperature, °R
 T_{pr} = pseudoreduced temperature, dimensionless
 z = gas compressibility factor, dimensionless

References

  1. 1.0 1.1 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 (PETSOC-75-03-03).