Difference between revisions of "Fanning correlation"

From wiki.pengtools.com
Jump to: navigation, search
(→‎Nomenclature)
Line 35: Line 35:
 
:<math> T </math> = temperature, °R or °K, follow the subscript
 
:<math> T </math> = temperature, °R or °K, follow the subscript
 
:<math> v </math> = velocity, ft/sec
 
:<math> v </math> = velocity, ft/sec
−
:<math> WOR </math> = water-oil ratio, bbl/bbl
 
 
:<math> z </math> = gas compressibility factor, dimensionless
 
:<math> z </math> = gas compressibility factor, dimensionless
  
Line 41: Line 40:
  
 
:<math> \varepsilon </math> = absolute roughness, ft
 
:<math> \varepsilon </math> = absolute roughness, ft
−
:<math> \varepsilon' </math> = pseudo wall roughness, ft
 
 
:<math> \mu </math> = viscosity, cp
 
:<math> \mu </math> = viscosity, cp
 
:<math> \rho </math> = density, lb<sub>m</sub>/ft<sup>3</sup>
 
:<math> \rho </math> = density, lb<sub>m</sub>/ft<sup>3</sup>
−
:<math> \bar \rho </math> = slip density, lb<sub>m</sub>/ft<sup>2</sup>
 
−
:<math> \sigma </math> = surface tension of liquid-air interface, dynes/cm
 
  
 
===Subscripts===
 
===Subscripts===
Line 52: Line 48:
 
K = °K<BR/>
 
K = °K<BR/>
 
L = liquid<BR/>
 
L = liquid<BR/>
−
m = gas/liquid mixture<BR/>
 
−
o = oil<BR/>
 
 
R = °R<BR/>
 
R = °R<BR/>
−
SL = superficial liquid<BR/>
 
 
SG = superficial gas<BR/>
 
SG = superficial gas<BR/>
−
w = water<BR/>
 
  
 
== References ==
 
== References ==

Revision as of 11:33, 7 April 2017

Brief

The Fanning correlation is the name used to refer to the calculation of the hydrostatic pressure difference and the friction pressure loss for the dry gas.

Fanning correlation is the default VLP correlation for the dry gas wells in the PQplot.

Math & Physics

Following the law of conservation of energy the basic steady state flow equation is:

144 \frac{\Delta p}{\Delta h} = \rho_g + \rho_g \frac{f v_g^2 }{2 g_c D} + \rho_g \frac{\Delta{(\frac{v_g^2}{2g_c}})}{\Delta h}

Colebrook–White [1] equation for the Darcy's friction factor:

\frac{1}{\sqrt{f}}= -2 \log \left( \frac { \varepsilon} {3.7 D} + \frac {2.51} {\mathrm{Re} \sqrt{f}} \right)[2]

Reynolds number:

Re = 1488\ \frac {\rho_g v_g D}{\mu_g}
\rho_g = \frac{28.967\ SG_g\ p}{z\ 10.732\ T_R} [3]
v_{SG} = \frac{q_g \times 10^6}{86400 A_p}\ \frac{14.7}{p}\ \frac{T_K}{520}\ \frac{z}{1}

Discussion

Why Fanning correlation ?

The Gray correlation was found to be the best of several initially tested ...
— Nitesh Kumar l[4]

Nomenclature

h = depth, ft
f = friction factor, dimensionless
p = pressure, psia
Re = Reynolds number, dimensionless
SG = specific gravity, dimensionless
T = temperature, °R or °K, follow the subscript
v = velocity, ft/sec
z = gas compressibility factor, dimensionless

Greek symbols

\varepsilon = absolute roughness, ft
\mu = viscosity, cp
\rho = density, lbm/ft3

Subscripts

g = gas
K = °K
L = liquid
R = °R
SG = superficial gas

References

  1. ↑ Colebrook, C. F. (1938–1939). "Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws"Paid subscription required. Journal of the Institution of Civil Engineers. London, England. 11: 133–156. 
  2. ↑ Moody, L. F. (1944). "Friction factors for pipe flow"Paid subscription required. Transactions of the ASME. 66 (8): 671–684. 
  3. ↑ Lyons, W.C. (1996). Standard handbook of petroleum and natural gas engineering. 2. Houston, TX: Gulf Professional Publishing. ISBN 0-88415-643-5. 
  4. ↑ Kumar, N.; Lea, J. F. (January 1, 2005). "Improvements for Flow Correlations for Gas Wells Experiencing Liquid Loading"Free registration required (SPE-92049-MS). 

Cite error: <ref> tag with name "Gray" defined in <references> is not used in prior text.
Cite error: <ref> tag with name "HB" defined in <references> is not used in prior text.

Retrieved from "https://wiki.pengtools.com/index.php?title=Fanning_correlation&oldid=1975"