Difference between revisions of "Fanning correlation"

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Reynolds number:
 
Reynolds number:
 
:<math> Re = 1488\ \frac {\rho_g v_g D}{\mu_g}</math>
 
:<math> Re = 1488\ \frac {\rho_g v_g D}{\mu_g}</math>
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== Discussion  ==
 
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Why [[Fanning correlation]] ?
 
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{{Quote| text = The Gray correlation was found to be the best of several initially tested ... | source = Nitesh Kumar l<ref name= Kumar />}}
 
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== Workflow ==
 
  
 
:<math> \rho_g = \frac{28.967\ SG_g\ p}{z\ 10.732\ T_R} </math><ref name= Lyons/>
 
:<math> \rho_g = \frac{28.967\ SG_g\ p}{z\ 10.732\ T_R} </math><ref name= Lyons/>
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:<math> v_{SG} = \frac{q_g \times 10^6}{86400 A_p}\ \frac{14.7}{p}\ \frac{T_K}{520}\ \frac{z}{1}</math>
 
:<math> v_{SG} = \frac{q_g \times 10^6}{86400 A_p}\ \frac{14.7}{p}\ \frac{T_K}{520}\ \frac{z}{1}</math>
  
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== Modifications ==
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== Discussion ==
  
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1.  Use [[Fanning correlation]] for dry gas (WGR=0 and OGR=0).
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Why [[Fanning correlation]] ?
  
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2. Use watercut instead of WOR to account for the OGR=0 case.
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{{Quote| text = The Gray correlation was found to be the best of several initially tested ... | source = Nitesh Kumar l<ref name= Kumar />}}
  
 
== Nomenclature  ==
 
== Nomenclature  ==
  
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:<math> A </math> = correlation group, dimensionless
 
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:<math> A_p </math> = flow area, ft2
 
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:<math> B </math> = correlation group, dimensionless
 
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:<math> B </math> = formation factor, bbl/stb
 
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:<math> C </math> = no-slip holdup factor, dimensionless
 
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:<math> D </math> = pipe diameter, ft
 
 
:<math> h </math> = depth, ft
 
:<math> h </math> = depth, ft
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:<math> H </math> = holdup factor, dimensionless
 
 
:<math> f </math> = friction factor, dimensionless
 
:<math> f </math> = friction factor, dimensionless
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:<math> GLR </math> = gas-liquid ratio, scf/bbl
 
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:<math> M </math> = total mass of oil, water and gas associated with 1 bbl of liquid flowing into and out of the flow string, lb<sub>m</sub>/bbl
 
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:<math> N_D </math> = pipe diameter number, dimensionless
 
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:<math> N_V </math> = velocity number, dimensionless
 
 
:<math> p </math> = pressure, psia
 
:<math> p </math> = pressure, psia
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:<math> q_c </math> = conversion constant equal to 32.174049, lb<sub>m</sub>ft / lb<sub>f</sub>sec<sup>2</sup>
 
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:<math> q </math> = production rate, bbl/d
 
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:<math> R </math> = superficial liquid to gas ratio, dimensionless
 
 
:<math> Re </math> = Reynolds number, dimensionless
 
:<math> Re </math> = Reynolds number, dimensionless
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:<math> R_s </math> = solution gas-oil ratio, scf/stb
 
 
:<math> SG </math> = specific gravity, dimensionless
 
:<math> SG </math> = specific gravity, dimensionless
 
:<math> T </math> = temperature, °R or °K, follow the subscript
 
:<math> T </math> = temperature, °R or °K, follow the subscript

Revision as of 11:32, 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
WOR = water-oil ratio, bbl/bbl
z = gas compressibility factor, dimensionless

Greek symbols

\varepsilon = absolute roughness, ft
\varepsilon' = pseudo wall roughness, ft
\mu = viscosity, cp
\rho = density, lbm/ft3
\bar \rho = slip density, lbm/ft2
\sigma = surface tension of liquid-air interface, dynes/cm

Subscripts

g = gas
K = °K
L = liquid
m = gas/liquid mixture
o = oil
R = °R
SL = superficial liquid
SG = superficial gas
w = water

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.

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