Difference between revisions of "Fanning correlation"

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== Brief ==
 
== Brief ==
  
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The [[Fanning correlation|Fanning]] is the name used to refer to the calculation of the hydrostatic pressure difference and the friction pressure loss for the dry gas.
+
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 flow.
  
−
[[Fanning correlation|Fanning]] is the default [[VLP]] correlation for the '''dry gas wells''' in the [[:Category:PqPlot|PQplot]].
+
[[Fanning correlation]] is the default [[VLP]] correlation for the '''dry gas wells''' in the [[PQplot]].
 +
 
 +
[[File: Fanning.png|thumb|500px|link=https://www.pengtools.com/pqPlot?paramsToken=49064d9f7a281b1810e28e8bee255fb2|Fanning in PQplot Vs Prosper & Kappa |right]]
  
 
== Math & Physics ==
 
== Math & Physics ==
 
Following the law of conservation of energy the basic steady state flow equation is:
 
Following the law of conservation of energy the basic steady state flow equation is:
−
:<math> 144 \frac{\Delta p}{\Delta h} =  \bar \rho_m + \rho_m \frac{f v_m^2 }{2 g_c D} + \rho_m \frac{\Delta{(\frac{v_m^2}{2g_c}})}{\Delta h}</math>
+
:<math> 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}</math>
−
 
 
−
where
 
−
:<math> \bar \rho_m = \rho_L (1-H_g) + \rho_g H_g</math>,  slip mixture density <ref name= Gray />.
 
−
 
 
−
:<math> \rho_m = \rho_L C_L + \rho_g (1-C_L) </math>,  no-slip mixture density <ref name= Gray />.
 
  
 
Colebrook–White <ref name=Colebrook/> equation for the [http://en.wikipedia.org/wiki/Darcy_friction_factor_formulae Darcy's friction factor]:
 
Colebrook–White <ref name=Colebrook/> equation for the [http://en.wikipedia.org/wiki/Darcy_friction_factor_formulae Darcy's friction factor]:
−
:<math> \frac{1}{\sqrt{f}}= -2 \log \left( \frac { \varepsilon'} {3.7 D} + \frac {2.51} {\mathrm{Re} \sqrt{f}} \right)</math><ref name = Moody1944/>
+
:<math> \frac{1}{\sqrt{f}}= -2 \log \left( \frac { \varepsilon} {3.7 D} + \frac {2.51} {\mathrm{Re} \sqrt{f}} \right)</math><ref name = Moody1944/>
−
 
 
−
The pseudo wall roughness:
 
−
:<math> \varepsilon' = \begin{cases}
 
−
\frac{28.5}{453.592} \frac{\sigma_L}{\rho_m v_m^2},  &\mbox{if } R \geqslant 0.007 \\
 
−
\varepsilon + R \frac{\varepsilon'-\varepsilon}{0.007}, & \mbox{if } R < 0.007
 
−
\end{cases} </math>, with the limit <math> \varepsilon' \geqslant 2.77 \times 10^{-5}</math><ref name= Gray/>
 
−
 
 
−
Reynolds two phase number:
 
−
:<math> Re = 2.2 \times 10^{-2} \frac {q_L M}{D \mu_L^{C_L} \mu_g^{(1-C_L)}}</math><ref name= HB/>
 
−
 
 
−
== Discussion  ==
 
−
 
 
−
Why [[Gray correlation|Gray]] correlation?
 
−
 
 
−
{{Quote| text = The Gray correlation was found to be the best of several initially tested ... | source = Nitesh Kumar l<ref name= Kumar />}}
 
−
 
 
−
== Workflow  H<sub>g</sub> & C<sub>L</sub>==
 
−
 
 
−
:<math> M =SG_o\ 350.52\ \frac{1}{1+WOR}+SG_w\ 350.52\ \frac{WOR}{1+WOR}+SG_g\ 0.0764\ GLR</math><ref name="HB" />
 
  
−
:<math> \rho_L= 62.4\ SG_o \frac{1}{1+WOR} + 62.4\ SG_w\ \frac{WOR}{1 + WOR}</math>
+
Reynolds number:
 +
:<math> Re = 1488\ \frac {\rho_g v_g D}{\mu_g}</math>
  
 
:<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/>
−
 
−
:<math> v_{SL} = \frac{5.615 q_L}{86400 A_p} \left ( B_o \frac{1}{1+WOR} + B_w \frac{WOR}{1+WOR} \right )</math><ref name= Lyons/>
 
  
 
:<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>
  
−
:<math> C_L = \frac{v_{SL}}{v_{SG}+v_{SL}}</math>
+
== Discussion ==
−
 
 
−
:<math> v_m = v_{SL} + v_{SG} </math>
 
−
 
 
−
:<math> \rho_m = \rho_L C_L + \rho_g (1-C_L) </math>
 
  
−
:<math> \mu_L = \mu_o \frac{1}{1 + WOR} + \mu_w \frac{WOR}{1 + WOR}</math><ref name= Lyons/>
+
Why [[Fanning correlation]] ?
  
−
:<math> \sigma_L = \frac{\sigma_o\ q_o + 0.617\ \sigma_w\ q_w}{q_o + 0.617\ q_w}</math> <ref name= Gray/>
+
{{Quote| text = [[Fanning correlation]] actually is not a correlation, it's the fully explicit workflow to define the pressure drop. | source = www.pengtools.com}}
−
 
 
−
:<math> N_V = 453.592\ \frac{{\rho_m}^2 {v_m}^4}{g_c \sigma_L (\rho_L - \rho_g)} </math><ref name= Gray/>
 
−
 
 
−
:<math> N_D = 453.592\ \frac{g_c (\rho_L - \rho_g) D^2}{\sigma_L } </math><ref name= Gray/>
 
−
 
 
−
:<math> R = \frac{v_{SL}}{v_{SG}} </math><ref name= Gray/>
 
−
 
 
−
:<math> B = 0.0814 \left ( 1 - 0.554\ \ln \left (1 + \frac{730 R}{R+1} \right )  \right ) </math><ref name= Gray/>
 
−
 
 
−
:<math> A = -2.2314 \left ( N_V \left (1 + \frac{205}{N_D} \right )  \right )^B </math><ref name= Gray/>
 
−
 
 
−
:<math> H_g = \frac{1-e^A}{R+1}</math><ref name= Gray/>
 
−
 
 
−
== Modifications  ==
 
−
 
 
−
1.  Use [[Fanning correlation]] for dry gas (WGR=0 and OGR=0).
 
−
 
 
−
2. Use watercut instead of WOR to account for the OGR=0 case.
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==
  
−
:<math> A </math> = correlation group, dimensionless
 
−
:<math> A_p </math> = flow area, ft2
 
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:<math> B </math> = correlation group, dimensionless
 
−
:<math> B </math> = formation factor, bbl/stb
 
−
:<math> C </math> = no-slip holdup factor, dimensionless
 
−
:<math> D </math> = pipe diameter, ft
 
 
:<math> h </math> = depth, ft
 
:<math> h </math> = depth, ft
−
:<math> H </math> = holdup factor, dimensionless
 
 
:<math> f </math> = friction factor, dimensionless
 
:<math> f </math> = friction factor, dimensionless
−
:<math> GLR </math> = gas-liquid ratio, scf/bbl
 
−
:<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
 
−
:<math> N_D </math> = pipe diameter number, dimensionless
 
−
:<math> N_V </math> = velocity number, dimensionless
 
 
:<math> p </math> = pressure, psia
 
:<math> p </math> = pressure, psia
−
:<math> q_c </math> = conversion constant equal to 32.174049, lb<sub>m</sub>ft / lb<sub>f</sub>sec<sup>2</sup>
 
−
:<math> q </math> = production rate, bbl/d
 
−
:<math> R </math> = superficial liquid to gas ratio, dimensionless
 
 
:<math> Re </math> = Reynolds number, dimensionless
 
:<math> Re </math> = Reynolds number, dimensionless
−
:<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
 
:<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
  
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:<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===
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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 ==
 
<references>
 
<references>
−
 
−
<ref name= Gray>{{cite journal
 
−
|last1= Gray |first1=H. E.
 
−
|title=Vertical Flow Correlation in Gas Wells
 
−
|journal=User manual for API 14B, Subsurface controlled safety valve sizing computer program
 
−
|publisher = API
 
−
|date= 1974
 
−
}}</ref>
 
  
 
<ref name=Colebrook>{{cite journal
 
<ref name=Colebrook>{{cite journal
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  |url-access=subscription  
 
  |url-access=subscription  
 
}} </ref>
 
}} </ref>
−
 
−
<ref name=HB>{{cite journal
 
−
|last1=Hagedorn|first1=A. R.
 
−
|last2= Brown |first2=K. E.
 
−
|title=Experimental study of pressure gradients occurring during continuous two-phase flow in small-diameter vertical conduits
 
−
|journal=Journal of Petroleum Technology
 
−
|date=1965
 
−
|volume=17(04)
 
−
|pages=475-484
 
−
}}</ref>
 
  
 
<ref name= Lyons>{{cite book
 
<ref name= Lyons>{{cite book
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  |place=Houston, TX
 
  |place=Houston, TX
 
  |isbn=0-88415-643-5
 
  |isbn=0-88415-643-5
−
}}</ref>
 
−
 
−
<ref name=Kumar>{{cite journal
 
−
|first1=N. |last1=Kumar
 
−
|first2=J. F. |last2=Lea
 
−
|title=Improvements for Flow Correlations for Gas Wells Experiencing Liquid Loading
 
−
|number=SPE-92049-MS
 
−
|date=January 1, 2005
 
−
|url=https://www.onepetro.org/conference-paper/SPE-92049-MS
 
−
|url-access=registration
 
 
}}</ref>
 
}}</ref>
  
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[[Category:pengtools]]
 
[[Category:pengtools]]
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[[Category:pqPlot]]
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[[Category:PQplot]]
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[[Category:sPipe]
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{{#seo:
 +
|title=Fanning correlation dry gas flow
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|titlemode= replace
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|keywords=Fanning correlation
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|description=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 flow.
 +
}}

Latest revision as of 09:45, 6 December 2018

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 flow.

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

Fanning in PQplot Vs Prosper & Kappa

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 ?

Fanning correlation actually is not a correlation, it's the fully explicit workflow to define the pressure drop.
— www.pengtools.com

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. 
[[Category:sPipe]
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