Difference between revisions of "Gilbert choke equation"

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<div style='text-align: right;'>By Mikhail Tuzovskiy on {{REVISIONTIMESTAMP}}</div>
 
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==Brief==
 
==Brief==
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The most common used formula for multiphase flow through surface chokes by Gilbert <ref name=KermitBrown1984/>.
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The most common formula used for multiphase flow through surface chokes developed by '''Gilbert''' in 1954<ref name=Gilbert/>.
  
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Echometer is used to measure the fluid level in the wells.
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Gilbert developed his empirical equation from field data in California<ref name=KermitBrown1984/>.
  
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Fluid level is used to calculate and monitor the bottom hole pressure of the wells.
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==Math and Physics==
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:<math>P_{wh}=\frac{435 \times GLR^{0.546}}{D^{1.89}} \times q</math>
  
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==Math and Physics==
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Note that the equation is independent of the downstream pressure and assumes that the downstream pressure is less than 70% of the upstream pressure, i.e. the flow is "critical" i.e. fluid reach sonic velocity in the throat of the choke<ref name=Economides/>.
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:<math>P_{wh}=\frac{435 \times GLR^0.546}{D^1.89} \times q</math>
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==Example==
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===Given data===
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Oil rate = 600 bbl/d, GLR=400 scf/bbl, D=22/64 in, Line pressure = 180 psia
  
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===Flowing well fluids segregation===
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Calculate the well head pressure?
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When the well is flowing with the pump this is how fluids segregate in the well bore:
 
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*Oil, gas and water are produced through the tubing from the reservoir to the surface 
 
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*Gas is in the annulus from the surface to the fluid level, Hd
 
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*Oil and gas are between the fluid level Hd, and the pump setting depth, Hd
 
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*Water, oil and gas are between pump, Hd and the top of the perforations, Hperfs
 
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*Water is in the rathole
 
  
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===Equation to calculate the BHP from the fluid level===
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===Solution===
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:<math>P_{wf}=P_{ann}+\frac{(H_{perfs}-H_{pump})(SG_o(1-WCUT)+SG_w WCUT)+(H_{pump}-H_d)SG_o}{10.32}</math>
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:<math>P_{wh}=\frac{435 \times 0.4^{0.546}}{22^{1.89}} \times 600 = 460 psig = 460 +14.7 = 474.7 psia</math>
  
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Note that for the deviated wells TVD depths should be used.
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Validity check 180/474.7=0.38 < 0.7 OK
  
 
==Nomenclature==
 
==Nomenclature==
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:<math>g</math> = 9.81, m/s^2
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:<math>D</math> = choke beam diametr, 64th of an inch
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:<math>h</math> = depth, m
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:<math>GLR</math> = gas liquid ratio, Mscf/bbl or 10^3 scf/bbl
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:<math>H_d</math> = fluid level, m
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:<math>P_{wh}</math> = well head pressure, psig
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:<math>H_{perfs}</math> = top of the perforations, m
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:<math>q</math> = liquid flow rate, bbl/d
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:<math>H_{pump}</math> = pump setting depth, m
 
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:<math>P</math> = pressure, atm
 
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:<math>P_{ann}</math> = annulus presssure, atm
 
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:<math>P_{wf}</math> = well flowing bottomhole pressure, atm
 
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:<math>\rho</math> = density, kg/m^3
 
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:<math>SG_o</math> = oil specific gravity, dimensionless
 
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:<math>SG_w</math> = water specific gravity, dimensionless
 
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:<math>WCUT</math> = well water cut, fraction
 
  
 
== References ==
 
== References ==
 
<references>
 
<references>
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<ref name= Gilbert>{{cite book
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|last1= Gilbert |first1= W.E.
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|title=Flowing and Gas-Lift Well Performance
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|journal=Drilling and Production Practice API
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|date=1954
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|page=143
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}}</ref>
 
<ref name= KermitBrown1984 >{{cite book
 
<ref name= KermitBrown1984 >{{cite book
 
  |last1= Brown |first1= Kermit
 
  |last1= Brown |first1= Kermit
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  |place=Tulsa, Oklahoma
 
  |place=Tulsa, Oklahoma
 
}}</ref>
 
}}</ref>
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<ref name=Economides>{{cite book
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|last1= Economides |first1=M.J.
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|last2= Hill |first2=A.D.
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|last3= Economides |first3=C.E.
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|last4= Zhu |first4=D.
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|title=Petroleum Production Systems
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|edition=2
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|date=2013
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|publisher=Prentice Hall
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|place=Westford, Massachusetts
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|isbn=978-0-13-703158-0
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}}</ref>
 
</references>
 
</references>
  

Latest revision as of 19:10, 8 November 2024

By Mikhail Tuzovskiy on 20241108191031

Brief

The most common formula used for multiphase flow through surface chokes developed by Gilbert in 1954[1].

Gilbert developed his empirical equation from field data in California[2].

Math and Physics

P_{wh}=\frac{435 \times GLR^{0.546}}{D^{1.89}} \times q

Note that the equation is independent of the downstream pressure and assumes that the downstream pressure is less than 70% of the upstream pressure, i.e. the flow is "critical" i.e. fluid reach sonic velocity in the throat of the choke[3].

Example

Given data

Oil rate = 600 bbl/d, GLR=400 scf/bbl, D=22/64 in, Line pressure = 180 psia

Calculate the well head pressure?

Solution

P_{wh}=\frac{435 \times 0.4^{0.546}}{22^{1.89}} \times 600 = 460 psig = 460 +14.7 = 474.7 psia

Validity check 180/474.7=0.38 < 0.7 OK

Nomenclature

D = choke beam diametr, 64th of an inch
GLR = gas liquid ratio, Mscf/bbl or 10^3 scf/bbl
P_{wh} = well head pressure, psig
q = liquid flow rate, bbl/d

References

  1. ↑ Gilbert, W.E. (1954). Flowing and Gas-Lift Well Performance. Drilling and Production Practice API. p. 143. 
  2. ↑ Brown, Kermit (1984). The Technology of Artificial Lift Methods. Volume 4. Production Optimization of Oil and Gas Wells by Nodal System Analysis. Tulsa, Oklahoma: PennWellBookss. 
  3. ↑ Economides, M.J.; Hill, A.D.; Economides, C.E.; Zhu, D. (2013). Petroleum Production Systems (2 ed.). Westford, Massachusetts: Prentice Hall. ISBN 978-0-13-703158-0. 


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