Gilbert choke equation

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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.