Gilbert choke equation

By Mikhail Tuzovskiy on 20241108191031

Brief

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

Gilbert developed his empirical equation from field data in California.

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.

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