Gilbert choke equation

Brief

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

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