Gilbert choke equation

Brief

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

Gilbert developed his 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.

Example

Given data

Oil rate = 600 bbl/d, GLR=400 scf/bbl, S=22, Line pressure = 180 psi

Calculate well head pressure?

Solution

$P_{wh}=\frac{435 \times 0.4^{0.546}}{22^{1.89}} \times 600 = 460 psia$

Check validity 180/460=0.4 - OK

Nomenclature

$g$ = 9.81, m/s^2

$h$ = depth, m

$H_d$ = fluid level, m

$H_{perfs}$ = top of the perforations, m

$H_{pump}$ = pump setting depth, m

$P$ = pressure, atm

$P_{ann}$ = annulus presssure, atm

$P_{wf}$ = well flowing bottomhole pressure, atm

$\rho$ = density, kg/m^3

$SG_o$ = oil specific gravity, dimensionless

$SG_w$ = water specific gravity, dimensionless

$WCUT$ = well water cut, fraction