Gilbert choke equation

Brief

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

Echometer is used to measure the fluid level in the wells.

Fluid level is used to calculate and monitor the bottom hole pressure of the wells.

Math and Physics

The physics is based on the principal hydrostatics law:

$P=\frac{\rho g h}{101325}$

Flowing well fluids segregation

When the well is flowing with the pump this is how fluids segregate in the well bore:

• Oil, gas and water are produced through the tubing from the reservoir to the surface
• Gas is in the annulus from the surface to the fluid level, Hd
• Oil and gas are between the fluid level Hd, and the pump setting depth, Hd
• Water, oil and gas are between pump, Hd and the top of the perforations, Hperfs
• Water is in the rathole

Equation to calculate the BHP from the fluid level

$P_{wf}=P_{ann}+\frac{(H_{perfs}-H_{pump})(SG_o(1-WCUT)+SG_w WCUT)+(H_{pump}-H_d)SG_o}{10.32}$

Note that for the deviated wells TVD depths should be used.

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