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

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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