You must log in to edit PetroWiki. Help with editing

Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. More information

# Flow through chokes

A wellhead choke controls the surface pressure and production rate from a well. Chokes usually are selected so that fluctuations in the line pressure downstream of the choke have no effect on the production rate. This requires that flow through the choke be at critical flow conditions. Under critical flow conditions, the flow rate is a function of the upstream or tubing pressure only. For this condition to occur, the downstream pressure must be approximately 0.55 or less of the tubing pressure.

## Single-phase gas flow

For single-phase gas flow, Beggs presents Eq. 1, which relates the gas production rate through a choke to the wellhead pressure. ....................(1)

The pressure ratio, y, is the ratio of the downstream pressure to the wellhead pressure. Under critical flow conditions, the pressure ratio is replaced by the critical pressure ratio, yc. The critical pressure ratio is the pressure ratio at which flow becomes critical. This ratio depends on the ratio of the specific heats of the produced gas, as Eq. 2 shows. ....................(2)

## Two-phase critical flow

Empirical equations have been developed to estimate the relationship between production rate and wellhead pressure for two-phase critical flow. These correlations can be presented in a form similar to Eq. 3. ....................(3)

Gilbert was the first to present such a relationship based on field data collected from the Ten Section field of California. Ros and Beggs have also presented relationships that are often used. Table 1 summarizes the parameters for each equation.

## Example

This example illustrates the use of the multiphase choke equation (Eq. 3) to estimate the flowing wellhead pressure for a given set of well conditions. However, this equation can be used to estimate flow rate or choke diameter. The example well is producing 400 STB/D of oil with a gas-liquid ratio of 800 Scf/STB. Estimate the flowing wellhead pressure for a choke size of 12/64 in. with Gilbert’s choke equation.

## Solution

Use Eq. 3 and the proper variable from Table 1 to calculate

For these conditions, the estimated flowing wellhead pressure is 1,405 psia. If the Ros choke equation is used, an estimated flowing wellhead pressure of 1,371 psia is calculated. Each of the relationships provides slightly different estimates of the calculated value.

## Nomenclature

 A1–3 = coefficient in Eq. 3 Cd = discharge coefficient, dimensionless d = pipe diameter, L, in. k = specific heat capacity ratio, Cp/Cv in Eqs. 1 and 2, dimensionless psc = standard pressure, m/Lt2, psia pwh = wellhead pressure, m/Lt2, psia qg = gas flow rate, L3/t, Mscf/D qL = liquid flow rate, L3/t, STB/D Tsc = standard temperature, T, °R Twh = wellhead temperature, T, °R y = ratio of downstream pressure to upstream pressure, p1/p2, dimensionless z = gas compressibility factor, dimensionless γg = gas specific gravity, dimensionless