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.
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.
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.
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.
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.
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.
|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|
- Beggs, H.D. 1991. Production Optimization Using Nodal Analysis, 123-127. Tulsa, Oklahoma: OGCI Publications.
- Gilbert, W.E. 1954. Flowing and Gas-Lift Well Performanc. Drill. & Prod. Prac., 126-157. Dallas, Texas: API.
- Ros, N.C.J. 1960. An Analysis of Critical Simultaneous Gas/Liquid Flow Through a Restriction and Its Application to Flowmetering. Applied Scientific Research 9 (Series A): 374.
Noteworthy papers in OnePetro
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
Xiong, Hongjie. "Optimizing Cluster or Fracture Spacing: An Overview." The Way Ahead. Society of Petroleum Engineers. 25 May 2017. https://www.spe.org/en/twa/twa-article-detail/?art=3007