Choke SizingSingle-Phase Flow

Gas Mass Flow

The relationship which describes the mass flow of a single-phase gas through a choke can be generically written as:

where

With the gas density at standard conditions, the gas mass flowrate is readily converted into a daily standard volumetric flowrate.

This equation applies only at the critical pressure ratio, . The critical pressure ratio can be calculated from

Liquid Mass Flow

Single-phase liquids flowing through a restriction almost never reach the critical velocity, which is many times that for single-phase gas. The flowrate can be related to the pressure drop across the restriction with the following relationship:

where

The choke flow coefficient is a function of the Reynolds number in the choke throat and so the solution is necessarily iterative, but convergence is quite rapid.

Rawlins-Schellhardt

Rawlins and Schellhardt give us a form of the equation for gas flow through chokes under critical flow conditions which is dependent only on the upstream pressure. Rawlins and Schellhardt based their equation on ideal gas at a standard pressure of 14.4 psia. Correction for non-ideality and for a standard pressure other than 14.4 psia is included in the following equation:

where

Szilas

Szilas gives us an alternate form of the gas mass flow equation and with constants and conversion factors for field units, as:

where

This equation applies both at and above the critical pressure ratio, .

Multiphase Flow

Ashford-Pierce

Ashford and Pierce developed a correlation specifically describing multiphase flow through safety valves and tested it against field data. Their correlation has the form:

with

and where

This relationship applies both at and above the critical pressure ratio, .

Ashford and Pierce further define the critical pressure ratio, , as

where

As this is implicit in , it must be solved iteratively.

The Ashford-Pierce relationship cannot directly be applied here because oil may or may not be one of the flowing phases. However, their relationship for the fluid velocity downstream of the choke gives rise to an alternative approach which is amenable to solution with gas plus one or more liquid phases present:

where

Assuming critical flow in the choke throat, the downstream pressure and fluid velocity can be calculated, and with the latter plus the produced fluid ratios, the mass flowrate of each phase is obtainable.

Achong

Achong updated Gilbert’s relationship on the basis of data from oil wells in the Lake Maracaibo field of Venezuela. The rate of multiphase flow through a choke and the upstream pressure are, according to Achong, correlated by the following relationship:

where

Baxendell

Baxendell’s correlation linking the rate of multiphase flow through a choke and the upstream pressure – and fundamentally an update of the Gilbert correlation – is:

where

Gilbert

Gilbert developed a generalized correlation based on data from flowing oil wells in the Ten Section field of California. The rate of multiphase flow through a choke and the upstream pressure can be correlated, according to Gilbert, by the following relationship:

where

Omana et al.

Omana et al. carried out field experiments in the Tiger Lagoon field of Louisiana with natural gas and water flowing through restrictions. Carrying out a dimensional analysis, Omana derived the following correlation:

with

and where

Reliable use of Omana’s correlation is limited to an upstream pressure range of 400 – 1000 psig, 800 bbl/d maximum liquid flowrate, and choke sizes from 4/64" to 14/64". It should be applicable for both bottomhole and surface chokes.

Ros

The rate of multiphase flow through a choke and the upstream pressure are, according to Ros on the basis of Gilbert’s and other prior work, correlated by the following relationship:

where

References

Achong, I., "Revised Bean Performance Formula for Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct 1961

Ashford, F.E. and Pierce, P.E., "Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves", SPE Paper No. 5161, J. Pet. Tech., Sep 1975, 1145

Baxendell, P.B., "Bean Performance – Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct 1967

Gilbert, W.E., "Flowing and Gas-Lift Well Performance", Drill. & Prod. Practice, 1954, 126

Omana, R., Houssiere, C. Jr., Brown, K.E., Brill, J.P., and Thompson, R.E., "Multiphase Flow Through Chokes", SPE Paper No. 2682, paper presented at Annual Fall Meeting of the SPE of AIME, Denver, CO, Sep 28 – Oct 1, 1969

Ros, N.C.J., "An Analysis of Critical Simultaneous Gas-Liquid Flow Through a Restriction and Its