choke sizing

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Choke SizingSingle-Phase Flow

Gas Mass FlowThe relationship which describes the mass flow of a single-phase gas through a choke can be genericallywritten as:

where

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

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

Liquid Mass FlowSingle-phase liquids flowing through a restriction almost never reach the critical velocity, which is many timesthat for single-phase gas. The flowrate can be related to the pressure drop across the restriction with thefollowing relationship:

where

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

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where

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

where

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

Multiphase FlowAshford-PierceAshford and Pierce developed a correlation specifically describing multiphase flow through safety valves andtested it against field data. Their correlation has the form:

with


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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 theflowing phases. However, their relationship for the fluid velocity downstream of the choke gives rise to analternative 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, andwith the latter plus the produced fluid ratios, the mass flowrate of each phase is obtainable.

Achong


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where

P1 = upstream pressure, psia

q1 = liquid flowrate, bbl/d

Rp = producing gas-liquid ratio, scf/bbl

Dc = choke diameter, 64ths of an inch

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

where





GilbertGilbert developed a generalized correlation based on data from flowing oil wells in the Ten Section field ofCalifornia. 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 waterflowing through restrictions. Carrying out a dimensional analysis, Omana derived the following correlation:

with


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and where

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

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

where





ReferencesAchong, I., "Revised Bean Performance Formula for Lake Maracaibo Wells", internal co. report, Shell Oil Co.,Houston, TX, Oct 1961Ashford, F.E. and Pierce, P.E., "Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole SafetyValves", SPE Paper No. 5161, J. Pet. Tech., Sep 1975, 1145Baxendell, P.B., "Bean Performance – Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct1967Gilbert, W.E., "Flowing and Gas-Lift Well Performance", Drill. & Prod. Practice, 1954, 126Omana, 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,


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