Click to see subtopics:The following choke equations apply to single-phase flow and multiphase flow.
Specific heat ratio
where:
Cp = specific heat capacity of gas at constant pressure
Cv = specific heat capacity of gas at constant volume
Both of the above are evaluated at upstream pressure and temperature.
Critical pressure ratio
The critical pressure ratio is the theoretical minimum of downstream versus upstream pressure. It is calculated from the specific heat ratio, k:
Sonic velocity
The maximum velocity (or maximum rate) of flow through a choke is limited to the speed of sound. Therefore, the sonic velocity is the maximum velocity.
The sonic velocity is reached when the actual pressure ratio is less than the critical pressure ratio:
Empirical equations
Single-phase gas flow
Rawlins-Schellhardt
Szilas
Szils developed an equation for gas flow through chokes for both critical and subcritical flow.
where:
qg = gas rate, Mscfd
Dc = choke diameter, 64th of an inch
P1 = upstream pressure, psia
P2 = downstream pressure, psia
Psc = standard pressure, psia
Cd = choke discharge coefficient
Ύg = gas specific gravity (air = 1.0)
T1 = upstream temperature, *R
Z1 = upstream gas compressibility factor
k = CP / CV
This equation applies both at and above the critical pressure ratio, For more information, see references.
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:
where:
Cd = choke discharge coefficient
D = choke diameter, 64th of an inch
Bo = oil formation volume factor, rbbl / bbl
Fwo = water oil ratio, bbl / bbl
T1 = upstream temperature, *R
P1 = upstream pressure, psia
z1 = gas compressibility factor at upstream conditions
RF = producing gas oil ratio, scf / bbl
Rs = solution gas oil ratio, scf / bbl
ᵧ = ratio of downstream pressure to upstream pressure, P2 / P1
k = CF / Cs
Ύo = oil specific gravity (pure water = 1.0)
Ύw = water specific gravity (pure water = 1.0)
Ύg = gas specific gravity (air = 1.0)
This relationship applies both at and above the critical pressure ratio, ᵧc.
Ashford and Pierce further define the critical pressure ratio, ᵧc, as
As this is implicit in Ύc 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 that is amenable to solution with gas plus one or more liquid phases present:
where:
µ2 = downstream fluid velocity, ft / s
P1 = upstream pressure, psia
k = CP / CV
ᵧ = ratio of downstream pressure to upstream pressure, P2 / P1
g = mass weight equivalence factor, 32.174 lb ft / lb ft / ls s2
ρf1 = total fluid density at upstream conditions, lb / ft3
ρ1 = liquid density, lb / ft3
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.
For more information, see references.
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:
P1 = upstream pressure, psia
q1 = liquid flowrate, bbl / d
RP = producing gas liquid ratio, scf / bbl
DC = choke diameter, 64th of an inch
For more information, see references.
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:
P1 = upstream pressure, psia
q1 = liquid flowrate, bbl / d
RP = producing gas liquid ratio, scf / bbl
DC = choke diameter, 64th of an inch
For more information, see references.
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:
P1 = upstream pressure, psia
q1 = liquid flowrate, bbl / d
RP = producing gas liquid ratio, scf / bbl
DC = choke diameter, 64th of an inch
For more information, see references.
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:
P1 = upstream pressure, psia
q1 = liquid flowrate, bbl / d
RP = producing gas liquid ratio, scf / bbl
DC = choke diameter, 64th of an inch
For more information, see references.