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Simplified mathematical gas lift performance model

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The following equations have been proposed as a simplified means of evaluating gas lift performance.

Calculation of GLV stem movement

RTENOTITLE....................(1)

where

RTENOTITLE....................(2)

and

RTENOTITLE....................(3)


Calculation of equivalent port area open to gas flow

RTENOTITLE....................(4)

where

RTENOTITLE....................(5)

RTENOTITLE....................(6)

RTENOTITLE....................(7)

and

RTENOTITLE....................(8)

If A Ape > Ap , then Ape = Ap (fixed-ID orifice flow).

Calculation of gas rate through Ape

RTENOTITLE....................(9)

where

RTENOTITLE....................(10)

If Rdu < = 0.553, then Rdu = 0.553 (critical flow).

Nomenclature

Ab = effective area of bellows, in.2
Ap = valve port area (ball/seat-line contact area for sharp-edged seat), in.2
Ape = valve port equivalent area open to gas flow, in.2
Blr = bellows-assembly load rate, psi/in.
Bsr = bellows-assembly spring rate, lbf/in.
CT = temperature correction factor for nitrogen from PbvD at TvuD to Pb at 60°F, dimensionless
Mvs = movement of the gas lift valve stem, in.
Patm = atmospheric pressure, psia
PbvD = nitrogen-charged bellows pressure at valve temperature, psig
PioD = injection-gas pressure at valve depth, psig
PptD = flowing-production transfer pressure at valve depth, psig
Pvo = test-rack valve opening pressure at 60°F, psig
qgi = daily injection-gas rate through gas lift valve, Mscf/D
rb = radius of ball on gas lift valve stem, in.
rp = radius of valve port (ball/seat-line contact for sharp-edged seat), in.
rtf = top radius of frustum of right circular cone, in.
Rdu = ratio of downstream pressure/upstream pressure, psia
s = slant height of frustum of right circular cone, in.
TgiD = injection-gas temperature at valve depth, °F

References

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See also

Gas lift

Gas lift installation design

Gas lift installation design methods

Intermittent-flow gas lift

Intermittent-flow gas lift installation design

PEH:Gas_Lift

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