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# Simplified mathematical gas lift performance model

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

## Calculation of GLV stem movement

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

where

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

and

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

## Calculation of equivalent port area open to gas flow

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

where

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

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

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

and

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

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

## Calculation of gas rate through Ape

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

where

....................(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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