Page 223 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap14 Final Proof page 219 3.1.2007 9:10pm Compositor Name: SJoearun

OTHER ARTIFICIAL LIFT METHODS 14/219
p sh
p c ¼ p L max þ , (14:24) Gaul model is not rigorous, because it assumes constant
f sl friction associated with plunger rise velocities of 1,000 ft/
where min, does not calculate reservoir inflow, assumes a value
p c ¼ required casing pressure, psia for gas slippage past the plunger, assumes an open unre-
p Lmax ¼ maximum line pressure, psia stricted annulus, and assumes the user can determine
p sh ¼ slug hydrostatic pressure, psia unloaded gas and liquid rates independently of the
f sl ¼ slug factor, 0.5–0.6. model. Also, this model was originally designed for oil
well operation that assumed the well would be shut-in on
This rule takes liquid production into account and can plunger arrival, so the average casing pressure, Pc avg ,is
be used for wells with higher liquid production that require only an average during plunger travel. The net result of
more than 1–2 barrels/cycle. It is considered as a conser- these assumptions is an overprediction of required casing
vative estimate of minimum pressure requirements. To use pressure. If a well meets the Foss and Gaul (1956) criteria,
Eq. (14.24), first the total liquid production on plunger lift it is almost certainly a candidate for plunger lift.
and number of cycles possible per day should be estimated.
Then the amount of liquid that can be lifted per cycle
should be determined. That volume of liquid per cycle is 14.5.2.3 Plunger Lift Models
converted into the slug hydrostatic pressure using the 14.5.2.3.1 Basic Foss and Gaul Equations (modified
well tubing size. Finally, the equation is used to estimate by Mower et al) The required minimum casing pressure
required casing pressure to operate the system. is expressed as
It should be noted that a well that does not meet
minimum GLR and pressure requirements could still be Pc min ¼ P p þ 14:7 þ P t þ P lh þ P lf V slug
plunger lifted with the addition of an external gas source.
Design at this point becomes more a matter of the econo- 1 þ D , (14:25)
mics of providing the added gas to the well at desired K
pressures.
where
P c min ¼ required minimum casing pressure, psia
14.5.2.2.2 Analytical Method Analytical plunger lift P p ¼ W p =A t , psia
design methods have been developed on the basis of force W p ¼ plunger weight, lb f
balance. Several studies in the literature address the addition A t ¼ tubing inner cross-sectional area, in: 2
of makeup gas to a plunger installation through either exist- P lh ¼ hydrostatic liquid gradient, psi/bbl slug
ing gas lift operations, the installation of a field gas supply P lf ¼ flowing liquid gradient, psi/bbl slug
system, or the use of wellhead compression. Some of the P t ¼ tubing head pressure, psia
studies were presented by Beeson et al. (1955), Lebeaux and V slug ¼ slug volume, bbl
Sudduth (1955), Foss and Gaul (1965), Abercrombie (1980), D ¼ depth to plunger, ft
Rosina (1983), Mower et al. (1985), and Lea (1981, 1999). K ¼ characteristic length for gas flow in tubing, ft.
The forces acting on the plunger at any given point in
Foss and Gaul suggested an approximation where K
the tubing include the following:
and P lh þ P lf are constant for a given tubing size and a
1. Stored casing pressure acting on the cross-section of plunger velocity of 1,000 ft/min:
the plunger
2. Stored reservoir pressure acting on the cross-section of
the plunger Tubing P lh þ P lf
3. Weight of the fluid size (in.) K (ft) (psi/bbl)
4. Weight of the plunger 3 33,500 165
5. Friction of the fluid with the tubing 2 ⁄ 8 45,000 102
7
6. Friction of the plunger with the tubing 2 ⁄ 8
1
3 ⁄ 2 57,600 63
7. Gas friction in the tubing
8. Gas slippage upward past the plunger
9. Liquid slippage downward past the plunger To successfully operate the plunger, casing pressure must
10. Surface pressure (line pressure and restrictions) acting build to Pc max given by
against the plunger travel
A a þ A t
Several publications have been written dealing with this Pc max ¼ Pc min : (14:26)
A a
approach. Beeson et al. (1955) first presented equations for
high GLR wells based on an empirically derived analysis. The average casing pressure can then be expressed as
Foss and Gaul (1965) derived a force balance equation for
use on oil wells in the Ventura Avenue field. Mower et al. Pc avg ¼ Pc min 1 þ A t , (14:27)
(1985) presented a dynamic analysis of plunger lift that 2A a
added gas slippage and reservoir inflow and mathemati- where A a is annulus cross-sectional area in squared inch.
cally described the entire cycle (not just plunger ascent) for The gas required per cycle is formulated as
tight-gas/very high GLR wells.
The methodology used by Foss and Gaul (1965) was to V g ¼ 37:14F gs Pc avg V t (14:28)

,
calculate a casing pressure required to move the plunger ZT avg þ 460
and liquid slug just before it reached the surface, called
Pc min . Since Pc min is at the end of the plunger cycle, the where
energy of the expanding gas from the casing to the tubing V g ¼ required gas per cycle, Mscf
is at its minimum. Adjusting Pc min for gas expansion from F gs ¼ 1 þ 0:02 (D=1,000), modified Foss and Gaul
the casing to the tubing during the full plunger cycle results slippage factor
in the pressure required to start the plunger at the begin- V t ¼ A t (D V slug L), gas volume in tubing, Mcf
ning of the plunger cycle, or Pc max . L ¼ tubing inner capacity, ft/bbl
The equations below are essentially the same equations Z ¼ gascompressibilityfactorinaveragetubingcondition
presented by Foss and Gaul (1956) but are summarized T avg ¼ average temperature in tubing, 8F.
here as presented by Mower et al. (1985). The Foss and The maximum number of cycles can be expressed as