Plunger lift design and models

Plunger lift systems can be evaluated using rules of thumb in conjunction with historic well production, or with a mathematical plunger model. Because plunger lift systems typically are inexpensive and easy to install and test, most are evaluated by rules of thumb.

GLR and buildup pressure requirements

The two minimum requirements for plunger lift operation are:

• Minimum gas-liquid ratio (GLR)
• Well buildup pressure

Plunger lift operation requires available gas to provide the lifting force, in sufficient quantity per barrel of liquid for a given well depth. The minimum GLR requirement is approximately 400 scf/bbl per 1,000 ft of well depth and is based on the energy stored in a compressed volume of 400 scf of gas expanding under the hydrostatic head of 1 bbl of liquid. One drawback to this rule of thumb is that it does not consider line pressures. Excessively high line pressures relative to buildup pressure might increase the requirement. The rule of thumb also assumes that the gas expansion can be applied from a large open annulus without restriction, but slimhole wells and wells with packers that require gas to travel through the reservoir or through small perforations in the tubing will cause a greater restriction and energy loss, which increase the minimum GLR requirement to as much as 800 to 1,200 scf/bbl per 1,000 ft.

Well buildup pressure is the bottomhole pressure just before the plunger begins its ascent (equivalent to surface casing pressure in a well with an open annulus). In practice, the minimum shut-in pressure requirement for plunger lift is equivalent to one and a half times the maximum sales-line pressure, although the actual requirement might be higher. This rule of thumb works well in intermediate-depth wells (2,000 to 8,000 ft) with slug sizes of 0.1 to 0.5 bbl/cycle. It does not apply reliably, however, to higher liquid volumes, deeper wells (because of increasing friction), and excessive pressure restrictions at the surface or in the wellbore.

An improved rule of thumb for minimum pressure is that a well can lift a slug of liquid when the slug hydrostatic pressure (phs) equals 50 to 60% of the difference between shut-in casing pressure (pcs) and maximum sales-line pressure:

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

or

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

This rule of thumb accounts for liquid production, can be used for wells with higher liquid production that require slug sizes of more than 1 to 2 bbl/cycle, and is regarded as a conservative estimate of minimum pressure requirements. To use Eqs. 1a and 1b, first estimate the total liquid production on plunger lift and number of cycles possible per day. Then, determine the amount of liquid that can be lifted per cycle. Use the well tubing size to convert that volume of liquid per cycle into the slug hydrostatic pressure, and use the equations to estimate required casing pressure to operate the system (see example below).

A well that does not meet minimum GLR and pressure requirements still could be plunger lifted with the addition of an external gas source. At this point, design becomes more a matter of the economics of providing the added gas to the well at desired pressures. Several papers in the literature discuss adding makeup gas to a plunger installation through existing gas lift operations, installing a field gas supply system, or using wellhead compression.

Estimating production rates

The simplest and sometimes most accurate method of determining production increases from plunger lift is decline-curve analysis (Fig. 1). Gas and oil reservoirs typically have predictable declines, either exponential or hyperbolic. Initial production rates usually are high enough to produce the well above critical rates (unloaded) and establish a decline curve. When liquid loading occurs, a marked decrease and deviation from normal decline can be seen. Unloading the well with plunger lift can re-establish a normal decline. Production increases from plunger lift will be somewhere between the rates of the well when it started loading and the rate of an extended decline curve to the present time. Ideally, decline curves would be used with critical-velocity curves to predetermine when plunger lift should be installed. This would enable plunger lift to maintain production on a steady decline and to never allow the well to begin loading.

• 

  Fig. 1—Effects of plunger lift on a typical gas-well production decline. (Modified from Ferguson and Beauregard.)

Another method for estimating production is to build an inflow performance (IP) curve on the basis of the backpressure equation (Fig. 2). This is especially helpful if the well has an open annulus and is flowing up the tubing, and if the casing pressure is known. The casing pressure closely approximates bottomhole pressure. Build the IP curve on the basis of:

• Estimated reservoir pressure
• Casing pressure
• Current flow rate

• 

  Fig. 2—Inflow-performance-relationship analysis for estimating plunger-lift performance. Chart shows production increase resulting from reducing liquid hydrostatic pressure with a plunger-lift system. (After Vogel and Mishra and Caudle.)

Because the job of the plunger lift is to lower the bottomhole pressure by removing liquids, estimate the bottomhole pressure with no liquids. Use this new pressure to estimate a production rate with lower bottomhole pressures.

Models

Plunger lift models are based on the sum of forces acting on the plunger while it lifts a liquid slug up the tubing (Fig. 3). These forces at any given point in the tubing are:

• 

  Fig. 3—Plunger force balance. (Based on Lea.)

Stored casing pressure freely acting on the cross section of the plunger.

Stored reservoir pressure acting on the cross section of the plunger, based on inflow performance.

• Weight of the fluid.
• Weight of the plunger.
• Friction of the fluid with the tubing.
• Friction of the plunger with the tubing.
• Gas friction in the tubing.
• Gas slippage upward past the plunger.
• Liquid slippage downward past the plunger.
• Surface pressure (line pressure and restrictions) acting against the plunger travel.

Several publications have dealt with this approach. Beeson et al. first presented equations for high-GLR wells in 1955, on the basis of an empirically derived analysis. Foss and Gaul derived a force-balance equation for use on oil wells in the Ventura Avenue field in 1965. Lea presented a dynamic analysis of plunger lift that added gas slippage and reservoir inflow, and mathematically described the entire cycle (not just plunger ascent) for tight-gas/very high-GLR wells.

Foss and Gaul’s methodology was to calculate (p_c)min, the casing pressure required to move the plunger and liquid slug just before it reaches the surface. Because (p_c)min is at the end of the plunger cycle, the energy of the expanding gas from the casing to the tubing is at its minimum. Adjusting (p_c)min for gas expansion from the casing to the tubing during the full plunger cycle yields (p_c)_max , the pressure required to start the plunger at the beginning of the plunger cycle. The pressure must build to (p_c)_max to operate successfully.

The average casing pressure p¯c, maximum cycles C_max, and gas required per cycle (V_g) can be calculated from (p_c)min and (p_c)max . The equations below are essentially those presented by Foss and Gaul but are summarized here as presented by Mower et al. The Foss and Gaul model is not rigorous, it:

• Assumes constant friction associated with plunger rise velocities of 1,000 ft/min
• Does not calculate reservoir inflow
• Assumes a value for gas slippage past the plunger
• Assumes an open, unrestricted annulus
• Assumes that the user can determine unloaded gas and liquid rates independently of the model

Also, because this model originally was designed for oilwell operation that assumed the well would be shut in upon plunger arrival, p¯c is only an average during plunger travel. The net result of these assumptions is an overprediction of required casing pressure. If a well meets the Foss and Gaul criteria, it is almost certainly a candidate for plunger lift. For a full description of the Foss and Gaul model and for a description of improved models, see the references.,

Basic Foss and Gaul equations

Basic Foss and Gaul equations (Modified by Mower et al. and Lea)

Required pressures

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

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

and

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

where

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

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

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

and

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

Foss and Gaul suggested an approximation where K and p_lh + p_lf are constant for a given tubing size and a plunger velocity of 1,000 ft/min (Table 1).

• 

  Table 1

Gas (Mscf) required per cycle

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

where

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

Maximum cycles

........................(11)

Examples

Rules of thumb and Foss and Gaul calculations

Examples are based on the well data given in Table 2.

• 

  Table 2

Example of rule-of-thumb GLR calculation

The minimum GLR (Rgl) = 400 scf/bbl per 1,000 ft of well depth. The well’s GLR is:

........................(12)

........................(13)

where q_g is given in scf. The well GLR is >400 scf/bbl per 1,000 ft and is adequate for plunger lift.

Example of rule of thumb for casing pressure requirement to plunger lift (simple)

The rule of thumb for calculating the minimum shut-in casing pressure for plunger lift, in psia, is:

........................(14)

........................(15)

With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift. This is the absolute minimum pressure required for low liquid volumes, intermediate well depths, and low line pressures.

Casing pressure requirement

For this case, assume 10 cycles/day, equivalent to a plunger trip every 2.4 hours. Any reasonable number of cycles can be assumed to calculate pressures.

At 10 cycles/day and 10 bbl of liquid, the plunger will lift 1 bbl/cycle. The slug hydrostatic pressure (phs) of 1 bbl of liquid in 2 3/8-in. tubing with a 0.45-psi/ft liquid gradient is approximately 120 psia. Using Eq. 1b, the required casing pressure, in psia, is calculated as:

........................(16)

........................(17)

With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift.

Method to determine plunger lift operating range

In determining plunger-lift operating range, use Foss and Gaul K and plh + plf values for 2 3/8-in. tubing and average rise velocities of 1,000 ft/min. Calculate new friction factors if velocities are more or less than 1,000 ft/min.

Calculate the constants A_t, p_p, A_a, R_a, F_gs, L, and V_t:

Area of tubing, ft²:

........................(18)

........................(19)

Differential pressure required to lift plunger, psi:

........................(20)

where At is given as in.². Therefore:

........................(21)

Area of annulus, ft²:

........................(22)

........................(23)

Ratio of total area to tubing area:

........................(24)

........................(25)

Lea -modified Foss and Gaul slippage factor [Foss and Gaul used a 15% factor (1.15) that could be translated to approximately 2% per 1,000 ft]:

........................(26)

........................(27)

Length of 1 bbl of fluid in the tubing, ft/bbl (5.615 = scf in 1 bbl):

........................(28)

........................(29)

Volume of tubing above the slug (use for various slug sizes) (Eq. 16.10, but here in Mscf):

........................(30)

Assume some values for S (bbl) and construct Table 3.

• 

  Table 3

It was given that the estimated production when unloaded is 200 Mscf/D with 10 B/D of liquid (GLR = 200/10 = 20 Mscf/bbl), and that the available casing pressure (or the pressure to which the casing will build between plunger cycles) is 800 psia. The available casing pressure, p_c, is equivalent to the calculated (p_c)_max —or the pressure required to lift the assumed slug sizes. The well GLR is equivalent to the calculated required GLR. The maximum liquid production is a product of the slug size (S) and the maximum cycles per day (C_max). Importantly, C_max is not a required number of plunger trips, but rather the maximum possible on the basis of plunger velocities. In reality, most wells operate below C_max because well shut-in time is required to build any casing pressure. In Table 16.3, note that the casing pressure (p_c)_max of 810 psia, the GLR of 20 Mscf/bbl, and the production rate of 10 B/D occur at slug sizes between 0.1 and 2.5 bbl. The well will operate on plunger lift.

Nomenclature

Aa	=	cross-sectional area of annulus, ft2
At	=	cross-sectional area of tubing, ft2 or in.2
Cmax	=	maximum number of plunger round trips possible per day
d	=	tubing diameter, in.
fg	=	Darcy-Weisbach friction factor for gas flow through the tubing
Fgs	=	Foss and Gaul slippage factor of gas lost past plunger on rise cycle [approximately 2% per 1,000-ft depth ( = 1 + D/1,000 × 0.02); Foss and Gaul used 1.15 factor on 8,000-ft wells.]
fl	=	Darcy-Weisbach friction factor for the liquid slug
gg	=	gas specific gravity
K	=	gas friction in tubing
pc	=	casing pressure, psia
	=	average casing pressure during operation, psia
(pc)max	=	the pressure required to start the plunger at the beginning of the plunger cycle, psia
(pc)min	=	the casing pressure required to move the plunger and liquid slug just before it reaches the surface, psia
pcs	=	casing pressure at shut-in, psia
phs	=	slug differential hydrostatic pressure, psi
pl	=	line pressure, psia
plf	=	differential pressure required to overcome liquid friction per barrel, psi/bbl
plh	=	differential pressure required to lift liquid weight per barrel, psi/bbl
pp	=	differential pressure required to lift plunger weight, psi
pR	=	reservoir pressure, psia
pt	=	tubing pressure, psia
qg	=	gas flow rate, Mscf/D
ql	=	liquid flow rate, B/D
R	=	specific gas constant (air), 53.3 lbf-ft/(°R-lbm)
Ra	=	ratio of annulus + tubing cross-sectional area to the annulus cross-sectional area
v	=	velocity, ft/sec
	=	average velocity of plunger falling through gas, ft/min (typically 200 to 1,200 ft/min)
	=	average velocity of plunger falling through liquid, ft/min (typically 50 to 250 ft/min)
	=	average rise velocity of plunger, ft/min (typically 400 to 1,200 ft/min)
Vg	=	volume of gas required per cycle, Mscf
Vt	=	volume of the tubing above the liquid load, Mscf
Z	=	gas factor
γl	=	liquid gradient, psi/ft

Noteworthy papers in OnePetro

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External links

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See also

Plunger lift

Plunger lift applications

Plunger design considerations and selection

Plunger lift installation and maintenance

PEH:Plunger_Lift