System Analysis for

Sucker-Rod Pumping
z. Schmidt, SPE, and D.R. Doty, U. of Tulsa

Summary. Pumping free gas in an oil well can significantly decrease the efficiency of a sucker-rod-pumping installation. Pump placement
depth and use of a downhole gas/liquid separator (gas anchor) were found to be significant variables in improving the overall efficiency.
A procedure is presented that shows when and to what degree the use of a gas anchor improves the efficiency of a sucker-rod pumping
system. It was found that at lower pump intake pressures, the gas anchor usually improves efficiency, but at higher pump intake pressures,
use of a gas anchor will produce no positive effect. Also, elevating the pump to the highest position that still allows proper pump loading
was found to reduce the operating costs of a sucker-rod-pumping installation significantly. Finally, a procedure is presented to calculate
directly the pump volumetric efficiency and required volumetric pump displacement rate.

Introduction
The design of a sucker-rod-pumping system involves a number of In addition to controlling pump intake pressures, use of a
considerations encompassing the choice and operation of equipment downhole gas/liquid separator or gas anchor is another option for
and the proper production rate from the reservoir. Equipment de- controlling the quantity of gas entering the pump. The many different
cisions can be made only after production from the reservoir has techniques for producing downhole separation range from the natural
been considered. When maximum production from the well is separation that occurs by placing the pump intake below the perfo-
desired, many operators set their pumps near the perforations and rations to using various devices attached to the pump intake to
produce with liquid levels in the casing as low as possible. In many achieve separation. Although the correct use of a separator may
cases, however, it is not desirable to produce such high flow rates increase volumetric efficiency, it suffers from some potential
at low flowing pressures. For example, an overall analysis of the hazards, including the possibility of the pump's becoming choked
field may indicate that optimal production for the field may require with sand, paraffin, or other deposits, thereby further decreasing
that the well produce less than its maximum capacity. In such cases, the pump intake pressure and liberating additional gas. Also, in
the well flowing pressure will be increased to diminish the well's many installations, the gas anchor may become stuck, which makes
production to the desired rate. Even with higher flowing pressures, pulling the pump and gas anchor difficult.
however, it is often common practice to locate the pump at the well A simple composite equation can be developed for the pump volu-
bottom. This practice usually does not produce the well most eco- metric efficiency in terms of the volumtltric efficiency resulting from
nomically. the presence offree gas in the pump, fluid leakage past the plunger
Likewise, many operators may have standard rules concerning and valves, and the clearance between the plunfer on the bottom
the installation of bottomhole gas anchors in their wells. A uniform of its downstroke and the bottom of the pump :
decision often is made whether to operate with or without a gas
anchor. This decision may have resulted from past experience, even Ev=EvfgEveEvc· ................................. (1)
though past operating conditions may not apply to current conditions.
Once again, this practice may not result in the most economical The loss of volumetric efficiency resulting from leakage is usually
well production. very small for properly functioning'pumps, For certain types of
This paper addresses the issues of placement depth for the pump pumps and certain operating conditions, however, the loss ofvolu-
and use of a downhole gas anchor. Each of these design considera- metric efficiency resulting from clearance can be significant. A com-
tions can have a significant impact on the efficiency and the oper- plete analysis of this effect has already been performed 5 and
ating cost of a sucker-rod-pumping installation. therefore is not pursued further in this study.
Thus, in light of our objectives, we consider the case where no
Volumetric Pump Efficiency and Gas Interface leakage exists in the pump and where zero volume exists between
in Pumping Wells the plunger at the bottom of its downstroke and the standing valve.
These assumptions yield a pump volumetric efficiency that is slightly
Sucker-rod pumping of a gas/oil mixture is plagued by pumps
higher than the efficiency that really exists in the well. The influence
producing with low volumetric efficiency. )-4 This problem con-
on pump volumetric efficiency from these two conditions, however,
tributes directly to higher lifting costs because of the lower energy
is usually relatively small for properly functioning and adjusted
efficiency and to the indirect acceleration of equipment deterioration.
sucker-rod-pumping systems, With these two assumptions, Eq. I
Low volumetric efficiency has several causes, including leaking
reduces to volumetric efficiency, depending on the free gas in the
valves and fluid slippage past the plunger. Nevertheless, the greatest
pump. As such, pump volumetric efficiency can be simply defined
influence on decreased volumetric efficiency is usually the presence
as the ratio of the volume of the liquid produced at the surface
of gas in the fluid being pumped. In its extreme form (gas lock),
divided by the corresponding volumetric pump displacement re-
high quantities of gas entering the pump can result in the failure
quired to' produce that liquid. It is possible to define pump volu-
of the pump to produce any liquid. Under normal operating con-
metric efficiency as
ditions, the quantity of gas is usually much smaller (gas inter-
ference), and the correct procedure for coping with its presence Ev=(qo +qw)/Rpd =(qo +qw)/(qoBo +qwBw + FfgoqoBg/5.614),
in the pump can be of considerable concern. Because of the highly
............ , , , , , . , .... , .. , , ......... (2)
compressible nature of the gas phase, the pump intake pressure
becomes an important design parameter. At low intake pressures, where qo and qw represent the oil and water volumetric flow rates
even small quantities of gas can expand significantly, resulting in at the surface, Ffgo is the free GOR at the pump intake, and Rpd
deterioration of the pump volumetric efficiency. Conversely, higher is the volumetric pump displacement rate.
intake pressures result in higher volumetric efficiencies because Examination ofthe equation for volumetric efficiency illustrates
more gas remains in solution and any free gas occupies a smaller the importance of pump intake pressure along with free gas as a
volume. For pressures above the bubblepoint pressure, all gas determinant of volumetric efficiency, To illustrate the influence of
remains in solution, resulting in even higher volumetric efficiencies. these factors better, consider the example specified in Table 1. A
Pump intake pressures can be influenced directly by controlling the well 5,500 ft [1676 m] deep is to be produced with a pump that
pump placement depth and/or the liquid level in the casing. has a total volumetric displacement of 1,000 BID [159 m 3 /d]. The
fluids being produced consist of 35° API [O.85-g/cm 3 ] oil with a
Copyright 1989 Society of Petroleum Engineers 10% water cut and gas/liquid ratios of 200 and 300 scf/STB liquid

SPE Production Engineering, May 1989 125

 If pump volumetric efficiency were the only consideration in the
TABLE 1-EXAMPLE DATA
design of a sucker-rod-pumping installation, then two general con-
Pump displacement rate, B/D 1,000 clusions could be drawn. First, it would be desirable to locate the
Water/oil ratio 0.1 pump so that its intake pressure would be above the bubble~int
Oil gravity, °API 35 pressure, or if the well flowing pressure is below the bubblepom.t,
Gaslliquid ratio, scf/STB 200 then as deep as possible. Second, if the pump location results m
Gas/liquid ratio, scf/STB 300 low intake pressures, then a method of separating the gas before
Gas specific gravity 0.65 it enters the pump is necessary.
Well depth, ft 5,500
Flowing temperature at 5,500 ft, of 170
Downhole Gas/Liquid Separators. Downhole gas/liquid separators
Gas-anchor coefficient, Kga 0.03
Gas-anchor annular area, ft2 0.08856
(gas anchors) generally achieve separation by gravitational means.
Two-phase pressure-traverse Fig. 2 illustrates the usual configuration of a gas anchor. Although
correlation Hagedorn and Brown 6 the specific construction details for each type of gas anchor can
Oil FVF correlation Standing? differ, the anchors usually function by creating a relatively ~ar~e
Water FVF correlation Goulds cross-sectional area where bubble-rise velocity relative to the liqUid
Gas FVF 0.0283zT/p exceeds the downward velocity of the liquid. At low pressures,
where the bubbles are large and the density of the gas is low, and
also at low liquid velocities, the gas anchor tends to function very
[36 and 54 std m 3 /stock-tank m 3 ]. Commonly used correlations efficiently. At higher pressures and higher liquid velocities,
were chosen to predict the gas, oil, and water FVF's and the so- however, as the bubbles become smaller and the gas density in-
lution GOR. These values are also specified in Table I (a similar creases, the separation efficiency decreases. At high enough
analysis was performed by Clegg i). To study the influence of pressures and liquid velocities, the bubble-rise velocity relative to
pump intake pressure, the pump was located at different depths. the liquid eventually becomes less than the downward liquid ve-
Fig. 1 displays pump volumetric efficiency as a function of pump locity and all gas entering the gas anchor will be pumped.
intake pressure for several operating conditions. A quantitative description of the performance of a gas anchor
First, consider the extreme case where all free gas at the pump in terms of the free gas it allows to pass into the pump is given as 9
intake is vented into the casing. Thus, only solution gas is allowed
to enter the pump and Ffgo=O. As Fig. 1 shows, this results in Ffgo =KgaP'hv;t B o5.614/Bg SFgo -Fsgo , ............. (3)
high, but slightly decreasing, volumetric efficiencies as the pu.mp
where p=pressure inside the gas anchor and VsL = gas anchor su-
intake pressure is increased to the bubblepoint pressure. ThiS IS a
perficialliquid velocity. Eq. 3 is valid only when the quantity of
direct result of the increased volume of solution gas entering the
gas predicted to pass through the gas anchor is less than or equal
pump. As the pump intake pressure increases beyond the .bubblepoint
to the free gas. vsLcan be evaluated in terms of the oil and water
pressure, however, the additional compression of the oil and water
flow rates as
results in a very slight increase in volumetric efficiency.
Next, consider the opposite extreme of all gas being pum~ (i.e., vsL =[(qoBo+qwBw)5.614]/Aan 86,400, ............... (4)
Ffgo in Eq. 2 corresponds to the total free ~as at the pum~ mtake).
where Aan is the annular cross-sectional area of the gas anchor
For this case, low pump intake pressures (I.e., pump settmgs near
open to downward flow (see Fig. 2).
the liquid level in the tubing/casing annulus) result in extremely
The value of the coefficient Kga that appears in the correlation
low volumetric efficiencies. As the pump intake pressure increases
given in Eq. 3 varies slightly for different fluid physical properties
(i.e., the pump setting depth is lowered), the efficiency increases
for different types of gas anchors. General field experience tends
significantly until the bubblepoint pressure is reached. For pump
to indicate the following approximate values for K ga:
intake pressures above the bubblepoint pressure, where all gas is
in solution, the behavior is'identical to that of the first case. Kga =0.028 ...................................... (5a)

00----------------------------~B~U~B~BL~E~PO~I7.N=T-----------------------,

-
if ALL GAS VENTED
ALL GAS PUMPED

/"'" /"'"
---
----7-
____ - - :aBLE POINT
ALL GAS IN SOLUTION

@ @///
-7 ALL GAS PUMPED

,,/
/ Fg L = 200 SCF/STBL
/ F9 L =300 SCF/STBL
/
1000 2000
PUMP INTAKE PRESSURE (PSIG)
Fig. 1-Pump volumetric efficiency vs. pump intake pressure.

126 SPE Production Engineering. May 1989

for cup-type gas anchors,
Kga=0.036 ...................................... (5b)
for packer-type gas anchors, and
Kga=O.1 ........................................ (5c)
for poor-boy gas anchors.
Eqs. 2 through 5 can be combined to yield an equation for GAS
describing the total volumetric efficiency for both the pump and
the gas anchor. Returning to the example listed in Table 1, the total
volumetric efficiencies for the pump and gas anchor are also dis-
PUMP-+---W +
played in Fig. 1 for the two GOR's considered. As shown, the gas
anchor helps the total volumetric efficiency at low pump intake SEATING
pressures. As the pump intake pressure increases, however, the NIPPLE -+........1\.1'1
relative effectiveness of the gas anchor diminishes. Eventually, at '"
about 400 psig [2758 kPa] when FgL =200 scf/STB liquid [36 std
TUBING INTAKE rill
m 3 /stock-tank m 3 liquid], the effectiveness of the gas anchor is re-
duced to zero (Point A). If a gas anchor is used for pump intake
PERFORATIONS--:!N III
pressures above this value, then the gas anchor can only deteri- SUCTION I'
orate the total volumetric efficiency by further decreasing the pump OR DIP TUBE -+-+-~
intake pressure and consequently stimulating the additional liber-
ation of gas as the fluids pass through the separator. Fig. 1 also
shows the effect of using a gas anchor at higher gas/liquid ratios.
For example, when FgL is increased to 300 scf/STB liquid [54 std
m 3 /stock-tank m 3 liquid], the gas anchor has a positive effect for
pump intake pressures up to about 550 psig [3792 kPa] (Point B).
Thus, it is possible to conclude that the effectiveness of a gas anchor
is limited not only by the quantity of free gas, but also by the pump

"c
intake pressure.

~)
Pump Volumetric Displacement Rate and the Combined Volu-
.metric Efficiency for a Pump and Gas Anchor. The first pa-
rameter that has to be determined in the design of a sucker-rod-
pumping system is the volumetric pump displacement rate required ~ PRODUCING C
to obtain the desired production. Rather than assuming a volumetric ~~ZONE~C
efficiency, as is usually done, we can discretely calculate the re-
quired volumetric pump displacement rate from the total efficiency Fig. 2-Typical configuration of a gas anchor.
expression already developed for both the pump and gas anchor.
Combining Eqs. 2 through 4 allows the volumetric pump dis-
placement rate to be expressed in terms of the pump intake pressure
TABLE 2-WELL TEST DATA
and the desired total liquid production rate, qL:
Average reservoir pressure, psig 1,500
Flowing bottom hole pressure at 5,500 ft, psig 1,097
Measured liquid flow rate, STB/D 280
Water/oil ratio 0.1
Gas/liquid ratio, scf/STB 200
(1 +Fwo) Oil gravity, °API 35
Gas specific gravity 0.65 (air=1)
.................................... (6) Water specific gravity 1.07
where Fwo is the WOR. Eq. 6 can be used either directly to cal- Tubing 10, in. 1.995
culate the volumetric pump displacement rate when the other quan- Temperature at perforation depth at 5,500 ft, OF 170
Temperature gradient, °F/100 ft 1.6
tities are known or indirectly to calculate the total liquid production 4.950
Casing string 10, in.
rate when either the volumetric efficiency or volumetric pump dis- Flowing wellhead pressure (constant), psig 50
placement rate is assumed. Desired flow rate, STB Iiquid/D 520
The following hypothetical example is analyzed to accomplish
the objectives of this study and to illustrate the relative importance
of pump placement and gas-anchor use. Consider the data listed pressure, the corresponding liquid flow rate was calculated by iter-
in Table 2. A well 5,500 ft [1676 m] deep has been tested and will ating in Eq. 6 on qL' This calculation was then repeated for a
produce 280 STB liquidlD [44.5 m 3/d liquid] when the bottomhole number of different intake pressures until a single displacement
pressure is 1,097 psig [7564 kP'a]. The produced fluids consist of curve was obtained. The whole calculation was repeated for the
35° API [0.85-g/cm 3] oil with a 10% water cut and a gas/liquid series of pump displacements (the curves shown in Fig. 3). Using
ratio of 200 scf/STB liquid [36 std m 3 /stock-tank m 3 liquid]. A Vogel'slO inflow performance relationship (IPR) and the well test
natural gas anchor was chosen to perform the separation; therefore, data listed in Table 2, we can determine that the bottomhole flowing
the annular area, A an , is just the area between the casing ID and pressure must be 620 psig [4275 kPa] to produce 520 STB liquidlD
the tubing OD. Because of reservoir considerations, the decision [82.7 stock-tank m 3 /d liquid]. For convenience, this IPR curve is
was made to produce this well at a rate of 520 STB liquid/D [82.7 superimposed over the pump-performance data given in Fig. 3 and
stock-tank m 3/d liquid]. Although several artificial-lift techniques is valid when the pump is located at the perforations. Therefore
exist for producing this well, sucker-rod pumping was chosen. the pump, which can be set at different elevations, can have an intake
Eq. 6 was solved implicitly for the total liquid flow rate while pressure of 620 psig [4275 kPa] or less. As a practical consider-
the pump intake pressure was varied from 100 to 1,500 psig [690 ation, there is a lower limit for the pump intake pressure before
to 10 344 kPa], and the pump volumetric displacement rate was the pump will not load properly. For the purpose of this study, it
varied from 200 to 2,200 BID [31.8 to 349.8 m 3 /d]. In other will be assumed that the elevation of the pump will not be increased
words, for an assumed pump displacement and an assumed intake to create a pump intake pressure less than 100 psig [690 kPa].

SPE Production Engineering, May 1989 127

 1800r--O:---------------------------~~__,
~ 8 00 8 08 0 8
;N v 0 ~a:I ~ Q
gO_

_1500
52
ri~ I I BOTTOM-HOLE FLOWING PRESSURE (PSIG)
600
I
1200 1800

" VOGEL'S IPR

~ I
I
~1200
::> 1'-620 psig
(J)
I
13 I
...-...
-; 2000
.
g:900 I
I&J I
~ J: I
~ l-
e.. I
z 600 I
~
e.. .J
~
::> ~ 4000
e.. 300 ~

1200

6000~--------------------------~----~

Fig. 3-Total liquid flow fate vs. pump Intake pressure and
volumetric pump displacement fate. Fig. 4-Caslng pressure gfadlent.

Effects of Pump and Gas-Anchor Location on Volumetric in the system. 11 The information needed for the design either can
Pumping Efficiency. Examination of Fig. 3 shows that if the pump be measured at the well site or can be calculated if reliable data
and gas anchor are located at the perforations with a pump intake are available and proven predictive techniques exist. The following
pressure of 620 psig [4275 kPa] (Point A in Fig. 3), then the re- specific information is required for a sucker-rod-pumping system
quired volumetric pump displacement rate must be about 800 BID design.
[127.2 m 3 /d] to produce 520 STB liquid/D [82.7 stock-tank m 3 /d 1. The IPR or PI of the well.
liquid] at the surface. Therefore, the corresponding volumetric ef- 2. The flowing gradient between the perforations and the pump
ficiency is 520/800 x 100 = 65 %. If the pump and gas anchor are intake when the pump is to be located above the perforations.
elevated (Point B on Fig. 3) to reduce the pump intake pressure 3. The efficiency of the gas anchor.
to 100 psig [690 kPa] (maintaining 620 psig [4275 kPa] at the per- 4. Fluid physical properties, and whether any sand or corrosive
forations), then the required volumetric pump displacement rate materials are to be produced.
reduces to about 750 BID [119.2 m 3 /d]. The corresponding effi- 5. Data on the physical dimensions and geometry of the well.
ciency is therefore about 5201750 x 100=69%. 6. Data on any equipment. if specific equipment is to be used.
For the example considered, Fig. 3 shows that the highest volu- In addition, reliable predictive techniques have to be available
metric efficiency that can be obtained with a pump and gas anchor for the calculation of the design parameters for both the surface
occurs when the pump intake pressure is 100 psig [690 kPa] (Point and subsurface installations. For the purpose of this paper, the API
B). This also corresponds to the highest elevation for the pump and recommended design method 12 will be used because of its sim-
gas anchor. The lowest volumetric efficiency, which occurs when plicity and wide acceptance. More sophisticated mathematical simu-
the pump intake pressure is about 400 psig [2758 kPa] (Point C lation techniques, however, are available for the design of a
in Fig. 3), is about 520/1060 x 100=49%. sucker-rod-pumping instaliation. 13 •14 These methods should
always be used in preference to the API method, because large errors
Effects of Operating With and Without a Gas Anchor on Volu- may result if conditions are significantly different from those that
metric Efficiency. It is expected that a gas anchor will be most were assumed in the development of the API method.
effective at low pump intake pressures when the gravitational sepa-
ration will be the most effective. As Fig. I shows, the effectiveness Example Design. To illustrate the effect of pump placement and
of a gas anchor is limited when the pump intake pressure is in- use of a gas anchor, the following two extreme cases are considered:
creased. To illustrate this limit, the 800~B/D [127.2-m 3 /d] volu- a pump without a gas anchor located at the perforations with an
metric pump displacement rate curve in Fig. 3 was recalculated intake pressure of 620 psig [4275 kPa] and a pump with a gas anchor
without the influence of the gas anchor. Operating without a gas elevated so that the pump intake pressure is 100 psig [690 kPa].
anchor produces the same effect as operating with a gas anchor for The proper location of the pump for the second case can be deter-
pump intake pressures down to about 400 psig [2758 kPa] (Point mined by use of an appropriate multiphase pressure-loss correlation.
D in Fig. 3). For pump intake pressures below 400 psig [2758 kPa], For the example considered, the Hagedorn and Brown6 correlation
however, the absence of the gas anchor produces a significant was chosen. Fig. 4, which shows' the gradient curve for this case,
decrease in the total liquid flow rate at the surface. This effect is indicates that the pump should be located about 3,075 ft [937 m]
displayed as a dashed line in Fig. 3 from Points D to E. If this well above the perforations (Le., 2,425 ft [739 m] from the surface) to
were produced with and without a gas anchor when the pump intake produce a pump intake pressure of 100 psig [690 kPa].
pressure is 100 psig [690 kPa], then the total liquid flow rate at The design of a sucker-rod-pumping system with the pump lo-
the surface would decrease by about 90 STB liquidlD [14.3 stock- cated at the perforations is considered first. The procedure for cal-
tank m 3 /d liquid] (Le., by the difference between the flow rates culating the polished-rod stroke length and pumping speed is the
indicated by Points B and E) when the gas anchor is removed. This same as that given by Gipson and Swain. 15 A plunger diameter
corresponds to a decrease of volumetric efficiency from 69 to 54 %. of 2.25 in. [5.72 cm] was chosen for the pump volumetric flow
For pump intake pressures above 400 psig [2758 kPa], however, rate of 800 BID [127.2 m 3 /d]. This procedure indicates that the
the presence of a gas anchor will have no positive effect. polished-rod stroke is 120 in. [304 cm] and that the corresponding
pumping speed is 12 strokes/min. Using API RP llL, 12 we deter-
Sucker-Rod-Pumplng System Design mined that the correct sucker-rod taper should be No. 76.
General Overview. Design of a sucker-rod-pumping system re- The above information can be used to estimate the corresponding
quires good understanding of the performance of all components polished-rod horsepower when the pump is located at the perfo-
128 SPE Production Engineering, May 1989
rations. The total polished-rod horsepower is the combination of when the desired surface production and pump intake pressures are
the hydraulic horsepower and the frictional horsepower: known.
3. Pump location depth was found to be a significant variable
hpr=hhp+hf . .................................... (7)
in the polished-rod horsepower required. Considerable savings in
The hydraulic horsepower can be estimated from 16 equipment, maintenance, and energy cost could result if the pump
is located at the highest elevation that still maintains proper pump
hhp =7.36xlO- 6q.y£, .............................. (8) loading.
where £ =effective net lift, .y=average specific gravity, and
q=average total volumetric flow rate of the produced fluid. The Nomenclature
values of t,.y, and q, which can be calculated with the procedure Aan = gas anchor annulus area for downward flow, ft2 [m 2]
outlined in the Appendix, are 3,785 ft [1154 m], 0.766, and 610 Bg = gas FVF, ft3/scf [m3/std m 3]
B/D [97 m 3/d], respectively. Thus, the hydraulic horsepower for
Bo = oil FVF, bbllSTB [m 3 oil/stock-tank m 3 oil]
this case is about 13.0 hp [9.7 kW]. The frictional horsepower can
Bw = water FVF, bbllSTB [m 3 water/stock-tank m3 water]
be estimated in terms of the weight of the rods, polished-rod stroke
D = pump depth, ft [m]
length, and pumping speed from this correlation l6 :
E v = volumetric efficiency
hf =6.31 X 1O- 7 Wr DN, ............................ (9) F fgo = free GOR at pump intake, scf/STB [std m 3 /stock-
which gives 9.4 hp [7 kW]. Therefore, the total polished-rod horse- tank m 3 ]
power is estimated to be about 22.4 hp [16.7 kW]. Fg/ = gas/liquid ratio, scf/STB [std m 3/stock-tank m 3]
The polished-rod horsepower required to operate the well when Fgo = gas-oil ratio, scf/STB [std m 3/stock-tank m 3]
the pump is located at the perforations without a gas anchor can Fsgo = solution GOR, scf/STB [std m 3/stock-tank m 3]
be contrasted with the horsepower required when the pump is sup- Fwo = water/oil ratio (qw/qo), STB/STB [stock-tank m 3 /stock-
plied with a gas anchor and elevated so that the pump intake pressure tank m 3]
is reduced to 100 psig [690 kPa]. For the latter case, the pump volu- hf = frictional horsepower, hp [kW]
metric displacement rate is reduced from about 800 to about 750 hhp = hydraulic horsepower, hp [kW]
BID [127.2 to 119.2 m 3/d]. Using the procedure as outlined above hpr = polished-rod horsepower, hp [kW]
and the same pump plunger size yields an API polished-rod stroke Kga = gas anchor equation coefficient
length of 120 in. [305 cm], with a corresponding pumping speed f = effective net lift distance, ft [m]
of 11 strokes/min. The resultant API rod taper would be No. 76, L = polished-rod stroke length, in. [cm]
which is the same as in the first case. The hydraulic horsepower N = pumping speed, strokes/min
for this case was calculated to be 7.7 hp [5.7 kW], and the fric- P = pressure. psia [kPa]
tional horsepower was calculated to be 3.8 hp [2.8 kW]. This in- Pwf = pump intake pressure, psig [kPa]
dicates that the total polished-rod horsepower for the case where
Pwh = wellhead pressure, psig [kPa]
the pump is elevated to a depth of 2,425 ft [739 m] would be only
1I.5 hp [8.6 kW]. This is. a 50 % reduction in polished-rod horse-
q = average fluid volumetric flow rate, B/D [m3/d]
qL = total liquid volumetric flow rate (qo +qw), STB/D
power compared with that needed when the pump is operated at
the bottom of the well. Thus, a significant saving in operational [stock-tank m 3/d]
costs results when the pump is elevated to a lower intake pressure qo = oil volumetric flow rate, STB/D [stock-tank m 3/d]
and a gas anchor is used. qw = water volumetric flow rate, STB/D [stock-tank m 3/d]
A careful examination of Fig. 4 should be carried out to determine Rpd = volumetric pump displacement rate, B/D [m 3/d]
the main cause behind the dramatic reduction in hydraulic horse- T = temperature, OR [K]
power. It should be observed that the casing fluid gradient is sig- vsL = superficial liquid velocity in the gas anchor, ft/sec [m/s]
nificantly smaller for pressures below 250 psig [1724 kPa], Wr = weight of rods, Ibm [kg]
indicating that the pump can be elevated significantly with only a z = compressibility factor
moderate reduction in the corresponding pump intake pressure. The .y = average specific fluid gravity
tubing pressure gradient at the pump discharge is at its highest,
however, and any elevation of the pump will produce a significant References
decrease in hydraulic horsepower. This effect is amplified for in- 1. Clegg, J.D.: "Understanding and Combating Gas Interference in
creasing gaslliquid ratios and is diminished for decreasing gaslliquid Pumping Wells," Drill. & Prod. Prac., API (1963) 149-55.
ratios. The situation is somewhat different for the frictional horse- 2. Clegg, J.D.: "Gas Interference in Rod Pumped Wells," Proc., South-
power, which is much less sensitive to the presence of gas and much western Petroleum Short Course, Lubbock, TX (April 1979) 105-10.
more sensitive to pump depth and rod taper. 3. Clegg, J.D.: "Reducing Gas Interference in Rod Pumped Wells," World
In addition, consideration must also be given to the future produc- Oil (June 1979) 125.
tivity of the well. As the reservoir pressure decreases with time, 4. Connally, C.A., Sandberg, C.R., and Stein, N.: "Volumetric Efficiency
it will be necessary to lower the pump to maintain the minimum of Sucker Rod Pumps When Pumping Gas-Oil Mixtures," JPT (Oct.
1953) 265-70; Trans., AIME, 198.
intake pressure of 100 psig [690 kPa]. The additional cost of any
5. Ionel,. A.: "Influenta Gazelor Asupra Pompajului De Adincime Cu
such workovers could offset the savings gained by lower energy Prajini," Mine, Petrol Si Gaze (1984) 35, No.5, 248-52.
and equipment costs. As a compromise, it may be desirable to in- 6. Hagedorn, A.R. and Brown, K.E.: "Experimental Study of Pressure
crease the minimum pump intake pressure above 100 psig [690 kPa] Gradients Occurring During Continuous Two-Phase Flow in Small-
to postpone future workovers. Diameter Vertical Conduits," JPT(Aprill965) 475-84; Trans., AIME,
234.
Conclusions 7. Standing, M.B.: Volumetric and Phase Behavior of Oil Field
Hydrocarbon Systems, Reinhold Publishing Corp., New York City
1. The decision whether to use a gas anchor depends on the pump (1952).
intake pressure and on Fgo. At low pump intake pressures and 8. Gould, T.L.: "Vertical Two-Phase Steam-Water Flow in Geothermal
higher Fgo values, the gas anchor was beneficial. At higher pump Wells," JPT (Aug. 1974) 833-36.
intake pressures and lower Fgo values, however, use of a gas 9. Clegg, J.D.: "Multi-Chamber Gas Anchor," U.S. Patent No. 4,515,608
anchor did not increase the pump volumetric efficiency. Indeed, (May 7, 1985).
use of a gas anchor at higher pump intake pressures could actually 10. Vogel, J.V.: "Inflow Performance Relationships for Solution-Gas Drive
Wells," JPT (Jan. 1968) 83-93; Trans., AIME, 243.
result in poorer pump performance than operating without a gas
11. Eickmeier, J.: "How to Optimize Pumping Wells," Oil & GasJ. (Aug.
anchor. 6, 1973) 49-56.
2. A procedure is presented for directly calculating the reqUired 12. RP llL, Recommended Practice for Design Calculations for Sucker Rod
volumetric pump displacement rate and pump volumetric efficiency Pumping Systems, API, Dallas_(Feb. 1977).

SPE Production Engineering, May 1989 129

13. Gibbs, S.G.: "Predicting the Behavior of Sucker-Rod Pumping The second case considered has a pump with a gas anchor lo-
Systems," JPT (July 1963) 769-78; Trans., AIME, 228. cated at a depth of 2,425 ft [739 m]. Because the pump intake
14. Doty, D.R. and Schmidt, Z.: "An Improved Model for Sucker Rod pressure is only 100 psig [690 kPa] (Point B), the gas anchor ef-
Pumping," SPEI (Feb. 1983) 33-41. fectively reduces the amount of free gas entering the pump. The
15. Gibson, F.W. and Swain, H.W.: "Design Beam Pumping," Proc.,
Southwest Petroleum Short Course, Lubbock, TX (April 1972).
total amount of free gas at the pump intake after passing through
16. Brown, K.E.: The Technology ofArtificial Lift Methods, Petroleum Pub- the gas anchor can be calculated from Eq. 3, which yields 18.2
lishing Co., Tulsa, OK (1980) 2A, 43. scf/STB oil [33 std m3 /stock-tank m 3 oil] after conversion to
standard conditions. The solution gas at the pump intake conditions
Appendix of 100 psig and 121°F [690 kPa and 49.4 0c] can be estimated from
The average gravity of the produced fluid can be estimated once Standing's7 empirical correlation to be 15.0 scf/STB oil [2.7 std
the average pump discharge pressure is known (the wellhead m 3 /stock-tank m 3 oil]. This indicates that the total amount of gas
pressure is known to be 50 psig [345 kPaD. For the first example entering the pump is only 33.2 scf/STB oil [5.97 std m3/stock-tank
considered, where the pump without a gas anchor is located at the m 3 oil], which is less than the available gas of 220 scf/STB oil
depth of 5,500 ft [1676 m], the pump intake pressure is 620 psig [39.6 std m 3 /stock-tank m3 oil]. Using this quantity of gas in the
[275 kPa] (Point A in Fig. 3). Because the pump intake pressure procedure outlined above, we can determine the average gravity
exceeds 400 psig [2758 kPa] (Point D), all gas entering the gas of the produced fluid to be 0.853, the effective net lift to be 2,289
anchor must pass through to the pump. Therefore, it will be assumed ft [698 m], and the average fluid volumetric flow rate to be 533
that all g~s ~ill be pumped, which corresp.on~s to F$L =200 BID [84.7 m3 /d].
scf/STB lIqUId [36 std m 3 /stock-tank m 3 lIqUId]. Usmg this
quantity of gas and the data specified in Table 2, we can calculate 51 Metric Conversion Factors
the average pump discharge pressure using the Hagedorn and °API 141.5/(131.5+ o API) g/cm 3
Brown 6 multiphase correlation. Starting with the tubing surface bbl x 1.589 873 E-Ol m3
pressure of 50 psig [345 kPa], the average pump discharge pressure ft x 3.048* E-Ol m
is predicted to be 1,876 psig [12.9 MPa]. Dividing the difference ft2 x 9.290 304* E-02 m2
of the average pump discharge pressure and the surface pressure OF (OF-32)/1.8 °C
by the density of water yields 0.766 as the average gravity of the in. x 2.54* E+OO cm
produced fluid. With this information, the effective net lift for the psi x 6.894 757 E+oo kPa
fluid can be calculated from scf/bbl x 1.801 175 E-Ol std m3 /m 3
f=D-[(Pwj-Pwh)/0.434.y] ....................... (A-l)
·Conversion factor is exact. SPEPE
and turns out to be 3,785 ft [1154 m]. The average fluid volumetric
flow rate of 610 BID [97 m 3 /d] can be obtained by first calculating Original SPE manuscript received for review Oct. 5, 1986. Paper accepted for publication
Feb. 25, 1988. Revised manuscript received Sept. 19, 1988. Paper (SPE 15426) first
the total mass flow rate of the produced fluid and then dividing by presented at the 1986 SPE Annual Technical Conference and Exhibition held in New
the average fluid gravity. Orleans, Oct. 5-8.

130 SPE Production Engineering, May 1989