SUBSURFACE SUCKER-ROD PUMPS
8-5
TABLE 8.2-LOSSES RESULTING FROM SLIPPAGE
OF 3-cp OIL PAST 2%~in. PUMP PLUNGER’
Slippage Loss in Pump
Slippage Past Plunger
at 15 strokedmin
Diametral Slippage Rate
Percent Pump
Clearance (cu in./min)
cu in.lmin BID Displacement
0.003 11.43 5.72 0.85
0.2
0.006 91.5 45.8 6.8
1.6
0.010 424.0 212.0 31.5
7.4
0.020 3,390.o 1,695.O 251.8
59.2
‘48 in. long with 2,000 ps dlfferentml pressure and vmous plunger fits. Also shppage in
percent pump displacement wth fifteen 48-m slrokes per mmufe.
construction has any particular advantage over the other.
Many operators feel that grooves facilitate lubrication of
closely fitted plungers by providing spaces for the well
fluid to accumulate in considerable quantities. However,
there is considerable slippage past any plunger operating
under usual conditions where the differential pressure
across the plunger is several hundred or even thousands
of pounds per square inch. This slippage will provide
adequate lubrication with either type of plunger if the
fluid has any lubricating value. One possible advantage
of a grooved plunger is that any solid particle, such as a
sand grain or a steel chip that gets between the plunger
and the barrel, may become lodged in a groove and
minimize scoring of the barrel and plunger. With a plain
plunger, particles cannot escape from the finished sur-
faces until they have traveled the full length of the
plunger. On the other hand, a grooved plunger stroking
out of a barrel increases the probability of picking up and
carrying solid material into the barrel.
The high differential pressures encountered in pump-
ing deep wells require an effective sealing or packing
means on the plunger. For wells of extreme depth, a
closely fitted metallic plunger is almost always used to
form a satisfactory seal with the barrel. Such plungers
are commonly supplied with nominal clearances of
0.001, 0.002, 0.003, or 0.005 in. in the barrel. Such
plunger fits are commonly referred to as - 1, -2, -3,
or -5 fits. For metal-to-metal pumps the API tolerance
for barrels is +0.002 in., -0.000 in., and the tolerance
for plungers is +O.OOOO in., -0.0005 in., making it
possible for the fit of a - 1 plunger, for example, to vary
from 0.0010 to 0.0035 in. diametral clearance.
Slippage Past Plungers
In slippage past a closely fitted plunger, the flow be-
tween the plunger and the barrel is in the viscous range,
so leakage or slippage is inversely proportional to the ab-
solute viscosity and to the plunger length. It is directly
proportional to the plunger diameter, the differential
pressure between the two ends of the plunger, and the
cube of the diametral clearance.
The absolute viscosity of well fluids commonly
pumped will range from approximately 1 to 100 cp at
temperatures existing at the pump setting. In some cases
the viscosity may be as high as 1,000 cp. As a result of
viscosity variations, the slippage past the plunger of a
particular plunger-pump assembly with a given plunger
fit, length, and diameter may vary by as much as 100 to
1 under fairly common conditions. and as much as 1,000
to 1 under extreme conditions with the same differential
pressure across the plunger. Thus it is seen that a plunger
pump may operate with acceptable efficiency in a well
producing a highly viscous oil, whereas the same pump
operated at the same speed and stroke may fail to deliver
any oil to the surface when installed at the same depth in
a well producing oil of low viscosity.
The following equation can be used to determine slip-
page losses past a pump plunger with sufficient accuracy
for most purposes.
adApAd C 3
9=
pLx2.32x 1o-7 ) . .
where
4 = slippage loss, cu in./min (or 0.2371 cm’/s),
d = plunger diameter, in.,
Ap = differential pressure across plunger, psi,
Ad,. = diametral clearance, in.,
L = length of plunger, in., and
CL = absolute viscosity, cp.
A specific application of this equation will illustrate
the importance of plunger fits for a pump of a particular
bore and stroke, operating with various plunger fits in
fluids of various viscosities.
If we assume a 2%-in.-bore pump having a 0.003-in.
diametral clearance and operating with a pressure dif-
ferential of 2,000 psi between the two ends of a 48-in.
plunger at a rate of fifteen 48-in. strokes per minute in oil
having a viscosity of 3 cp, then Eq. 1 becomes
ax2.25x2,000x2.7x10-s
9=
3x48x2.32x lo-’
= 11.43 cu in./min.
If we assume that the volume of the barrel below the
plunger is completely filled during the upstroke, this rate
of leakage can occur only during the upstroke, or ap-
proximately one-half of the total time. The net slippage
past the plunger is 5.72 cu in./min, or 0.85 B/D. The
displacement of a 21/4-in. pump operating at fifteen
48-in. strokes per minute is 426 BID, and the slippage in
this case is only about 0.2%, which is insignificant. The
results of this and other plunger clearances with 3-cp oil
are shown in Table 8.2.
In the case of 0.020-in. plunger clearance, the slippage
loss when water or oil with a viscosity of 1 cp is pumped
would be 755 B/D, which is more than the pump
displacement, and it would be impossible to pump water