Slip Calculation of
Rotational Speed of
Electrical Submersible
Progressive Cavity Pumps
Desheng Zhou, Hong Yuan
IHS INC.
Driving System
• Surface Driving
• Bottom Driving
Bottom Driving System
•
•
•
•
•
Electric Submersible Motor
Protector
Gear Reducer
Flex Drive
Intake and PC Pump
Motor Rotational Speed
• Two, four-pole motors;
• At 60 HZ, motor speed is 3500
RPM for two-pole motors, and is
1700 RPM for four-pole motors;
• PC pump speed = Motor
speed/Gear reduction ratio.
Motor Speed
• The 3500 RPM and 1700 RPM are
only estimated values;
• Actual motor output speed varies
with the load on the motor;
• 3600 RPM for two-pole motors and
1800 RPM for four-pole motors at
60 HZ and no-load;
Electric Submersible
Motor
• Nameplate Horsepower
• Nameplate Voltage
• Nameplate Current
Motor Performance
3640
120
3600
100
Percent
Efficiency
80
3560
60
Speed
3469
40
20
3520
3500
3480
3440
Power Factor
0
20
40
60
80
100
120
3400
Load Factor = Load Power/NP Power, %
Motor Speed, RPM
%NP Current
Motor Performance
• Motor
Performance
•
•
•
•
Motor Speed, RPM
3640
%NP Current
3600
Efficiency
%NP Current
3560
3520
3500
Speed
3480
3440
3469
Power Factor
3400
0
20
40
60
80
Load Factor, %
100
120
3500 RPM is at 80% LF
3469 RPM at full load
3600 RPM at no-load
Speed varies with load
factor (LF)
• Speed slip = 3600 - n
Motor Load
• PC Pump
• Protector
• Gear Reducer & Flex Drive
Protector
• Set between gear reducer and electric
submersible motor
• Provide seals for the gear and the motor
from well fluid
• Equalizes internal motor pressure and gear
pressure with the wellbore pressure.
• Absorb the down thrust force from the PCP
Protector Horsepower
• Depends on its seal type,
protector size, and down thrust
force for seals with thrust
bearings
• Manufacturers may provide
correlations to calculate
• In the range of 0.1 hp to 2 hp
• An estimation 0.5 hp
Gear Reducer
• For the reasons of working life and
efficiency, a PCP has a maximum
operating speed (500 RPM)
• Gear reducer is used to reduce the
motor speed down to an acceptable
range for the PCP
• 9 : 1 for a two-pole motor or 4 : 1 for a
four-pole motor
• 389 RPM after the 9 : 1 reduction, and
425 RPM after the 4 : 1 reduction
Flex Shaft
• PCP rotor rotates eccentrically
• Convert the concentric rotation of
the gear reducer to the eccentric
rotation of the rotor
Gear Reducer and Flex
Shaft
• Affected by gear reduction ratio, gear
meshes (single or double reduction
gears), input rotational speed, tooth
geometry, and down thrust force on
the thrust bearing
• Test results from manufacturers
• Estimation of 0.98 for single planetary
reduction, and 0.96 for double
reduction.
PCP Horsepower
•
•
•
•
•
Brake horsepower
Hydraulic horsepower
Effective horsepower
Slip horsepower
Mechanical horsepower
Brake Horsepower
• Brake horsepower is the
horsepower required to drive a
PCP, which is the sum of hydraulic
horsepower and mechanical
horsepower
•
Hydraulic Horsepower
• The work done to pump the fluid
from pump intake pressure to the
discharge pressure
• Note that the work is done on all
the pumping fluid, including
leakage and delivered fluid
• Independent of fluid viscosity
Effective Horsepower
• The work done on pumping the
actual delivered fluid
• Does not include the volumetric
slip fluid.
Mechanical Horsepower
• The internal power losses in a PCP
• Consists of friction losses and fluid shearing
losses
• Friction losses are the losses from the
frictions of parts to parts and fluid to parts,
which include all the power to overcome the
frictions of all moving parts and the frictions
to the fluid flow
• Shearing losses come from the shearing
action in the fluid itself. They are affected by
rotor rotational speed, pump cavity
geometry, and fluid shearing characteristics
(Newtonian or non-Newtonian behavior).
PCP Efficiency
• Ep = Ev * Em
• Ev = qa / qt = (qt – qs)/qt
• Em = HPh / HPb
Motor Frequency Model with
Slip
Derived Model
Derived Model
for two-pole and
60 HZ
Simplied Model
fd =
(n pcp N gr + S ) f s
fd =
Ns
60 ( n pcp N gr + S )
fd =
3600
60 n pcp N
3500
gr
Motor Frequency Analysis
Algorithm
•
•
•
•
•
•
•
•
Estimate an initial pump speed.
For the pump speed, calculate the production
fluid rate
Calculate the hydraulic horsepower and the total
horsepower
Calculate the load factor at standard frequency
Calculate the motor output speed from motor
speed performance curve.
Solve a new pump speed using the calculated
speed slip
If the difference of the new pump speed and the
initial pump speed is in an acceptable range, the
new pump speed is the solution. Otherwise,
Use the new pump speed as the initial pump
speed and continue the iteration from step 2.
Conclusions
•
•
•
•
•
Presents simplified models and rigorous models to design motor
frequency at a given pump speed
Use the models to analyze pump speed or production rate at a given
motor frequency in a bottom driving PCP system.
The major difference between the simplified and the rigorous models
is that the simplified model neglects the slip of motor speed. Since
motor speed varies with its load, the simplified model only gives an
approximate relationship.
The simplified model uses the nominal speed of 3500 RPM for twopole motor and 1700 RPM for four-pole motor. The simplified model is
easy to use since the knowledge of motor specific performances is
not required.
The rigorous model requires calculating of total required horsepower
and using of motor performance curve. It is accurate but a computer
program is needed to complete the calculations. Pump speed
depends on motor slip and the motor slip is determined by the pump
speed. An iteration algorithm is employed to analyzing the effect of
motor frequency on the pump speed or production rate.