Design of Progressive Cavity Pump Wells - ALRDC - · PDF fileDesign of Progressive Cavity...
Transcript of Design of Progressive Cavity Pump Wells - ALRDC - · PDF fileDesign of Progressive Cavity...
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Design of Progressive Cavity Pump Wells
Desheng Zhou, SPE, H. Jasmine Yuan, SPE,
IHS INC.
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Introduction• About PCP
– Special type of rotary positive displacement pump
– Flow through the pump is almost axial
• Advantages of PCPs– Lower investment – Broader applications to fluid mixtures – Less maintenance– Higher efficiency
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Introduction …• PCPs in Petroleum Industry
– Single lobe pump– Non-pulsating smooth flow– Fluid viscosity will not degrade pump head– Normally no scale deposition– Low inertia of rotating parts
• Previous studies focused on– Working mechanism– Pumping behavior
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Introduction …
• Purpose of this study– Design of PCP in production
system• Rotational speed design• Production rate design• Fluid viscosity effect
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A PCP Rotor
e
A
A’
B
B’
C
C’
AA’ BB’ CC’
d
Rotor CenterRotor Axis
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A PCP Stator
S S’
Ps
AB
CD
A
A B C D
4ed
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A Rotor in Stator
Rotor Cross Center+
++ Rotor Axis
Stator Center Line4e
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Basic CorrelationsCross-sectional areas of the rotor and the stator
Fluid flow area at any place
2
41 dArotor π=
eddAstator 441 2 += π
edAf 4=
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Basic Correlations …Cavity moving speed along stator center line
n - rotational speedPs - length of a cavity is the pitch length of the stator
Flow rate in a PCP
snPv =
sft ednPvAq 4==
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Basic Correlations …Taking into account of the slip rate, actual discharge rate
Volumetric efficiency of a PCP
sssta qednPqqq −=−= 4
t
s
t
av q
qqqE −== 1
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Basic PCP Design
qtl – Total flow rate at pump intakeQt – Theoretical displacement per revolution
Correlation to calculate required rotational speed and total flow rate at pump intake
t
tlQ
qn =
ttl nQq =
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Production Rate Design
Where:
Qs - Theoretical displacementqs - slip raten - rotational speedqa - actual flow rate
sta qnQq −=
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Rotational Speed Design
H
q
Lift Capacity, ft
Flow
Cap
acity
, B/D
Speed n0 = 100 RPM
Speed n1 = 200 RPM
SlipQt
Qtn1/n0
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Rotational Speed Design …
q
p
d
Pump Depth
qdpwf
pi pd
pwh
0A B
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Rotational Speed Design
t
sa
Qqqn )(100 +
=
55
44
33
2210 HCHCHCHCHCCq +++++=
)( 55
44
33
221 HCHCHCHCHCqs ++++−=
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Rotational Speed Design …
H
q
Lift Capacity, ft
Flow
Cap
acity
, B/D
100 RPMQt
qa
qs
Ha
A
Qtn
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Production Rate Design …
• Assume the initial slip qs(1) is zero.
• Use Eq. 9 to calculate the total flow rate qa(1) at the PCP's intake for a given rotational speed n and theoretical flow rate Qt at 100 RPM.
• Use the calculated total flow rate qa(1) to calculate the inflow from reservoir to the pump intake and the outflow from wellhead to pump discharge. The outflow is in the annular between sucker rods and tubing for wellhead driving or in tubing for bottom driving. The flow rate for the inflow is the sum of the qa(1) and the separated gas at pump intake.
Algorithm to Solve Total Flow Rate:
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Production Rate Design …• Obtain the differential pressure across the pump
from the calculated inflow and outflow pressure profile, and change the differential pressure to head H(1) by using the average fluid density through the pump.
• Check the required head H(1) with the lift capacity of the pump. If the head is greater than the lift capacity, stop the calculation. A longer PCP should be selected and start from step one. Otherwise,
• Calculate the volumetric slip rate qs(2) at the head H(1) from pump performance curves.
• Use the slip qs(2) and repeat the process from step two until the difference of qs(n)-qs(n-1) is less than an acceptable value.
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Production Rate Design …
q
H
Flow Rate, B/D
Hea
d, ft
S
n0 =100 RPM 2n0 3n0n Well System Curve
Qt qtqa
Ha
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Production Rate Design …
q
p
Flow Rate, B/D
Pres
sure
,psi
a
qi
pwf
Inflow
Outflow
Δpi
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Viscosity Effect - on slip
Viscosity effect on slip
qs-µ - Slip of viscous fluid
qs - Slip of water
µ - Viscous fluid viscosity in SSU
ss qqµµ32
_ =
µ_sta qnQq −=
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Viscosity Effect - on slip …• Obtain pump’s theoretical capacity
Qt at zero head
• For a series of given heads, H(1), H(2), and H(i), obtain corresponding flow rates q(1), q(2), and q(i)
• Calculate the volumetric slips of water by qs(i) = Qt – q(i) at any head H(i).
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Viscosity Effect - on slip …• Calculate in-situ fluid viscosity of the
fluid, µ.
• Calculate the corrected slip rates qs-
µ(i) for the fluid.
• Calculate corrected flow rates, qc(i) = Qt
– qs-µ(i).
• Construct the corrected performance curve using H(i) and qc(i).
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Viscosity Effect - Cavity Filling …
π(d+4e)
Psls
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Viscosity Effect - Cavity Filling …
t
w
Ac
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Viscosity Effect - Cavity FillingCritical Pump Intake Pressure for Fluid Filling the Cavity (Newtonian Fluid)
Where:
)(604.8
1_3 µµ st
sin qnQ
dtl
Ep −=
s
s
ss
lePt
edPl
π
π4
)))4((( 2/122
=
++=
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Viscosity Effect - Cavity Filling …
Critical Speed for Fluid Completely Filling the cavity
tss
in Qql
pdtEn /)604.8( _
3
µµ+=
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Conclusions• Algorithms and procedures to design pump
rotational speed and production rate from well inflow and outflow performances are presented.
• A method to account for the effect of viscosity on pump volumetric slip is proposed.
• Simplified models to calculate the critical pump intake pressures are developed for both Newtonian and non-Newtonian fluids.