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Calculating Pump
Slippage
Kyle Chambliss
Oxy Permian
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Objective
Model pump slippage and verify with collected
data.
– Increases operating efficiency of wells which is abenefit to operators
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Presentation Outline
What is Pump Slippage?
Review of Historical Pump Slippage Equations
Experimental Slippage Test
Experimental Results
ARCO-HF-COP Formula
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What is Pump Slippage ?
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What is Pump Slippage ?
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Economics of Pump Slippage
Need enough slippage to properly lubricate
barrel, typically 2 to 5% of total production
Improper slippage will damage pump and rodstring causing need for costly repair
Too much slippage is lost production, or in the
case of stripper wells, increased electrical cost
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Historical Slippage Data and Equations
Robinson (1935)
Davis and Stearns (1944)
Robinson and Reekstin (1960) Davis, Stearns and Reekstin (1960)
ARCO-Harbison Fisher (2000)
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Comparison of Historical Formulas
1 ½ inch by 72 inch Plunger
Viscosity of 7 centipoise
Pressure of 2230 psi
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Comparison of Historical Formulas
0
2
4
6
8
10
12
14
0.000 0.001 0.002 0.003 0.004 0.005
Clearance (inches)
P u m p S l i p p a g e ( B a r r e l s p e
r D a y
Robinson Data
Davis and Stearns
Robinson and Reekstin
ARCO-HF
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Failure of Historical Equations
Equations do not agree
Plunger leakage calculations can vary by a
factor of 15 or more Equations were derived from field and
experimental data which may be inaccurate
A new theoretical equation could determinewhich historical leakage equation, if any, isaccurate
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Questions About Slippage
Which, if any, of the Historical Formulas are
correct?
Does Pumping Rate Effect Slippage?
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Experimental Slippage Test
Texas Tech Test Well
– Red Raider # 1 – Measure Pump Slippage in Controlled
Environment
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Red Raider # 1
Depth
– Measured - 4006.6 ft
Casing
– 9 5/8”
– N-80
– 43.5 lb/ft
Location
– East Loop 289 and 4th Street
– 10 minutes from Campus
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Production Equipment
C 456-305-144
– 5 Sheave Sizes – 16”, 12”, 10”, 8.5” and 6”
– ABB Variable Speed Drive
Rod String
– 7/8 and 3/4 Rod String
– 1” Rod String
– 1” Fiberglass String with 1 5/8” Sinker Bars
Tubing
– 2 7/8” J-55 6.5 lb/ft
Sucker Rod Pump
– 2” Barrel 0.009” Clearance 48” Plunger
– 1.5” Barrel 0.005” Clearance 48” Plunger
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Data Control Equipment
Lufkin Automation SAM Controller
Echometer Well Management System
Wood Group Smart Guard RTU package ION Power Measurement System
ABB Variable Speed Drive Micromotion Mass Flow Meter
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Experimental Procedure
Measure Pump Displacement with EchometerEquipment and Lufkin SAM Controller
Measure Actual Production at Surface usingMicromotion Mass Flow Meter
Difference of Pump Displacement and PumpProduction is Slippage assuming no Leakage throughTraveling and Standing Valves – This is a goodassumption for new pump with clean fluid
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Test Data – 2” Pump
Test # Date
Rod
String
Stroke
Lengt
h (in)
Control
Method 3Frequency
(Hz) 4
Pump
Speed
(spm)
Pump Intake
Pressure
Woodgroup
(psig)
Pump
Intake
Pressure
Echometer
(psig)
Echometer
Inferred
Production
(bpd)
Lufkin
Inferred
Production
(bpd)
Surface
Production
(bpd)
Echometer
Slippage
(bpd)
Lufkin
Slippage
(bpd)
Average
Slippage
(bpd)
Pump
Efficinc
y (%)
1-01 7/8/05 76 1 105.6 ABB (12") 60 9.73 gauge dow n 161.5 427.72 424.8 367.1 60.6 57.7 59.1 86.1
1-02 7/8/05 76 1 105.6 12" sheave 60 9.74 gauge dow n 152.6 428.11 425.6 368.0 60.1 57.6 58.8 86.21-03 7/8/05 76 1 105.6 ABB (12") 51 8.25 gauge dow n 165.5 357.49 350.2 301.3 56.2 48.9 52.6 85.1
1-04 7/8/05 76 1 105.6 ABB (12") 43 6.93 167 167.7 297.36 292.6 242.4 55.0 50.2 52.6 82.2
1-05 7/8/05 76 1 105.6 ABB (12") 31.5 5.03 165.7 172 214.7 214.0 163.5 51.2 50.5 50.9 76.3
1-06 7/8/05 76 1 105.6 ABB (12") na 1.82 183.2 182.7 81.5 81.0 41.6 39.9 39.4 39.6 51.2
2-01 7/28/05 88 105.6 ABB (12") .8 spm 0.80 175 178.1 39.2 NA 5.6 33.6 na na 14.2
2-02 7/28/05 88 105.6 ABB (12") .7 spm 0.70 178 178.1 34.4 NA 4.4 30.0 na na 12.82-03 7/28/05 88 105.6 ABB (12") .6 spm 0.60 179 178.1 29.55 NA 0.0 29.6 na na 0.0
2-05 7/28/05 88 105.6 12" sheave 60 9.72 150 165.4 444.6 437.8 377.9 66.7 59.9 63.3 85.6
2-06 7/28/05 88 105.6 ABB (12") 60 9.71 150 151.7 444.6 440.0 378.2 66.4 61.8 64.1 85.5
2-07 7/28/05 88 105.6 ABB (12") 51 8.22 153 149.9 371.6 370.0 308.6 63.0 61.4 62.2 83.2
2-08 7/28/05 88 105.6 ABB (12") 43 6.90 156 154.6 313.4 312.6 250.9 62.5 61.7 62.1 80.2
2-09 7/28/05 88 105.6 ABB (12") 31.5 5.01 156 163 224 223.6 170.2 53.8 53.4 53.6 76.0
3-01 7/5/05 76 1 105.6 16" Sheave 60 12.97 gauge dow n na na 591.1 496.4 na 94.7 na 84.0
4-01 7/14/05 FG 2 87.5 16" Sheave 60 12.95 145 na na 641.7 565.8 na 75.9 na 88.2
5-01 7/14/05 FG 2 87.5 ABB (16") 72.5 15.47 138 na na 868.3 777.2 na 91.1 na 89.5
6-01 7/26/05 88 105.6 16" Sheave 60 12.92 146 na na 625.7 540.1 na 85.6 na 86.3
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Pump Slippage vs. Pump Speed
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16
Speed (spm)
S l i p p a g e ( b p d )
76 String 2 " Pump
76 String 1.5 " Pump
88 String 2 " Pump
FG String 2 " Pump
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Pump Speed vs. Pump Efficiency
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16
Speed (spm)
E f f i c i e n c y ( % )
76 String 1.5 " Pump
76 String 2 " Pump
88 String 2 " Pump
FG String 2 " Pump
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Comparison to ARCO-HarbisonFisher Formula
Measured Slippage Not Constant, Changes
with Pumping Speed
ARCO-Harbison Fisher
– 59.0 bpd for 2” pump
– 23.0 bpd for 1.5” pump
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Pump Slippage vs. Pump Speed
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16
Speed (spm)
S
l i p p a g e ( b p d )
76 String 2 " Pump
76 String 1.5 " Pump
88 String 2 " Pump
FG String 2 " Pump ARCO-HF 1.5" Pump
ARCO-HF 2" Pump
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ARCO-HF-COP
( )[ ]µ L
DPC SPM
52.1
114.0452 +⋅⋅
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ARCO-HF-COP
0
20
40
60
80
100
120
0 2 4 6 8 10 12 14 16
Speed (spm)
S l i p p a g e ( b p d
)
76 String 2 " Pump
76 String 1.5 " Pump
88 String 2 " Pump
FG String 2 " Pump
ARCO-HF 1.5" Pump
ARCO-HF 2" Pump
ARCO-HF-COP 1.5 " Pump
ARCO-HF-COP 2 " Pump
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Conclusions
Pumping Rate affects Slippage. As Pump
Speed Increases, Pump Efficiency Increases
and Slippage Increases
The experimental setup works as intended,
producing reliable data
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Recommendations
Test should be continued
– Using more pumps to determine if coefficients of
ARCO-Harbison Fisher equation are correct
– More test of pumps at different pumping rates
– Using different stroke lengths
Adjust Slippage formula as needed with newdata
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Development and Assistance Sponsors
Harbison-Fischer MFG. Co.
Key Energy Service
Key Energy Trucking
Lufkin Oil Field Services
Norris Rods
Wood Group Production Technology
Wood Group Telecom, LLC
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Research Sponsors
BP America
ChevronTexaco Exploration and Production Technology
ConocoPhillips Co.
Echometer Co.
Lufkin Automation
Occidental Oil & Gas Corporation (Oxy Permian)
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Calculating Pump
Slippage
Kyle Chambliss
Oxy Permian
ARCO HF Sli E i
ARCOARCO HF Sli E iHF Sli E ti
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ARCO ARCO--HF Slippage EquationHF Slippage EquationDoes Not Include Effects of:Does Not Include Effects of:
1) Rod Design1) Rod Design2) Speed (SPM)2) Speed (SPM)
3) Plunger Velocity3) Plunger Velocity
ARCO-HF Slippage EquationARCOARCO--HF Slippage EquationHF Slippage Equation
Slippage: Fluid thatSlippage: Fluid that
falls back betweenfalls back between
the plunger OD andthe plunger OD and
the barrel ID whenthe barrel ID when
traveling ball is ontraveling ball is on
seat into the chamberseat into the chamber
between the standingbetween the standing
valve and travelingvalve and travelingvalve.valve.
A th Ad t f U i ABBA th Ad t f U i ABB
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0 105.6-3.13
0
3.13
6.25
9.38
12.50
15.63
105.0
Fo Max
Wrf
Wrf + Fo Max
0 105.6-3.13
0
3.13
6.25
9.38
12.50
15.63
104.0
Fo Max Fo From Fluid Level
Wrf
Wrf + Fo Max
22”” Plunger, 1Plunger, 1”” Rod String, 0.009Rod String, 0.009”” Clearance, 12Clearance, 12”” SheaveSheave
0.7 SPM, Input 5 HP,0.7 SPM, Input 5 HP,
2.4% System Efficiency2.4% System Efficiency
4.7 BPD in Tank,4.7 BPD in Tank,
34.4 BPD34.4 BPD @@ 105105”” Pump StrokePump Stroke
0.6 SPM, Input 4.8 HP,0.6 SPM, Input 4.8 HP,
0% System Efficiency0% System Efficiency
0 BPD in Tank,0 BPD in Tank,
29.0 BPD29.0 BPD @@ 104104”” Pump StrokePump Stroke
Another Advantage of Using ABBAnother Advantage of Using ABB
0.6 HP0.6 HP 0.7 HP0.7 HP
85.53 Sec/Stroke85.53 Sec/Stroke100 Sec/Stroke100 Sec/Stroke
Wh P d i W t th S f Fl R t i Di tl
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When Producing Water the Surface Flow Rate is Directly
Related to the Plunger Velocity on Upstroke & Down Stroke
D t C dD t C d 5 01 SPM5 01 SPM
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0 105.6-2.50
0
2.50
5.00
7.50
10.00
12.50
15.00
17.50
98.6
Fo Max Fo From Fluid Level
Wrf
Wrf + Fo Max
22”” Plunger, 0.009Plunger, 0.009”” Clearance, 12Clearance, 12”” Sheave, 31.5 HZSheave, 31.5 HZ
170 BPD in Tank,170 BPD in Tank,56 BPD Slippage56 BPD Slippage
Dynamometer CardsDynamometer Cards – – 5.01 SPM5.01 SPM
1 Inch Rod String1 Inch Rod String
91.391.3”” Pump StrokePump Stroke
215 BPD215 BPD @@ PumpPump
Peak Load 12,324 LbPeak Load 12,324 Lb
Peak Load 16,588 LbPeak Load 16,588 Lb
76 API Taper Rods76 API Taper Rods
95.295.2”” Pump StrokePump Stroke
226 BPD226 BPD @@ PumpPump
163 BPD in Tank,163 BPD in Tank,51 BPD Slippage51 BPD Slippage
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Davis and Stearns (1944)
µ Ld
d d PC B DS 1.0
2
21
22
9.161017.4 −×=
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Robinson and Reekstin (1960)
µ L
C PD B RR
3.37.081080.1 ×=
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ARCO-Harbison Fisher (2000)
µ L
DPC B AH 52.1
870=
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Velocity Profile
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Velocity Profile Equation
( ) ( )
0
0
0
02
0
22
0
2
ln
ln
ln
ln
4)(
R
R
R
r
V
R
R
R
r
R R Rr p
r V i
P i
i z +
−−−−
=µ
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Slippage Calculation
B = (Annular Area)x
(Average Velocity)x
(Plunger Travel Time)
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Concentric and Eccentric Plungers
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Slippage Calculation for Eccentric Plunger
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Derivation of Theoretical Slippage Equation
Velocity Profile of Annulus
– Moving Plunger Factors
– Eccentricity
– Pumping Rate
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Concentric and Eccentric Plungers
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Comparison to Historical Formulas
1 ½ inch by 72 inch Plunger
Viscosity of 7 centipoise
Pressure of 2230 psi Pumping Rate of 10 strokes per minute
Stroke Length of 55 inches
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Average Velocity of Flow Through Annulus
( )( )
( ) ( )
−
+
+
−
−−−
−=
0
22
0
2
0
0
0
2
0
22
0
2
2
022
0
44
0
lnln
ln
ln
24
R
R
R R
R
R
R
R R
R
R
R R
R R
R R
R R P V
i
i
i
i
i
i
i
i
i ψ ψ
µ
( )
( )
( )
−
−
+
−
0
0
0
22
0
0
0
2
0
ln
ln
lnln
ln
R
R
R
R
R R R
V
R
R
R R
ii
i
P i
ψ
−−
−= 2
1ln
2
1ln 2020 ii R R R Rψ
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Slippage Compared to Historical Data
0
2
4
6
8
10
12
14
0.000 0.001 0.002 0.003 0.004 0.005
Clearance (inches)
P u m p S l i p p a g e ( B a r r e l s p e r D a y )
Davis and Stearns
Robinson and Reekstin
ARCO-HF
New Method (Concentric)
New Method (Eccentric)
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ARCO-HF Formula and New Method
0
20
40
60
80
100
120
140
0.000 0.005 0.010 0.015 0.020
Clearance (Inches )
S l i p p a
g e ( B a r r e l s p e r D a y )
ARCO-HF
New Method (Concentric)
New Method (Eccentric)
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Comparison of Pumping Rate
3 inch by 24 inch
Viscosity of 7 centipoise
Pressure of 2620 psi
Pumping Rate of 8
strokes per minute
Stroke Length of 55
inches
3 inch by 24 inch
Viscosity of 7 centipoise
Pressure of 2620 psi
Pumping Rate of 16
strokes per minute
Stroke Length of 55
inches
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Comparison of Pumping Rate
0
1
2
3
4
5
6
7
8
0.000 0.001 0.002 0.003 0.004 0.005
Pump Tolerance (in)
8 SPM Concentric
16 SPM Concentric
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Ratio of Eccentric to Concentric Slippage
Historically believed to be 2.5
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Ratio of Eccentric to Concentric Slippage
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Pump Clearance (in)
R a t i o o f E c c e
n t r i c t o C o n c e n
t r i c S l i p p a g e
Pump 1
Pump 2
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Ratio of Eccentric to Concentric Slippage
1 ½ inch by 72 inchPlunger
Viscosity of 7 centipoise
Pressure of 2230 psi
Pumping Rate of 10
strokes per minute
Stroke Length of 55
inches
5 inch by 24 inchPlunger
Viscosity of 15
centipoise
Pressure of 1000 psi
Pumping Rate of 5
strokes per minute
Stroke Length of 144
inches
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Conclusions from Theoretical Formula
Pumping Rate has small effect on slippage
Eccentricity as a large effect on slippage
Ratio of eccentric to concentric slippage is not2.5 for all pump clearances
ARCO-Harbison Fisher Equation agrees with
new equation up to a Plunger Clearance of0.005 inches