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Feb. 6 - 10, 2012 2012 Gas-Lift Workshop 1
Accuracy of Nitrogen Temperature Correction Factors
Rob Sutton
35th Gas-Lift Workshop Houston, Texas, USA February 6 – 10, 2012
Objectives
• Definitions • Need for nitrogen temperature factors (TCF) • Methods to determine nitrogen TCF
– Charts – Tables – Equations
• Method accuracy – Conventional pressure and temperature conditions – HPHT
• Observations and Recommendations
Background
• Nitrogen charged bellows • Temperature effect • Pressure effect • Valve setup in shop • Valve setup in field
Classical TCF References
• Graphs – Kermit Brown: Gas Lift Theory and Practice, Appendix B,
Fig. 24A & 24B (1967). – H.W. Winkler and S.S. Smith: Camco Gas Lift Manual,
Appendix A2, Fig. A2-2 (1962).
• Tables – API Gas Lift Book 6 of the Vocational Training Series,
Table 4-1 (1984). – API Gas Lift Book 6 of the Vocational Training Series,
Third Edition, Table 4-1 (1994).
Classical TCF References
• Equations – H.W. Winkler: “Here’s how to improve your gas lift
installations, Part 6: The Use of Gas Lift Valve Specifications and Force Balance Equations,” (Jan. 1960) 129-135.
– Winkler, H.W. and Eads, P.T.: “Algorithm for More Accurately Predicting Nitrogen-charged Gas-Lift Valve Operation at High Pressures and Temperatures,” paper SPE 18871 presented at the SPE Productions Operations Symposium, Oklahoma City, OK (March 13-14, 1989).
– Takacs, G.: Gas Lift Manual, (2005) 174-175.
Theory – Real Gas Law
TRZnVp =where
p = pressure, psia
V = volume, ft3
n = number of moles
Z = gas compressibility factor
R = universal gas constant =10.73147 psia-ft3/°R-lbm mol
T = temperature, °R
Changing P & T for constant volume and moles of gas
22
2
11
1
TZp
TZp
=
Theory
22
1121 TZ
TZpp =
Condition 2 = operating pressure and temperature.
Condition 1 = test rack (60 °F = 520 °R)
Z = f(p,T) so solving this equation is iterative
Background – TCF
• Dependencies – Gas composition (nitrogen) – Pressure – Temperature
7.147.14
60
−
−=
Td
dt p
pC
Early Sources (1950-60’s) for Nitrogen TCF Multi-Core Processors Limited Apps Available
Problems with 4G Network
Dual-Core Processors
Nitrogen TCF Chart
600
800
1,000
1,200
1,400
1,600
1,800
2,000
2,200
2,400
2,600
600 800 1,000 1,200 1,400 1,600 1,800 2,000
Dome Pressure at 60°F, psig
Dom
e Pr
essu
re a
t Ope
ratin
g Te
mpe
ratu
re, p
sig
100 °F120 °F140 °F160 °F180 °F200 °F220 °F240 °F260 °F280 °F300 °F320 °F340 °F360 °F380 °F400 °F
Nitrogen TCF Chart from Brown
Original Nitrogen TCF Table for 60°F
Derived from Winkler 1960 Eqn
Still used today – API RP 11V6
(Continuous Design – IPO,
1999)
( )[ ]6000215.011
−+=
TCt
Why 60°F for Test Rack Temperature? Nitrogen Z Factors
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
500 1,000 1,500 2,000 2,500 3,000
Pressure, psia
Z Fa
ctor
50 °F60 °F80 °F100 °F
Constant over pressure range of
interest ~0.992
Development of Winkler 1960 TCF
• Plot vs where Z60 = 0.992 ( )
5204601
6060 ZTZ
pp
CTT
T
+== 60−T
Development of Winkler Equation
y = 0.00215x + 1.00000R2 = 0.99968
1.00
1.10
1.20
1.30
1.40
1.50
1.60
0 50 100 150 200 250 300Temperature - 60, °F
1 / C
t
1,000 psia
Development of Winkler Equation
y = 0.00215x + 1.00000R2 = 0.99968
1.00
1.10
1.20
1.30
1.40
1.50
1.60
0 50 100 150 200 250 300Temperature - 60, °F
1 / C
t
1,000 psia 800 psia
Development of Winkler Equation
y = 0.00215x + 1.00000R2 = 0.99968
1.00
1.10
1.20
1.30
1.40
1.50
1.60
0 50 100 150 200 250 300Temperature - 60, °F
1 / C
t
1,000 psia 800 psia2,000 psia
Error in TCF Table from 1960 Eqn
Error in Literature Temperature Correction Factor
-1
0
1
2
3
4
5
6
50 100 150 200 250 300 350
Temperature, °F
Tem
pera
ture
Cor
rect
ion
Fact
or
400 psig600 psig800 psig1000 psig1200 psig1400 psig1600 psig1800 psig2000 psig2200 psig2400 psig2600 psig2800 psig3000 psig
Evaluation of Pressure Error
• Assume operating pressure and temperature • Use “method” being evaluated to calculate the
pressure at test rack temperature = 60°F • Use NIST Refprop program for nitrogen Z factor to
accurately calculate the resulting pressure at operating temperature
• Determine the pressure error
Method Error
-50
-25
0
25
50
75
100
0 500 1,000 1,500 2,000 2,500 3,000
Dome Pressure at Operating Temperature, psig
Pres
sure
Err
or a
t Ope
ratin
g C
ondi
tions
, psi
100 °F200 °F300 °F400 °FError Bar
Error in TCF Table from 1960 Eqn
±10 psi Error Bars
Nitrogen Z Factor
0.990
0.995
1.000
1.005
1.010
1.015
1.020
1.025
1.030
1.035
0 50 100 150 200 250 300 350 400 450
Temperature, °F
Z Fa
ctor
Nitrogen Z Factor
y = -4.954E-07x2 + 3.102E-04x + 9.769E-01R2 = 9.976E-01
0.990
0.995
1.000
1.005
1.010
1.015
1.020
1.025
1.030
1.035
0 50 100 150 200 250 300 350 400 450
Temperature, °F
Z Fa
ctor
Nitrogen Z Factor
y = -4.954E-07x2 + 3.102E-04x + 9.769E-01R2 = 9.976E-01
0.990
0.995
1.000
1.005
1.010
1.015
1.020
1.025
1.030
1.035
0 50 100 150 200 250 300 350 400 450
Temperature, °F
Z Fa
ctor
Nitrogen Z Factor
y = -4.954E-07x2 + 3.102E-04x + 9.769E-01R2 = 9.976E-01
0.990
0.995
1.000
1.005
1.010
1.015
1.020
1.025
1.030
1.035
0 50 100 150 200 250 300 350 400 450
Temperature, °F
Z Fa
ctor
Let’s Build A Correlation
Actual Value
Updated Nitrogen TCF Table (1989)
1989 Method of Winkler & Eads
For pd60 < 1,238 psia
For 1,238 < pd60< 3,000 psia
)60(60
−+= TMPP ddT
2760
60
1084.1
002298.0267.0
d
d
p
pM−×
++−=
2760
60
10054.3
001934.000226.0
d
d
p
pM−×
++−=
( )[ ] 1
60600.1
−
−+= dt pMTC
Method Error
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 1,000 2,000 3,000 4,000 5,000
Dome Pressure at Operating Temperature, psig
Pres
sure
Err
or a
t Ope
ratin
g C
ondi
tions
, psi
100 °F200 °F300 °F400 °FError Bar
Error in Updated TCF Table (1989)
±10 psi Error Bars
Takacs Nitrogen Z Factor
• Curve fit to Sage and Lacy nitrogen Z factors – 0-3,000 psia and 60-400°F
21 pcpbZ ++=
( ) 522437 10781.410122.510302.110207.1 −−−− −×+×−×= TTTb
( ) 822538 10880.110058.110640.210461.2 −−−− +×−×+×−= TTTc
Stated accuracy is ±0.1% at the indicated pressure and temperature range
Method Error
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 1,000 2,000 3,000 4,000 5,000
Dome Pressure at Operating Temperature, psig
Pres
sure
Err
or a
t Ope
ratin
g C
ondi
tions
, psi
100 °F200 °F300 °F400 °FError Bar
Error in Takacs Method
±10 psi Error Bars
Dranchuk & Abou-Kassem Z Factor
( )( ) ( )
( ) ( ) ( )211
3221110
52879
22876
55
44
3321
exp1
1
rrrr
rrrrrr
rrrrr
ATAA
TATAATATAA
TATATATAAZ
ρρρ
ρρ
ρ
−+
++−++
++++++=
r
rcr TZ
pZ=ρ
Coefficient Natural Gas Nitrogen A1 0.3265 0.414453 A2 -1.0700 -0.885611 A3 -0.5339 -1.372537 A4 0.01569 -1.307205 A5 -0.05165 2.943774 A6 0.5475 0.244662 A7 -0.7361 -0.253387 A8 0.1844 0.281159 A9 0.1056 0.313724 A10 0.6134 0.307269 A11 0.7210 0.135200 Zc 0.27 0.2916
Method Error
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 1,000 2,000 3,000 4,000 5,000
Dome Pressure at Operating Temperature, psig
Pres
sure
Err
or a
t Ope
ratin
g C
ondi
tions
, psi
100 °F200 °F300 °F400 °FError Bar
Error in DAK (Natural Gas Z)
±10 psi Error Bars
Method Error
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 1,000 2,000 3,000 4,000 5,000
Dome Pressure at Operating Temperature, psig
Pres
sure
Err
or a
t Ope
ratin
g C
ondi
tions
, psi
100 °F200 °F300 °F400 °FError Bar
Error in DAK Z (Adapted for Nitrogen)
±10 psi Error Bars
Reference Temperature
• Field testing at temperatures other than 60 °F • Winkler-Eads developed only for 60 °F
– Reference temperature other than 60 °F • Correct operating pressure to pressure at 60 °F • Correct this pressure to new reference temperature
• TCF for temperatures other than 60 °F should be calculated from fundamental relationships – Real gas law – Nitrogen Z routine (Sutton modification of DAK)
• Reference temperature 60-100 °F, the pressure error is < ±10 psi for operating pressure < 9,000 psig at 100-400 °F
Observations & Recommendations
• Reviewed 5 methods to correct Nitrogen charged dome pressures to 60 °F shop temperature
• Errors for all methods acceptable below 1,200 psig operating pressure (OP)
• Winkler-Eads method acceptable below 4,000 psig OP – If tables are used, need several tables to cover pressure range
• Takacs method acceptable below 3,000 psig OP • Methods from Winkler-Eads and Takacs offer no advantage over
original DAK method which is developed to model the Standing-Katz natural gas Z factor chart
• Sutton tuned DAK equation to Nitrogen Z factors offers accuracy to 9,000 psig OP at temperatures (60-400 °F)
Additional References • Dranchuk, P.M. and Abou-Kassem, J.H.: "Calculation
of Z Factors For Natural Gases Using Equations of State," J. Cdn. Pet. Tech. (July-Sept., 1975) 34-36.
• Sutton, R.P.: “Fundamental PVT Calculations for Associated and Gas/Condensate Natural-Gas Systems,” SPE Reservoir Evaluation & Engineering, v. 10, no. 3 (June 2007) 270-284.
• Lemmon, E.W., Huber, M.L., McLinden, M.O. : NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2010.
• http://webbook.nist.gov/chemistry/fluid/
Additional References
• Sage, B.H. and Lacey, W.N.: Thermodynamic Properties of the Lighter Paraffin Hydrocarbons and Nitrogen, Monograph on API Research Project 37, API (1950) 85-114.
• Eilerts, C.K.: Phase Relations of Gas-Condensate Fluids,Vol. II, Monograph 10, Bureau of Mines, American Gas Association (1959) 763-764.
Feb. 6 – 10. 2012 2012 Gas-Lift Workshop 32
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Feb. 6 – 10, 2012 2012 Gas-Lift Workshop 33
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