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

Anyone got an App?

N2 TCF

Sources for Nitrogen TCF

Early Sources (1950-60’s) for Nitrogen TCF Multi-Core Processors Limited Apps Available

Problems with 4G Network

Dual-Core Processors

1950 Sage & Lacey Nitrogen Z Factor

Nitrogen TCF Chart from Winkler

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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