Assessment of Uncertainty in the Measurement of NG Using Orif

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5004-MI20-OP00-0108

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Bijupirá & Salema Field Development

Document Title:

VOLUME 1 CHAPTER 8 – PROCEDURE FOR ASSESSMENT OF UNCERTAINTY IN NATURAL GAS MEASUREMENT BY ORIFICE PLATE SYSTEMS

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Volume 1 – Facility Management System Structure Chapter 4 – Operations & Maintenance Documentation Document No. 5004-MI20-OP00-0108

AMENDMENT RECORD CHAPTER REVISION INFORMATION Rev.

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Assessment of uncertainty in the measurement of NG using orif

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Volume 1 – Facility Management System Structure Chapter 8– Performance Measurement Documentation Document No. 5004-MI20-OP00-0108

PROCEDURE FOR ASSESSMENT OF UNCERTAINTY IN NATURAL GAS MEASUREMENT BY ORIFICE PLATE SYSTEMS TABLE OF CONTENTS Section

Page

1.0

Introduction ......................................................................................................................2

2.0

Evaluation of uncertainty..................................................................................................4

Appendix A – List of Standard Industry Reference Codes........................................................14 3.0

Acknowledgement Record .............................................................................................15


Page 1


1.0

Introduction 1.1 Purpose This document outlines the procedure to assess the uncertainty in natural gas measurement by orifice plate systems. It is presented the main influence quantities and the way to estimate the standard uncertainty of each variable. The procedure is based on the definitions and guidelines presented in the ISO 5168 Measurement of Fluid Flow – Evaluation of Uncertainty.

1.2 Scope The requirements given in this document apply to the following metering systems installed on board the FPSO Fluminense: TAG

Service

Description

FE-0904-1 FE-0904-2 FE-1010-1 FE-1015-1 FE-1020-1 FE-1125-1 FE-1140B-2 FE-2410-1 FE-2415-1 FE-2525-1

Operational Operational Assignment Assignment Assignment Operational Operational Fiscal Fiscal Assignment

Gas lift flow to Bijupira field Gas lift flow to Salema field Test separator gas outlet flow Bijupira separator gas outlet flow Salema separator gas outlet flow I.P. separator gas outlet flow Electrostatic treater “A” + “B” gas outlet flow Sales gas outlet flow Import gas inlet flow Fuel gas filter outlet flow for users

1.3 References  Petroleum and Natural Gas Measurement Technical Regulation, approved by the Joint Directive ANP/INMETRO Nº 1 of 19.June.2000.  API–MPMS, Chapter 14–Natural Gas Fluids Measurement, Section 3–Concentric, Square-Edged Orifice Meters: Part 1–General Equations and Uncertainty Guidelines, Third Edition, September 1990; Part 2–Specification and Installation Requirements, Third Edition, February 1991; Part 3–Natural Gas Applications, Third Edition, August 1992;


Page 2




  



Part 4–Background, Development, Implementation Procedures and Subroutine Documentation. API–MPMS, Chapter 14–Natural Gas Fluids Measurement, Section 2– Compressibility Factors of Natural Gas and Other Related Hydrocarbon Gases (AGA Report #8, 2nd edition, 1992). API–MPMS, Chapter 14–Natural Gas Fluids Measurement, Section 1–Collecting and Handling of Natural Gas Samples for Custody Transfer. ASTM D 1945-Standard Test Method for Analysis of Natural Gas by Gas Chromatography. ISO 5167 Measurement of Fluid Flow by Means of Pressure Differential Devices Inserted in Circular Cross-section Running Full, Part 1-General Principles and Requirements, Part 2-Orifice Plates. ISO/TR 5168 Measurement of Fluid Flow-Evaluation of Uncertainties.

1.4 Definitions Uncertainty: Parameter, associated with the results of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand. Standard uncertainty u(x): Uncertainty of the result of a measurement expressed as a standard deviation. Combined standard uncertainty u c (y): Standard uncertainty of the result of a measurement when that result is obtained from the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or covariances of these other quantities weighted according to how the measurement result varies with changes in these quantities. Expanded uncertainty U =k u c (y): Quantity defining an interval about the result of a measurement that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand : the fraction may be viewed as the coverage probability or the level of confidence of the interval. Coverage factor k: Numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded uncertainty : k is typically in the range 2 to 3. s( x ) experimental standard deviation of the arithmetic mean x . Type A evaluation of uncertainty: Method of evaluation of uncertainty by the statistical analysis of a series of observations. Type B evaluation of uncertainty: Method of evaluation of uncertainty by means other than the statistical analysis of a series of observations. Sensitivity coefficient c i: Change in the output estimate y produced by a unit change in the input estimate x i . Degrees of freedom ν: The number of independent observations under a given constraint.


Page 3


1.5 Responsibilities The Area Operations Manager is responsible to the VP of Operations for the preparation of O&M documentation in compliance with the procedures contained in this chapter.

2.0

Evaluation of uncertainty 2.1

Mathematical model The mathematical model used to calculate the natural gas volume through an orifice plate is: Volume 

 Qv * dt

or

Volume 

 (Qv * t )

Eq.1

The standard uncertainty in a volume V in a certain period T, in which is included n volume measurements can be approximated by:

u (V ) T 



2

 V   V    u (Qv)     u (t )    Qv   t n

2

Eq.2

As the uncertainty due to time measurement is small compared to flowrate uncertainty, this can be neglected. The uncertainty in the volume measurement is mainly due to changes on the gas flowrate along the operation. Uncertainty in flowrate will vary strongly according to the differential pressure. For low differential pressures, measurement uncertainty of this parameter will imply a high standard uncertainty in the flow measurement. The volumetric flow of the gas is obtained by: Qv  Cd 

where: Qv Cd  Y

1 1  4

 Y  ( / 4)  d 2 

2  P



Eq.3

= volumetric flow rate = orifice plate discharge coefficient = d/D = expansion factor


Page 4


 = Universal constant 3,14159... d = orifice plate bore diameter calculated at flowing temperature (T f ) D = tube diameter calculated at flowing temperature (T f )  = density of the fluid at flowing conditions (P f , T f ) Density is calculated using: 

P  MM Z  R T

Eq.4

As it’s necessary to measure in base condition, it’s used:  P  T   Z  Qb  Qv   o    b    b   Pb   To   Z o 

Eq.5

The final standard uncertainty in flow measurement in base condition is: 2

2

 Qb   Qb   Qb    u (Qv)     u ( Po)     u (To)     Qv Po To      u (Qb)   2 2  Qb   Qb    u ( Zb)     u ( Zo)    Zb Zo    

2

Eq.6

and

u (Qv) 

2

2

2

2

 Qv   Qv   Qv   u (Cd )     u (Y )     u ( D)      Cd Y D      

2

   Qv  Qv   Qv   u ( d )     u (  )     u (p )   d      p 

Eq.7

2

and 2

2

2

             u (To)   u(Z )     u ( MM )     u ( Po)    u( )      To   Z  Po   MM

2.2

2

Eq.8

Sensitivity coefficients Since it was obtained the mathematical model, it’s known the main input quantities for the uncertainty budget. The partial derivatives in this equation are the respective sensitivity coefficients:


Page 5


From Eq.3: Qv Qv Qv Qv Qv Qv Qv Qv Qv 2  4 Qv Qv 2Qv   , , , , ,     4 D 1   4 D Cd Cd Y Y  2  p 2p d 1  d





From Eq.4:    Po Po

,

   Zo Zo

,

   MM MM

Qb Qb  Po Po

,

Qb Qb  To To

,

   To To

From Eq.5: Qb Qb  Qv Qv

2.3

,

,

Qb Qb Qb Qb ,   Zb Zb Zo Zo

Standard uncertainty Different sources of uncertainty contribute to the overall standard uncertainty to each parameter: - calibration, measurement: u(d), u(D), u(Po), u(To) and u(P); - operational variations: u(Po), u(To), u(P), u(Qv),u(Zb),u(Zo),u(),u(MM); - origin equation: u(Zo),u(Zb), u(CD),u(Y). To simplify, the different uncertainty distributions is considered: - as rectangular distribution: calibration - as normal distribution: operational variations 2.3.1 Discharge coefficient – u(C d ) From AGA 3, part 1, General Equations and uncertainty Guidelines: For >0.175

100 x

Ci ( FT )  0.5600  0.2550   1.9316  8 Cd ( FT )

For 0.175

100 x

Ci ( FT )  0.7000  1.0550  8 Cd ( FT )


Page 6


and Cd ( FT ) Cd ( FT )



Cd ( FT ) Ci ( FT )  Ci ( FT ) Cd ( FT )

U (Cd )  Cd 

Cd ( FT ) Ci ( FT )  Ci ( FT ) Cd ( FT )

Therefore, as this equationing is declared as expanded uncertainty: u (Cd )  U (Cd ) / 2

 (Cd) = infinite 2.3.2 Expansion factor – u(Y) From AGA 3, part 1, General Equations and uncertainty Guidelines, is used:  P  U (Y )  4    Pf 

This is declared as expanded uncertainty and the standard uncertainty therefore is: u (Y )  U (Y ) / 2

 (Y) = infinite

2.3.3 Molecular mass – u(MM) The standard uncertainty in molecular mass must use values from variation in composition. As it will be taken 1 sample to composition measurement per month and it’s assumed that variation in composition is low, it can be used: u ( MM )  variation in MM due to composition

2

 (MM) = infinite 2.3.4 Orifice diameter – u(d) The standard uncertainty is obtained from standard deviation in dimensional measurements on the orifice plate. For n measurements:



u (d )  s d

n

 (d) = n-1 Assessment of uncertainty in the measurement of NG using orif

Page 7


2.3.5 Tube diameter – u(D) The standard uncertainty is obtained from standard deviation in dimensional measurements on the orifice plate. For n measurements:

 

u ( D)  s D

n

 (D) = n-1 2.3.6 Absolute pressure – u(Po) The absolute pressure is given by: Absolute pressure  Static pressure  Atmospheric pressure

Consequently the standard uncertainty for absolute pressure is: 2

2

2

  Pabs   Pabs   Pabs u ( Pabs)    u ( Patm)    u ( Pe)    u ( Pe)   var iation  var iation  Patm  calibration  Pe  Pe

or u ( Pabs ) 

2 2 2 u ( Pe) calibratio n  u ( Pe)  var iation  u ( Patm)  var iation

u(Pe) calibration is obtained from error in instrumentation. It’s used a rectangular distribution: u ( Pe) calibration  error ( Pe)

3

 (Pe) cal = 2 ( considering that calibration is up-down-up) u(Pe) variation is obtained from variation during measurements u ( Pe) var iation  variação na pressão estática

2

 (Pe) variation = infinite u(Patm) variation is obtained from variation during measurements. It can be used a barometer and taken notes about variation in pressure atmospheric. u ( Patm)  variation local in atmospheric pressure

2

 (Patm) = infinite


Page 8


2.3.7 Temperature – u(To) The standard uncertainty is obtained from calibration and variations during measurement. u (T )calibration  error(T)

3

 (T) cal = 2 ( considering that calibration is up-down-up) u (T ) var iation  variation in temperature

2

 (T) var = infinite 2.3.8 Compressibility – u(Zo), u(Zb) AGA 8 supplies the expanded uncertainty in the calculation of compressibility factor. The uncertainty is given by the following figure:

Figure 1 – Compressibility factor expanded uncertainty

Compressibility factor has two contributions to the standard uncertainty: u ( Z )calculation  result from figure 1

2

u ( Z ) var iation  variation in compressibility

2

(Z) = infinite ( both calculation as variation)


Page 9


This variation in compressibility must be given by differences obtained due to variations in composition, pressure and temperature. u(Zo) is influenced by composition, pressure and temperature while u(Zb) is influenced only by composition.

2.3.9 Density – u() Density uncertainty is composed by Eq.8 using the parameters required. Its degree of freedom () is calculated using the Welch-SatterthWaite formula. 2.3.10 Volumetric flowrate – u(Qv) Volumetric flowrate uncertainty is composed by Eq. 7. Its degree of freedom (Qv) is calculated using the Welch-SatterthWaite formula.


Page 10


3.0

Uncertainty Budget The uncertainty budget is divided in three parts according to equations 6, 7 and 8. Uncertainty budget for density () Source

Estimate

Degree of freedom

xi

Standard uncertainty u(x i )

Xi Absolute pressure

c i u(x i )

i

Sensitivity coefficient ci

Component participation in combined uncertainty (%)

Pe

u(Pe cal )

(Pe cal )

/Pe

u(Pe cal )/Pe

u c (Po cal )/u c ()

Pe

u(Pe var )

(Pe var )

/Pe

u(Pe var )/Pe

u c (Po var )/u c ()

Patm

u(Patm)

(Patm var )

/Patm

u(Patm var )/Patm

u c (P atm ) /u c ()

Temperature

To

u(To cal )

(To cal )

-/To

u(To var )(-/To)

u c (To cal ) /u c ()

To

u(To cal )

(To cal )

-/To

u(To var )(-/To)

u c (To var ) /u c ()

Molecular Mass

MM

u(MM)

(MM)

/MM

u(MM)(/MM)

u c (MM) /u c ()

Compressibility

Z

u(Z cal )

(Z cal )

-/Zo

u(Z cal )(-/Zo)

u c (Po cal ) /u c ()

Z

u(Z var )

(Z var )

-/Zo

u(Z var ) )(-/Zo)

u c (Po cal ) /u c ()

density



(Po var )

100%

Uncertainty budget for volumetric flowrate Source

Estimate

Degree of freedom

xi


Xi Discharge coefficient

Cd

Expansion Factor Tube diamenter

Orifice diameter

c i u(x i )

i



u(Cd)

(Cd)

Qv/Cd

u(Cd)Qv/Cd

u c (Cd)/u c (Qv)

Y

u(Y)

(Y)

Qv/Y

u(Y)Qv/Y

D

u(D)

(D)

2  Qv 1  4 D 2 Qv 1  4 d

d

(d)

u(d)

u c (Y) /u c (Qv)

4

u(D)

2  Qv 1  4 D

u c (D) /u c (Qv)

u(d)

2 Qv 1  4 d

u c (d) /u c (Qv)

4

density



u()

()

Qv/

u()Qv/

u c ()/u c (Qv)

Differential pressure

P

u(P) cal

(P cal )

Qv/2P

u(P cal )Qv/P

u c (P cal ) /u c (Qv)

P

u(P) var

(P var )

Qv/2P

u(P var )Qv/P

u c (P var ) /u c (Qv)

Volumetric flowrate

Qv


(Qv)

100%

Page 11


Uncertainty budget for volumetric flowrate in base condition Source

Estimate

Degree of freedom

xi


Xi Absolute pressure

c i u(x i )

i



Pe

u(Pe cal )

(Pe cal )

Qb/Pe

u(Pe cal )Qb/Pe

u c (Po cal )/u c (Qb)

Pe

u(Pe var )

(Pe var )

Qb/Pe

u(Pe var )Qb /Pe

u c (Po var ) /u c (Qb)

Patm

u(Patm)

(Patm)

Qb/Patm

u(Patm) Qb /Patm

u c (P atm ) /u c (Qb)

To

u(To cal )

(To cal )

-Qb/To

u(To var )(- Qb /To) u c (To cal ) /u c (Qb)

Temperature

To

u(To cal )

(To cal )

-Qb/To

u(To var )(- Qb /To) u c (To var ) /u c (Qb)

Operational Compressibility

Zo

u(Z cal )

(Z cal )

-Qb/Zo

u(Zo cal )(- Qb /Zo)

Zo

u(Z var )

(Z var )

-Qb/Zo

u(Zo var )(- Qb /Zo) u c (Zo cal ) /u c (Qb)

Base Compressibility

Zb

u(Z cal )

(Z cal )

QbZb

u(Zb cal )(- Qb /Zo)

Zb

u(Z var )

(Z var )

Qb/Zb

u(Zb var )(- Qb /Zo) u c (Zb cal ) /u c (Qb)

Volumetric flow rate

Qv

u(Qv)

(Qv)

Qb/Qv

Base volumetric flow rate

Qb

U(Qv)Qb/Qv

u c (Zo cal ) /u c (Qb) u c (Zb cal ) /u c (Qb) u c (Qv) /u c (Qb)

(Qb)

100%

The degree of freedom is calculated given a parameter y by: y 

u 4 ( y) n

u c i4

i 1

i



Eq.9

4

Combined uncertainty is calculated given a parameter y by: n

u c2 ( y ) 

u

2 c (i )

Eq.10

i 1

4.0

Expanded uncertainty and reported result Using k = Coverage factor of approximately 95%: take (k) the appropriate value for Students t using  V degrees of freedom with approximately 95% of probability. Uncertainty in measurements must be presented as: U ( y)  k  u( y)


Page 12


5.0

Metering System Differences 

Calculation using flow computer

When using flow computer in fiscal measurement, it is supposed: - Gas composition measurement once a month;



Using PLC

Measurement uncertainty of the orifice plate metering system should be evaluated according to the directions contained in the ISO/TR 5168 Measurement of Fluid Flow – Evaluation of Uncertainties. According to the ANP/INMETRO Regulation, uncertainty requirements for natural gas measurements are as follows:   

Fiscal measurement: lower than 1,5% Assignment measurement: lower than 2,0% Operational measurement: lower than 3,0%


Page 13


Appendix A – List of Standard Industry Reference Codes Code

Definition

ABNT

Associação Brasileira de Normas Técnicas

AGA

American Gas Association

ANP

Agência Nacional do Petróleo

API

American Petroleum Institute

ASTM

American Society for Testing and Materials

NBR

National Electrical Code

IEC

International Electro-technical Commission

INMETRO

Instituto Nacional de Metrologia, Normalização e Qualidade Industrial

ISO

International Standardization Organization


Page 14


6.0

Acknowledgement Record With my signature, I do hereby acknowledge that I have read and understood the preceding document and all appendices, if applicable. Signature

Date


Signature

Date

Page 15

Assessment of Uncertainty in the Measurement of NG Using Orif

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