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This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required tobecome an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with theapproval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved.

1

Manual of Petroleum Measurement StandardsChapter 12 Calculation of Petroleum Quantities

Section 2 Calculation of Petroleum Quantities Using Dynamic Measurement

Methods and Volumetric Correction Factors

DRAFT, MARCH 2015

May, 2015

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Forward

This publication consolidates parts 1 through 5 of previous editions of Chapter 12.2 and presents standardcalculations for metering petroleum fluids using flow meters such as turbine or displacement meters. Units of

measure in this publication are in International System (SI) and United States Customary (USC) units consistent withNorth American industry practices.

Nothing contained in any API publication is to be construed as granting any right, by implication or otherwise, for themanufacture, sale, or use of any method, apparatus, or product covered by letters patent. Neither should anythingcontained in the publication be construed as insuring anyone against liability for infringement of letters patent.

This document was produced under API standardization procedures that ensure appropriate notification andparticipation in the developmental process and is designated as an API standard. Questions concerning theinterpretation of the content of this publication or comments and questions concerning the procedures under whichthis publication was developed should be directed in writing to the Director of Standards, American PetroleumInstitute, 1220 L Street, N.W., Washington, D.C. 20005. Requests for permission to reproduce or translate all or anypart of the material published herein should also be addressed to the director.

Generally, API standards are reviewed and revised, reaffirmed, or withdrawn at least every five years. A one-timeextension of up to two years may be added to this review cycle. Status of the publication can be ascertained fromthe API Standards Department, telephone (202) 682-8000. A catalog of API publications and materials is publishedannually by API, 1220 L Street, N.W., Washington, D.C. 20005.

Suggested revisions are invited and should be submitted to the Standards Department, API, 1220 L Street, NW,Washington, D.C. 20005, [email protected].

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Contents

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Introduction

This standard presents the calculation procedures for dynamic measurement tickets (meter tickets), meter proving,and prover calibration.

Earlier versions of this standard were written when mechanical desk calculators and tabulated values were widelyused for calculating measurement documentation. Rules for rounding and the choice of how many figures to enter ineach calculation step were often made on the spot, resulting in different operators obtaining different results from thesame data. Introduction of computers and solid-state scientific desk calculators improved the process, but differentmanufacturers machines often produced slightly different results. To address this problem, the previous version ofthis Standard rigorously specified the equations for computing correction factors, rules for rounding, calculationsequence, and the discrimination levels employed with the purpose of standardizing calculations to produce thesame unbiased answer from given data. With the advent of IEEE standards and the predominance of 64-bit floating-point operations, additional calculation methods were desired by the petroleum industry. The implementationprocedures presented in this standard are designed to use current computer technology, simplify the associatedarithmetic operations, and incorporate current API MPMS Chapter 11 Standards.

This standard was developed to allow multiple parties to obtain the same numerical results from the same

raw/measured data basis using a standardized calculation methodology. This standard does not address the

differences in the raw/measured data due to differences in the precision of the instrumentation. It is expected that

the end user will apply the appropriate rules to determine the level of accuracy in the display of the decimals in the

final answer based upon the accuracy of the devices used in the collection of the original data.

This standard was developed to allow multiple parties to obtain the same numerical results from the same

raw/measured data basis using a standardized calculation methodology. This standard does not address the

differences in the raw/measured data due to differences in the precision of the instrumentation. It is expected that

the end user will apply the appropriate rules to determine the level of accuracy in the display of the decimals in the

final answer based upon the accuracy of the devices used in the collection of the original data.

This standard presents two methods for calculating meter tickets and meter provings:

Method A - Discrete Data Method (Traditional Method)

Method B - Continuous Data Method (Dynamic Method)

In the Discrete Data Method, flow-weighted averages (however each average is determined) of temperature,pressure and density are used to correct the total actual volume at operating conditions for the entire ticket period, asmeasured by the flow meter and corrected by the meter factor, to what that total actual volume would be at standardtemperature and pressure conditions for the entire ticket period. Thus, the total indicated volume for the entire ticketperiod is corrected by the meter factor to determine the total gross volume for the entire ticket period; and, then thetotal gross volume is corrected to the gross standard volume for the entire ticket period.

In the Continuous Data Method, the process variables of density, temperature and pressure are sampled every scancycle and the indicated volume of the meter is determined for each scan cycle as well. In the Continuous DataMethod, flow-weighted averages (however each average is determined) of temperature, pressure and density areused to correct the total actual volume at operating conditions for each scan cycle period, as measured by the flow

meter and corrected by the meter factor, to what that total actual volume would be at standard temperature andpressure conditions for each scan cycle period. Thus, the total indicated volume for any given scan cycle period iscorrected by the meter factor to determine the total gross volume for that scan cycle period; and, then the total grossvolume is corrected to the gross standard volume for that same given scan cycle period. The incremental grossstandard volumes determined for each scan cycle period would be summed on an accumulative basis for the entiremeasurement period to yield the total gross standard volume for the entire batch.

Volumetric calculations and process variable acquisitions in the Continuous Data Method are not continuous, butnear continuous. As scan times in flow computers decrease, the process variable acquisition increases and will becloser to continuous. A hidden assumption in the Continuous Data Method is that the samplings of the process

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variables are the flow-weighted averages during the scan cycle to which they are applied. Strictly speaking, thisassumption is not true. As scan times decrease, these readings approach the true flow-weighted average.

When a ticket has been calculated by a flow computer using the Continuous Data Method, the reported data can beused to make a calculation comparison using the Discrete Data Method. When this is done, the flow-weightedaverage temperature, pressure and gross observed density is used to calculate the flow weighted average basedensity. The discrimination levels of temperature, pressure and density should be the same as those reported on the

Continuous Data Method report for comparison purposes. While these two methods might yield slightly differentresults due to the different rounding routines employed and the manner in which the data is acquired and processed,the difference between the two results should lie within a maximum range of 0.02%.

The following will illustrate the comparison process:

Discrete Data Method A:

Continuous Data Method B:

1

( , ,RHO )n

B i i i i i

i

GSV IV MF CTPL T P

Since:1

n

A i

i

IV MF IV MF

And:

Then:

,1

1

1

1

( , )( , , avg)

% 100

( , , )

i

n

i i ii

n

i

n

in

i

CTPL T P RHOCTPL Tavg Pavg RHO

i

CTPL Ti Pi RHOi

i

Rounding or truncating initial and intermediate values in the Continuous Data Method has been eliminated.

Rounding will only be applied to the measurement ticket reported values; thus, older computer processor technologyor manual calculations may not reproduce the same exact results as modern machines or manual calculations usingthis revised standard. Un-rounded numbers in no way imply measurement accuracies to those levels. Measurementaccuracies are solely dependent upon each measurement device. The intent of this standard is to allow forincreased accuracy and discrimination levels of inputs as they become available. Identical input data should givedifferent users identical results.

Annexes provided in this standard will contain methods for calculation of base prover volumes derived fromcalibration of provers.

( , ,RHO )A AGSV IV MF CTPL Tavg Pavg avg

B AGSV GSV

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The intent of this document is to serve as a rigorous standard. Examples are provided to aid the user in checkingcomputations developed using the requirements of this standard.

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3.4base prover volume (BPV)The volume of the prover at base conditions as shown on the calibration certificate.

3.5calibrated prover volume (CPV)

The volume of the prover at base conditions as determined from one prover calibration run by the waterdraw methodor from one prover calibration run set by the master meter method.

3.6calibration certificate

A report documenting the calibration of a measurement device such as a meter prover, a thermometer or pressuregauge and its traceability to a national metrological institute (e.g., National Institute of Standards and Technology forthe USA).

3.7calibration run set

A series of defined events at a single flow rate that involve proving a master meter with a master prover, making aseries of calibration runs on a field prover with the master meter, and then re-proving the master meter to form a

single Calibrated Prover Volume as one of the three consecutive sets required in the calibration of a meter prover bythe master meter method.

3.8certified temperature or pressure device

A temperature or pressure measurement device documented to have been calibrated over the operating rangeagainst an appropriate standard traceable to primary standards maintained by an internationally recognizedstandards organization such as the National Institute of Standards and Technology.

3.9combined correction factor (CCF)

A factor that combines two or more correction factors (e.g., CTS, CPS, CTL, CPL, and MF )

3.10composite K-factor (CKF)

A K-factor, adjusted at the time of proving, from assumed normal operating meter pressure during the ticket period tobase pressure, when it is desired to not have to calculate the correction for compressibility at the time of themeasurement ticket calculation, and where it is assumed that the pressure, temperature and density are constantduring the ticket period.

3.11composite meter factor (CMF)

A meter factor, adjusted at the time of proving, from assumed normal operating meter pressure during the ticketperiod to base pressure, when it is desired to not have to calculate the correction for compressibility at the time of themeasurement ticket calculation, and where it is assumed that the pressure, temperature and density are constantduring the ticket period.

3.12correction for temperature of steel (CTS)Correction for changes in length, area or volume of a steel prover, tank, tank car or other vessel, due to changes inthe steel temperature between its reference temperature and its operation or calibration temperature.

3.13density weighted average (DWA)The volume weighted average density at the meter for the measurement period.

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3.14gauge pressurePressure measured relative to atmospheric pressure with one atmosphere taken as zero.

3.15gross standard volume (GSV)The gross volume (GV) corrected to base temperature and pressure conditions.

.3.16gross volume (GV)The actual volume of fluids at flowing temperature and pressure.

3.17high vapor pressure liquid

A liquid that at operating conditions has a vapor pressure equal to, or greater than, atmospheric pressure.

3.18indicated standard volume (ISV)The indicated volume corrected to base temperature and pressure.

3.19indicated volume (IV)The transferred quantity, in indicated (uncorrected) volume units, at operating conditions, that occurs betweenopening and closing gauges on a tank, during a meter proving with each run, or that occurs from start to stop of areceipt or delivery being measured by a flow meter.

3.20K-FactorThe number of pulses generated by the meter per gross unit volume.

3.21low vapor pressure liquid

A liquid that at operating conditions has a vapor pressure less than or equal to atmospheric pressure.

3.22master meter

A meter that transfers traceability from a master prover to another flow meter or to a field prover.

3.23master meter factor (MMF)

A factor used to correct the indicated volume (IVmm) of the master meter at operating conditions to the gross volume(GVmm) of the master meter at operating conditions.

3.24master prover (mp)

A displacement or open tank prover which is calibrated by the waterdraw or gravimetric method with volumetric ormass standards traceable to a national metrological institute and which is subsequently used to prove other field

meters or to calibrate another field prover.

3.25measurement ticketThe generalized term used to embrace and supersede expressions of long standing such as run ticket, meterticket, and receipt and delivery ticket that are used to document the measurement of a custody transfer ofhydrocarbon liquid.

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3.26meter accuracy (MA)

A divisor used to correct the indicated volume (IVm) of the meter at operating conditions to the gross volume (GVm)of the meter at operating conditions.

3.27meter factor (MF)

A factor used to correct the indicated volume (IVm) of the meter at operating conditions to the gross volume (GVm) ofthe meter at operating conditions.3.28meter reading (MR)The instantaneous display of the register on a meter head or in a flow computer.

3.29net standard volume (NSV)The gross standard volume (GSV) corrected to exclude non-merchantable components such as sediment and water(S&W).

3.30Newtonian fluid

A fluid, whose viscosity is unaffected by the kind of magnitude of motion or agitation to which it may be subjected, aslong as the temperature remains constant.

3.31NIST traceabilityProperty of a measurement result whereby the result can be traced back to NIST by an unbroken chain ofcalibrations.

3.32nominal K-factor (NKF)The number of pulses generated or electronically manufactured by the meter per indicated unit volume.

3.33

passA single movement of the displacer, in a displacement prover, that activates the start-stop detectors.

3.34pressure weighted average (PWA)The volume weighted average pressure at the meter for the measurement period.

3.35primary standard

A measurement standard whose value is determined by NIST or other National Metrological Institute.

3.36prover calibration certificate

A document package stating the Base Prover Volume (BPV) which includes the physical and run data used to

calculate the base prover volume, and the traceability documentation.

3.37proving report

A document showing all the meter and prover data, together with all the other parameters used to calculate thereported meter factor.

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3.38reference conditionsThe base conditions of temperature and pressure (e.g., 60 degrees F and 0 psig, 60 degrees F and equilibrium vaporpressure, 15 degrees C and 101.325 kPa, or 15 degrees C and equilibrium vapor pressure) to which measuredvolumes are to be corrected.

3.39

reference pressure (Pb)The base conditions of pressure (e.g., 0 psig, 14.696 psia, 101.325 kPa, and equilibrium vapor pressure) to whichmeasured volumes are to be corrected.

3.40reference temperature (Tb)The base conditions of temperature (e.g., 60 degrees F and 15 degrees C) to which measured volumes are to becorrected.

3.41round tripThe combination of a single pass of the displacer in one direction (e.g., forward) followed by a single pass of thedisplacer in the opposite direction (e.g., back) in a bi-directional displacement prover.

3.42runOne pass of the displacer between detectors on a unidirectional prover; one round trip of the displacer betweendetectors on a bi-directional prover; one filling or emptying of an atmospheric tank prover between the upper neckscale level reading and the lower neck scale level reading or zero reference on an open tank prover; or, a single startand stop proving test run with a master meter in series with a line meter.

3.43secondary standard

A measurement standard whose value is traceable to, but one step removed from, the primary standard.

3.44

standard conditionsStandard temperature and pressure in a given geographic region that may or may not be the same as the base orreference temperature and pressure used for custody transfer calculations of liquid hydrocarbons in that region orunder a given contract.

3.45target BPV

A term associated with the calibration of an open tank prover which refers to adjusting the sight glass scale(s) so thatthe target volume as indicated by the scale(s) agrees with the base prover volume as determined by calibration.

3.46temperature weighted average (TWA)The volume weighted average temperature at the meter for the measurement period.

3.47weighted average

An average in which each incremental component of the average is weighted according to its impact upon the whole.

4 Symbols and Abbreviations

For the purposes of this document the following symbols and abbreviations apply. These symbols and abbreviationshave been translated into words to aid in providing clarity and specificity of the mathematical treatments given in thetext; however, the words used are not to be considered to be complete definitions. In many cases the symbols have

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additional letters added at the end to help clarify their meaning and application. Subscripts have been avoided. Theuse of capital and lower case letters is intentional in the manner portrayed.

4.1Units

- SI International System of Units (e.g., bars, kPa, cubic meters, kilograms, C)

- USC U.S. Customary Units (e.g., psi, cubic inches, gallons, barrels, pounds, F)

4.2Pipe Dimensions

- ID Inside diameter of prover pipe

- OD Outside diameter of prover pipe

- WT Wall thickness of prover pipe

4.3Liquid Density

- API API Gravity Scale, expressed in API, that is derived from Relative Density

- APIb API Gravity Base, at base temperature (Tb) and pressure (Pb)

- APIgobs API Gravity Gross Observed, AFTER any necessary corrections to APIobs (e.g., HYC and DMF)have been applied to the observed API gravity (APIobs)

- APIobs API Gravity Observed, at observed temperature (Tobs or Tdm) and pressure (Pobs or Pdm) of the liquid being measured by the density device, BEFORE any necessary corrections (e.g., HYC and DMF) have been applied

- APIalt API Gravity Alternate, is the calculated API Gravity at the primary device (e.g., PD, turbine,Coriolis, USM) at its operating temperature and pressure

- APIwa Flow-weighted Average, of the gross observed API gravity (APIgobs) for the measurement

period of the batch or batch segment at TWAdm and PWAdm

- DEN Density in kilograms of mass per cubic meter (kg/m3) units

- DENb DEN Base, at base temperature (Tb) and pressure (Pb)

- DENgobs DEN Gross Observed, AFTER any necessary corrections (e.g., HYC and DMF) have beenapplied to the observed density (DENobs)

- DENobs DEN Observed, at observed temperature (Tobs or Tdm) and pressure (Pobs or Pdm) of the liquid being measured by the density device, BEFORE any necessary corrections (e.g., HYC and DMF) have been applied

- DENalt DEN Alternate, is the calculated density at the primary device (e.g., PD, turbine, Coriolis,USM) at its operating temperature and pressure

- DENwa Flow-weighted Average, of the gross observed density (DENgobs) for the measurementperiod of the batch or batch segment at TWAdm and PWAdm

- RD Relative Density

- RDb RD Base, at base temperature (Tb) and pressure (Pb)

- RDgobs RD Gross Observed, AFTER any necessary corrections (e.g., HYC and DMF) have beenapplied to the observed relative density (RDobs)

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- RDobs RD Observed, at observed temperature (Tobs or Tdm) and pressure (Pobs or Pdm) of the liquid being measured by the density device, BEFORE any necessary corrections (e.g., HYC and DMF) have been applied

- RDalt RD Alternate, is the calculated relative density at the primary device (e.g., PD, turbine, Coriolis,USM) at its operating temperature and pressure

- RDwa Flow-weighted Average, of the gross observed relative density (RDgobs) for the measurement

period of the batch or batch segment at TWAdm and PWAdm

- RHO Generic expression for density, relative density and API Gravity

- RHOb RHO Base, at base temperature (Tb) and pressure (Pb)

- RHOgobs RHO Gross Observed, AFTER any necessary corrections (e.g., HYC and DMF) have beenapplied to the observed density (RHOobs)

- RHOobs RHO Observed, at observed temperature (Tobs or Tdm) and pressure (Pobs or Pdm) of the liquid being measured by the density device, BEFORE any necessary corrections (e.g., HYC and DMF) have been applied

- RHOalt RHO Alternate, is the calculated density at the primary device (e.g., PD, turbine, Coriolis,USM) at its operating temperature and pressure

- RHOwa Flow-weighted Average, of the gross observed density (RHOgobs) for the measurementperiod of the batch or batch segment at TWAdm and PWAdm

- RHOP Density of the water in the prover during a waterdraw calibration

- RHOM Density of the water in the field standard test measurement during a waterdraw calibration

4.4Temperature

- C Celsius temperature scale

- F Fahrenheit temperature scale

- T Temperature

- Tb Temperature at base conditions

- Td Temperature at the detector mounting shaft on a prover with external detectors

- TdAVG Average Td during proving or calibration

- Tdm Temperature at the density meter

- TdmAVG Average Tdm during proving or calibration

- Tm Temperature at the flow meter

- TmAVG Average Tm during proving or calibration

- Tmm Temperature at the master meter

- TmmAVG Average Tmm during proving or calibration

- Tmp Temperature at the master prover

- TmpAVG Average Tmp during proving or calibration

- Tobs Temperature of the fluid observed at the hydrometer or densitometer

- Tp Temperature at the field prover

- TpAVG Average Tp during proving or calibration

- Tfstm Temperature at the field standard test measure

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- TWA Flow-weighted average temperature during the measurement period of the batch or segment

- TWAdm TWA for the online density meter

- TWAm TWA for the flow meter

4.5Pressure

- Bar Unit of pressure in bars

- Bara Bars in absolute pressure units

- Barg Bars in gauge pressure units

- kPa Unit of pressure in Kilopascals

- kPaa Kilopascals in absolute pressure units

- kPag Kilopascals in gauge pressure units

- P Pressure

- Pa Pressure in absolute pressure units

- Pg Pressure in gauge pressure units

- Pb Pressure at base conditions

- Pba Pb in absolute pressure units

- Pbg Pb in gauge pressure units

- PE Equilibrium vapor pressure in absolute pressure units

- PEb Equilibrium vapor pressure at base temperature in absolute pressure units

- PEdm Equilibrium vapor pressure at the density meter in absolute pressure units

- PEm Equilibrium vapor pressure at the meter in absolute pressure units

- PEmm Equilibrium vapor pressure at the master meter in absolute pressure units

- PEmp Equilibrium vapor pressure at the master prover in absolute pressure units

- PEp Equilibrium vapor pressure at the field prover in absolute pressure units

- PEG Equilibrium vapor pressure in gauge pressure units

- PEGb Equilibrium vapor pressure at base temperature in gauge pressure units

- PEGdm Equilibrium vapor pressure at the density meter or hydrometer in gauge pressure units

- PEGm Equilibrium vapor pressure at the meter in gauge pressure units

- PEGmm Equilibrium vapor pressure at the master meter in gauge pressure units

- PEGmp Equilibrium vapor pressure at the master prover in gauge pressure units

- PEGobs Equilibrium vapor pressure observed at the hydrometer or densitometer

- PEGp Equilibrium vapor pressure at the field prover in gauge pressure units

- Pdm Pressure at the density meter in gauge pressure units

- Pm Pressure at the flow meter in gauge pressure units

- Pmm Pressure at the master meter in gauge pressure units

- Pmp Pressure at the master prover in gauge pressure units

- Pobs Pressure of the fluid observed at the hydrometer or densitometer

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- Pp Pressure at the field prover in gauge pressure units

- Pfstm Pressure at the field standard test measure in gauge pressure units

- PdmAVG Average Pdm during proving or calibration in gauge pressure units

- PmAVG Average Pm during proving or calibration in gauge pressure units

- PmmAVG Average Pmm during proving or calibration in gauge pressure units

- PmpAVG Average Pmp during proving or calibration in gauge pressure units

- PpAVG Average Pp during proving or calibration in gauge pressure units

- psi Units of pressure in pounds per square inch

- psia Pounds per square inch in absolute pressure units

- psig Pounds per square inch in gauge pressure units

- PWA Flow-weighted average pressure during the measurement period of the batch or segment

- PWAdm PWA for the online density meter in gauge pressure units

- PWAm PWA for the flow meter in gauge pressure units

4.6Correction Factors and Coefficients

- CCF Combined correction factor

- CCFcomp Combined correction factor for a measurement ticket using a composite meter factor

- CCFm Combined correction factor for the meter during proving, calibration or a measurement ticket

- CCFmm Combined correction factor for the master meter during proving or calibration

- CCFmp Combined correction factor for the master prover during proving or calibration

- CCFp Combined correction factor for the field prover during proving or calibration

- CCTS Combined correction factor for the effect of temperature on the steel of the prover and test measure

- CKF Composite K-factor

- CMF Composite meter factor

- CPL Correction for the compressibility effect of pressure on a liquid

- CPLnormal CPL for calculating a composite meter factor at the normal operating pressure on a meter

- CPLm CPL for the meter during a meter proving, calibration or measurement ticket

- CPLmm CPL for the master meter during proving or calibration

- CPLmp CPL for the master prover during proving or calibration

- CPLp CPL for the field prover during a meter proving or calibration

- CPLfstm CPL for the field standard test measure

- CPLwa CPL for the flow meter during the measurement period of the batch or segment

- CPS Correction for the effect of pressure on the steel

- CPSmp CPS for the master prover

- CPSp CPS for the field prover

- CSW Correction for suspended sediment and water

- CTL Correction for the effect of temperature on a liquid

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- CTDW Correction for the effect of temperature differences in the water

- CTLm CTL for the meter during a meter provng, calibration or measurement ticket

- CTLmm CTL for the master meter during a meter proving or calibration

- CTLmp CTL for the master prover during a meter proving or calibration

- CTLp CTL for the field prover during a meter proving or calibration

- CTLwa CTL for the flow meter during the measurement period of the batch or segment

- CTS Correction for the effect of temperature on the steel

- CTSfstm Correction for the volumetric effect of temperature on the steel of the field standard test measure

- CTSmp Correction for the volumetric effect of temperature on the steel of the master prover

- CTSp Correction for the volumetric effect of temperature on the steel of the field prover

- CTSA CTS for thermal area expansion of steel

- CTSAmp CTSA for the master prover with external detectors

- CTSAp CTSA for the field prover with external detectors

- CTSC CTS for thermal cubic expansion of steel- CTSCmp CTSC for the master prover with a free displacer or the master tank prover

- CTSCp CTSC for the field prover with a free displacer or the field tank prover

- CTSfstm CTSC for the field standard test measure

- CTSCD CTSC for the prover with external detectors

- CTSCDmp CTSCD for the master prover with external detectors

- CTSCDp CTSCD for the field prover with external detectors

- CTSL CTS for thermal linear expansion of steel

- CTSLmp CTSL for the master prover with a free displacer

- CTSLp CTSL for the field prover with a free displacer

- CTSLfstm CTSL for the field standard test measure

- CTSLD CTSL for the detector rod on a prover with external detectors

- CTSLDmp CTSLD for the master prover with external detectors

- CTSLDp CTSLD for the field prover with external detectors

- DMF Density meter factor (synonym for DCF)

- DCF Density Correction Factor (synonym for DMF)

- E Modulus of elasticity of the steel

- Emp Modulus of elasticity of the steel of a master prover

- Ep Modulus of elasticity of the steel of a field prover

- F Compressibility factor of a liquid

- Fm F factor at the meter

- Fmm F factor at the master meter

- Fmp F factor at the master prover

- Fn F factor for normal operating conditions

- Fp F factor at the prover

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- Fs Scaled compressibility factor of a liquid as calculated in Chapter 11.1

- GA Mean coefficient of thermal area expansion

- GAmp GA for the master prover with external detectors

- GAp GA for the field prover with external detectors

- GC Mean coefficient of thermal cubic expansion

- GCmp GC for the master prover with a free displacer or the master tank prover

- GCp GC for the field prover with a free displacer or the field tank prover

- GCfstm GC for the field standard test measure

- GL Mean coefficient of thermal linear expansion

- GLmp GL for the master prover barrel

- GLp GL for the field prover barrel

- GLfstm GL for the field standard test measure

- GLD GL for the detector mounting shaft on a prover with external detectors

- GLDmp GLD for the master prover with external detectors- GLDp GLD for the field prover with external detectors

- HYC Hydrometer Correction Factor (reference API Chapter 9 for details)

- IKF Intermediate K-factor

- IMF Intermediate meter factor

- IMMF Intermediate master meter factor

- KF K-Factor

- MA Meter accuracy factor

- MF Meter Factor

- MMF Master meter factor

- MMFstart MMF at the start of each master meter calibration run

- MMFstop MMF at the stop of each master meter calibration run

- MMFavg Average MMF

- NKF Nominal K-Factor for the meter during a measurement period

- NKFm Nominal K-Factor for the meter during a meter proving

- NKFmm Nominal K-Factor for the master meter during a meter proving

4.7Volumes

- BMV Base test measure volume

- BMVa Base test measure volume adjusted for scale reading

- BPV Base prover volume

- BPVa Base tank prover volume adjusted for upper and lower scale readings

- BPVamp BPVa of the tank master prover

- BPVmp BPV of the master prover

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- CPV Calibrated prover volume

- GSV Gross standard volume

- GSVm GSV of the meter during a measurement ticket

- GSVmm GSV of the master meter during a meter proving or calibration

- GSVmp GSV of the master prover during a meter proving or calibration

- GSVp GSV of the field prover during a meter proving or calibration

- GV Gross volume

- IV Indicated volume

- IVm IV for the meter during a meter proving, calibration or measurement ticket

- IVmm IV for the master meter during a meter proving or calibration

- ISV Indicated standard volume

- ISVm ISV for the meter during a meter proving or measurement ticket

- ISVmm ISV for the master meter during a meter proving or calibration

- MMRc Closing master meter reading- MMRo Opening master meter reading

- MPc Closing meter pulse count

- MPo Opening meter pulse count

- MRc Closing meter reading

- MRo Opening meter reading

- N Number of whole pulses for a single proving run

- Nb N pulses corrected to base conditions

- Ni Number of interpolated pulses for a single proving run

- Nib Ni Pulses corrected to base conditions

- N(avg) Average number of whole pulses

- Ni(avg) Average number of interpolated pulses

- Nb Number of whole or interpolated pulses under base or standard conditions

- NSV Net standard volume

- Q Gross volume per unit pulse

- %S&W Volume percent of suspended sediment and water

- SR Scale reading of test measure

- SRL Lower scale reading of atmospheric tank prover

- SRU Upper scale reading of atmospheric tank prover

- SWV Sediment and water volume

- V Volume

- Vb Volume of container at base conditions

- Vtp Volume of container at operating temperature and pressure conditions

- WD Waterdraw test measure volume adjusted for scale reading and corrected for base temperature

- WDz Sum of all WD values for a single pass

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- WDzb Sum of all WDz values corrected to base pressure

5 Field of Application

5.1 Applicable Fluids

This standard applies to fluids that, for all practical purposes, are considered to be Newtonian, single-phase, andhomogeneous at metering conditions. Most fluids and dense phase fluids associated with the petroleum andpetrochemical industries are considered to be Newtonian.

The application of this standard is limited to fluids that utilize appropriate density and volume correlations. If multipleparties are involved in the measurement, the method for determining the densities of the liquid shall be mutuallyagreed upon by all concerned.

It is the intent of this standard that measurement tickets and meter provings utilize the physical property standardsfrom API, ASTM, and GPA as appropriate to the fluids being measured.

5.2 Base Conditions

Historically, the measurement of all petroleum fluids, for both custody transfer and process control is stated in volumeunits at base (or reference or standard) conditions. The base conditions for the measurement of fluids, such ascrude petroleum and its liquid products, having a vapor pressure equal to or less than atmospheric at basetemperature are as follows:

International System (SI) Units:

Pressure: 101.325 kPa (14.696 psia)

Temperature: 15.00C (59.00F)

United States Customary (USC) Units:

Pressure: 14.696 psia (101.325 kPaa)

Temperature: 60.0F (15.56C)

For hydrocarbon fluids having a vapor pressure that is greater than atmospheric pressure at base temperature, thebase pressure shall be the equilibrium vapor pressure at base temperature.

For liquid applications, base conditions may change from one country to the next due to governmental regulations orto different national standards requirements. Therefore, it is necessary that the base conditions shall be identifiedand specified for standardized volumetric flow measurement by all parties involved in the measurement.

6 Uncertainty

6.1 General

A custody transfer facility should be considered from a comprehensive perspective. It shall be designed, built,operated, and maintained properly to meet a predefined uncertainty. Uncertainties are a combination ofmeasurement, calculating and reporting errors.

All measurement facilities have one or both of two types of errors: bias or systematic type errors, which are fixed orpredictable offsets of the average of many readings from the true value; and random type errors, which are readingsrandomly scattered about the true value of the bias offset.

The uncertainty of metered quantities results from a combination of the following:

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a. the traceability chain associated with the field standards.

b. the calculation procedures and means of computation, including chart integrators, flow computers,mainframes, and personal computers.

c. the uncertainty associated with the liquid density predictions.

d. the sensitivity of the liquid temperature and pressure correction factors to errors in pressure, temperature and

base density determinations.e. the design, installation, and operation of the metering facility.

f. the choice of measurement equipment, including charts, transmitters, A/D converters, and data loggers.

g. the methods of calibration, calibration procedures, and types of calibration equipment.

h. the data transmission means, including analog, pneumatic, digital and manual types.

i. the operating and calibration equipment effects due to such influences as ambient temperature, liquidtemperature, liquid pressure, response time, local gravitational forces, and atmospheric pressure.

j. human factors.

6.2 Hierarchy of Accuracies (Traceability)

There is a hierarchy of accuracies in petroleum measurement, often referred to as a traceability chain, comprising ofboth bias or systematic components, and random uncertainty components.

The concept of traceability describes how an instrument can be related to a national standard by calibrating it againstanother device that is closer to the national standard in the traceability chain. For example, the waterdraw methodfor calibrating provers consists of displacing the contents between detectors into a series of calibrated volumetric fieldstandard test measures, which have in turn been calibrated against a national primary standard by the nationalweights and measures authority. The primary standard itself might be a volumetric type, a mass type or acombination thereof. The traceability chain can be represented as:

National standardvolumetric field test measuresbase prover volumemeter

A meter will be three levels removed from the primary national standard, each successive level having a greateruncertainty than the previous. This is because the uncertainty (systematic and random) of higher standards is partof the uncertainty of lower standards. To expect equal or lower uncertainty in a lower level of the traceability chainthan that which exists in a higher level is mathematically impossible, given the bias uncertainty componentassociated with the respective level in the chain. Taking a large number of determinations with high precisiondevices and then finding their mean value minimizes random uncertainty.

In summary, the simplified traceability chain associated with a base prover volume contains both bias and randomcomponents. The random component can be reduced during calibration by a large number of repeatedmeasurements, but no amount of repeated measurement can reduce the bias component, which provides a fixedsystematic contribution to the uncertainty of subsequent measurements.

7 Precision, Rounding and Averaging

Outline of Calculations

This procedure gives instructions and increments for rounding density, temperature, pressure, thermal expansioncoefficient, and volume correction factor values. These rounding rules are needed to generate the final volumecorrection factor due to temperature and pressure and to generate the tables in printed tabular format. All inputvalues shall be rounded when generating the tables in format.

Calculation Procedure

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Step 1: The following table shows acceptable units for the input and calculated variables and the increment to whichthey should be rounded.

Variable Type Units Rounding Increment ()

Density API 0.1

Relative

Density

0.0001

kg/m3 0.1

Temperature F 0.1

C 0.05

Pressure psig 1

kPa (gauge) 5

bar (gauge) 0.05

Thermal Expansion Coefficient (60) F-1

0.0000001

(0.110-6)

C-1

0.0000002(0.210-6)

CTL 0.00001

Scaled Compressibility Factor ( FP ) psi-1

0.001

kPa-1

0.0001

bar-1

0.01

CPL 0.00001

CTPL 0.00001

Step 2: Normalize the input variable.

Where X is the value to be rounded, X is its absolute value, is the rounding increment, and Y is the

normalized variable.

Step 3: Find the integer closest to the normalized variable. If the decimal portion of Y is not exactly equal to 0.5 thenuse the following equation for rounding:

trunc 0 .5I Y

where tr u n c is the truncation function and I is the rounded value for the normalized variable. However, ifthe decimal portion of is exactly equal to 0.5 then use the following equation for rounding:

trunc 1 if trunc is odd

trunc if trunc is even

Y YI

Y Y

.

Step 4: Rescale the integer from Step 3:

roundX I

XY

Y

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where Xround is the rounded variable. The sign of the rounded value is chosen to match that of the original

value.

Step 5: Exit from this procedure.

Examples

A temperature of 5.34C is rounded to the nearest 0.05 C as:5.34

106.80.05

Y

t ru nc 1 06 .8 0 .5 t ru nc 1 07 .3 1 07I

0.05 107 5 .35roundX

A temperature of -5.34C is rounded to the nearest 0.05 C as:

5.34106.8

0.05Y

t ru nc 1 06 .8 0 .5 t ru nc 1 07 .3 1 07I

0.05 107 5 .35roundX

A temperature of 10.05F should be rounded to the nearest 0.1 F as follows:10.05

100.50.1

Y

t runc 100.5 100I (rounding towards the even integer)

0.1 100 10.0roundX

7.1 Rounding for Discrete Data Method A

7.1.1 Precision (Method A)

The minimum precision of the computing hardware shall be equal to or greater than a ten-digit calculator to obtain thesame answer in all calculations. The general rounding rules and discrimination levels are described in the following

subsections.

7.1.2 Rounding (Method A)

Specific rules apply, for when and where to round, when rounding is to be performed using Method A. Allcalculations are to be rounded in strict accordance with the exact discrimination levels for Method A in Section 7.4 ofthis document. In keeping with the hierarchy of accuracies, these levels may vary with the different applications ofmeasurement tickets, meter provings, and prover calibrations.

There are combinations of factors that are derived by chain multiplication to produce a combined correction factor.When chain multiplying is allowed for this purpose, the combined correction factor is also rounded in accordance withthe exact discrimination levels for Method A in Section 7.4 of this document.

General procedures for rounding in accordance with Method A:

a) Convert the raw number to be rounded to an absolute number (i.e., change a negative sign to positive)

b) Determine the incremental rounding value (e.g., 0.01, 0.10, 0.25)

c) Divide the raw number to be rounded by the incremental rounding value for the quotient

d) If the decimal portion is less than 0.50000 the value of the quotient integer remains unchanged

e) If the decimal portion is greater than 0.50000 the value of the quotient integer is incremented by one

f) If the decimal portion is equal to 0.50000 the value of the quotient integer is incremented by one

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g) Multiply the new integer value by the incremental rounding value

h) Assign a value of -1 to s if the original raw number < 0 or assign a value of +1 to s if the original rawnumber < 0.

Formula when value at the retention point remains unchanged:

0aINTEGER b s Final Rounded Value FRVb

(1)

Formula when value at the retention point is to be incremented by one:

1a

INTEGER b s Final Rounded Value FRVb

(2)

Where:

a = raw number to be rounded expressed as an absolute number

b = the incremental rounding value (e.g., 0.01, 0.10, 0.25)

s = value used to restore the sign of the FRV to that of the original raw number

Examples of Rounding (Method A):

Example for rounding 10.62499 to the nearest incremental rounding value of 0.25: Divide 10.62499 by 0.25 to obtain42.49996. Since the decimal portion is less than 0.50000 the integer portion will remain unchanged at 42. Multiply42 by 0.25 to obtain the final rounded value of 10.50.

Example for rounding 10.62501 to the nearest incremental rounding value of 0.25: Divide 10.62501 by 0.25 to obtain42.50004. Since the decimal portion is greater than 0.50000 the integer portion will be incremented by one tobecome 43. Multiply 43 by 0.25 to obtain the final rounded value of 10.75.

Example for rounding 10.62500 to the nearest incremental rounding value of 0.25: Divide 10.62500 by 0.25 to obtain42.50000. Since the decimal portion is equal to 0.50000 the integer portion will be incremented by one to become43. Multiply 43 by 0.25 to obtain the final rounded value of 10.75. See Method B for a variation in this scenario.

Illustration 1 Examples of Rounding (Method A)

(a)

(b)

Quotient

Integer

Decimal

Odd

or

Even

New

Integer

FRV

10.12499 0.25 40.49996 40 0.49996 N/A 41 10.25

10.37499

0.25

41.49996

41

0.49996

N/A 42 10.50

10.62499

0.25

42.49996

42

0.49996

N/A

43

10.75

10.87499 0.25 43.49996 43 0.49996 N/A 44 11.00

7.1.3 Field Data (Method A)

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All required field data shall be recorded and rounded in accordance with the exact discrimination levels for Method Ain Section 8 of this document. In keeping with the hierarchy of accuracies, these levels may vary with the differentapplications of measurement tickets, meter proving reports, and prover calibration reports.

Discrimination levels greater than those specified shall not be used for discrete data method. In most cases thenumber of decimal places is influenced by the source of the data itself. For example, if the parties agree to use athermometer graduated in 0.2 F increments, then the device is normally read to levels of 0.1 F. Another example

would be, if the parties agree to use a thermometer graduated in 0.1 C increments, then the device is normally readto levels of 0.05 C. If the parties agree to use a smart temperature transmitter, which can indicate to 0.01F or0.005C, the readings shall be rounded to the nearest 0.1F or 0.05C as indicated in Table 3 prior to recording forcalculation purposes.

7.2 Rounding for Continuous Data Method B

7.2.1 Precision (Method B)

The minimum precision of the computing hardware shall be equal to or greater than 64-bit floating point IEEEoperations to obtain the same answer in all calculations. The general rounding rules and discrimination levels aredescribed in the following subsections.

7.2.2 Rounding (Method B)

Specific rules apply for when and where to round. When rounding is performed, it shall be done in strict accordancewith the discrimination levels for Method B in Section 8 of this document. In keeping with the hierarchy of accuracies,these levels may vary with the different applications of measurement tickets, meter provings, and prover calibrations.There may be occasions, such as measurement reports, displays, data logs and communications, where rounding ortruncating is performed at the end of a multiplication chain in order to meet a special need.

General procedures for rounding in accordance with Method B:

a) Convert the raw number to be rounded to an absolute number (i.e., change a negative sign to positive)

b) Determine the incremental rounding value (e.g., 0.01, 0.10, 0.25)

c) Divide the raw number to be rounded by the incremental rounding value for the quotient

d) If the decimal portion is less than 0.50000 the value of the quotient integer remains unchanged

e) If the decimal portion is greater than 0.50000 the value of the quotient integer is incremented by one

f) If the decimal portion is equal to 0.50000 determine whether the quotient integer is odd or even

a. If the quotient integer is odd increment the quotient integer by one

b. If the quotient integer is even the quotient remains unchanged

g) Multiply the new integer value by the incremental rounding value

i) Assign a value of -1 to s if the original raw number < 0 or assign a value of +1 to s if the original raw number

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