Chapter 12 2 Pt 1 Final Manual of Petroleum Measurement Standards Chapter 12—Calculation of Petroleum Quantities Section 2—Calculation of Petroleum Quantities Using Dynamic Measurement Methods and Vol[.]
Purpose
In the past, mechanical desk calculators were commonly used for measurement documentation, leading to a reliance on tabulated values Rounding rules and the number of figures entered in calculations were often determined spontaneously, resulting in varying outcomes from the same data by different operators.
This five-part publication standardizes calculations for metering petroleum liquids with turbine or displacement meters, ensuring clarity by eliminating regional variations in terminology.
Standardizing calculations ensures that the same unbiased results are achieved from the same data, allowing different operators to obtain identical outcomes This process involves adhering to specific rules regarding sequence, rounding, and figure discrimination.
(or decimal places) have been defined.
Scope
This document outlines standardized methods for calculating liquid quantities and determining base prover volumes under specific conditions, applicable regardless of origin, destination, or measurement units mandated by governmental regulations The criteria established herein enable diverse entities to utilize various programming languages across different hardware platforms.
(or manual calculations) to arrive at identical results using the same standardized input data.
The publication clearly outlines the equations for determining correction factors, rounding rules, calculation sequences, and discrimination levels to be used in the computations Adherence to these specifications is mandatory, as the document aims to establish a strict standard.
Organization of Standard
Part 1—Introduction
This article discusses the standard volumetric determination of metered quantities, outlining essential terms for solving various equations It specifies general rules for rounding numbers, including field data, intermediate calculations, and discrimination levels Additionally, it provides guidance on predicting the liquid's density under flowing and base conditions for proper application of the standard.
An explanation of the principal correction factors associ- ated with dynamic measurement are presented in a clear,concise manner.
Part 2—Measurement Tickets
This standard outlines the calculation of metered quantities for base volumetric calculations in line with North American industry practices It specifies the recording of field data, rounding rules, calculation sequences, and discrimination levels, accompanied by example calculations These examples serve to assist in the verification of any routines developed according to the stated requirements.
Part 3—Proving Reports
This standard is applied to the calculation of proving reports for base volumetric calculations in line with North American industry practices Proving reports are essential for calculating meter correction and performance indicators, including meter factors (MF), composite meter factors (CMF), K-factors (KF), composite K-factors (CKF), and meter accuracy factors (MA) The selection of the appropriate term depends on the hardware used and the user's preferences.
The article outlines the procedures for recording field data, including rules for rounding, calculation sequences, and discrimination levels It also provides example calculations to assist with checkout procedures for routines developed according to these specified requirements.
Part 4—Calculation of Base Prover Volumes by Waterdraw Method
The BPV may be determined by one of two methods— waterdraw or master meter The waterdraw method involves
Chapter 12—Calculation of Petroleum Quantities
Section 2—Calculation of Petroleum Quantities Using Dynamic Measurement
Methods and Volumetric Correction Factors
In Chapter 12, the calculation of petroleum quantities involves the displacing of water from certified volumetric field measures into provers For open tank provers, the waterdraw method may also involve displacing water from certified volumetric test measures into the prover It is essential that the certification of these field measures is traceable to the relevant national weights and measures organization, such as the National Institute of Standards and Technology.
The article outlines the procedures for recording field data, including rules for rounding, calculation sequences, and discrimination levels It also provides example calculations to assist with checkout procedures for routines developed according to these specified requirements.
Part 5—Calculation of Base Prover Volumes by Master Meter Method
PROVER VOLUMES BY MASTER METER METHOD
The BPV can be measured using two methods: the waterdraw method or the master meter method The master meter method utilizes a master meter, which is verified under real operating conditions by a master prover calibrated using the waterdraw method In this setup, the master prover, master meter, and field prover are connected in series, enabling fluid to flow through all three devices at the same time.
The article outlines the procedures for recording field data, including rules for rounding, calculation sequences, and discrimination levels It also provides example calculations to assist with checkout procedures for routines developed according to these specified requirements.
Field of Application
Applicable Liquids
This standard pertains to liquids that are effectively clean, single-phase, homogeneous, and Newtonian under metering conditions Typically, most liquids and dense phase liquids in the petroleum and petrochemical sectors are regarded as Newtonian.
This standard applies exclusively to liquids that require tables or procedures to adjust metered volumes at varying temperatures and pressures to standard conditions To achieve this, the density of the liquid must be established using recognized technical standards or, if needed, suitable correlations or equations of state In cases where multiple parties are involved in the measurement process, the method for determining the liquid's density must be agreed upon by all parties.
Base Conditions
Historically, the measurement of some liquids for custody transfer and process control have been stated in volume units at base (reference or standard) conditions.
The fundamental criteria for measuring liquids, including crude oil and its derivatives, require that their vapor pressure is equal to or lower than atmospheric pressure at the specified base temperature.
United States Customary (USC) Units:
At a pressure of 14.696 psia (101.325 kPa a) and a temperature of 59.00˚F (15.00˚C), liquids like liquid hydrocarbons exhibit a vapor pressure that exceeds atmospheric pressure at the base temperature Therefore, the base pressure is defined as the equilibrium vapor pressure at this base temperature.
Base conditions for liquid applications can vary between countries due to differing governmental regulations It is essential for all parties involved in volumetric flow measurement to identify and specify these base conditions to ensure standardization.
1 American Society for Testing and Materials, 1916 Race Street, Philadel- phia, Pennsylvania 19103
2 U.S Department of Commerce, National Institute of Standards and Tech- nology, Washington, D.C 20234 (formerly National Bureau of Standards)
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Uncertainty
General
When utilizing this standard, it is essential for the user to adopt a comprehensive perspective on the custody transfer facility Clearly defining the desired level of uncertainty to the designer is crucial for the effective construction, operation, and maintenance of the facility.
At a single metering facility, two types of uncertainty can affect measurements: bias error, which occurs when the average of multiple readings deviates from the true value, and random error, characterized by the random scattering of readings around this offset.
The uncertainty of the metered quantities depends on a combination of the following: a The traceability chain associated with the field standards. b The calculation procedure and means of computation
The accuracy of liquid density predictions is influenced by various factors, including the sensitivity of prediction correlations to errors in pressure, temperature, and base density determinations Additionally, the design, installation, and operation of the metering facility play a crucial role, as does the selection of measurement equipment such as charts, transmitters, A/D converters, and data loggers Effective data transmission methods—whether analog, pneumatic, digital, or manual—are also essential Furthermore, the performance of operating and calibration equipment can be affected by ambient temperature, liquid temperature, liquid pressure, response time, local gravitational forces, and atmospheric pressure.
Uncertainty arises from various factors, including the performance of hardware and software, the calculation methods employed, the calibration equipment used, the procedures followed for calibration, and the influence of human factors.
Hierarchy of Accuracies
In petroleum measurement, there exists a natural hierarchy of accuracies, commonly known as a traceability chain This hierarchy includes both bias and random uncertainty components, highlighting the inherent complexities in achieving precise measurements.
Traceability refers to the process of linking an instrument to a national standard through calibration against a device that is closer to that standard For instance, the waterdraw method for calibrating provers involves transferring contents between detectors into a certified volumetric field standard test measure, which has been calibrated through repeated fillings from a secondary standard laboratory measure This laboratory measure is maintained and calibrated by the national weights and measures authority, which is ultimately linked to the country's national primary volumetric and/or mass standard.
It is physically impossible to expect equal or lower uncertainty at a lower level of the traceability chain compared to a higher level due to the inherent bias uncertainty associated with each level To minimize random uncertainty, it is essential to conduct a large number of measurements using high-precision instruments and calculate their mean value.
The traceability chain linked to a BPV includes both bias and random components While the random component can be minimized through extensive calibration involving repeated measurements, the bias component remains unchanged, representing a consistent systematic contribution to the uncertainty in future measurements.
Precision, Rounding, and Discrimination Levels
Rounding of Numbers
When rounding a number to a specific number of decimal places, it should be done in a single step rather than through multiple successive rounds The rounding rules are as follows: if the digit immediately to the right of the last retained decimal is 5 or greater, the last retained digit is increased by 1 Conversely, if this digit is less than 5, the last retained digit remains unchanged.
Discrimination Levels
For field measurements of temperature and pressure, the levels specified in the various tables are maximum discrim- ination levels
When parties agree to use a thermometer with whole ˚F increments, readings are typically taken with a resolution of 0.5˚F In contrast, if a "smart" temperature transmitter is utilized, capable of indicating to 0.01˚F or 0.005˚C, the readings must be rounded to the nearest 0.1˚F or 0.05˚C before being recorded for calculations.
4 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
Definitions, Symbols, and Abbreviations
Definitions
1.8.1.1 barrel (bbl): a unit volume equal to 9,702.0 cubic inches, or 42.0 U.S gallons.
1.8.1.2 base prover volume (BPV): the volume of the prover at base conditions as shown on the calibration certifi- cate and obtained by arithmetically averaging three consec- utive successful CPV determinations.
1.8.1.3 calibrated prover volume (CPV): the volume at base conditions between the detectors in a pipe prover or the volume of a proving tank between specified “empty” and
“full” levels The calibrated volume of a bidirectional prover is the sum of the two volumes swept out between detectors during a roundtrip.
1.8.1.4 composite meter factor (CMF): a meter factor corrected from normal operating pressure to base pressure A
CMF may be used for meter applications where the relative density, temperature, and pressure are considered constant during the measurement ticket period.
1.8.1.5 cubic meter (M 3 ): a unit of volume equal to
1.8.1.6 gross standard volume (GSV): the volume at base conditions corrected also for the meter’s performance
1.8.1.7 indicated standard volume (ISV): the IV corrected to base conditions It does not contain any correc- tion for the meter’s performance (MF, MMF, or CMF).
1.8.1.8 indicated volume (IV): the change in meter reading that occurs during a receipt or delivery The word registration, though not preferred, often has the same meaning.
1.8.1.9 liter (l): a unit of volume equal to 1,000.0 milliliters (ml).
1.8.1.10 master meter: a meter proved using a certified prover and then utilized to calibrate other provers or prove other meters.
1.8.1.11 master meter factor (MMF): a dimensionless term obtained by dividing the gross standard volume of the liquid passed through the master prover (during the proving of the master meter) by the indicated standard volume
(ISV m ) as registered by the master meter during proving.
1.8.1.12 master prover:refers to a volumetric standard
(conventional pipe prover, SVP, or open tank prover), which was calibrated by the waterdraw method, and is used to cali- brate a master meter.
1.8.1.13 measurement ticket: the generalized term used in this publication to embrace and supersede long- standing expressions such as “run ticket,” “meter ticket,” and
1.8.1.14 meter factor (MF): a dimensionless term obtained by dividing the volume of the liquid passed through the prover corrected to standard conditions during proving by the indicated standard volume (ISV m ) as registered by the meter.
1.8.1.15 meter reading (MR o , MR c , MMR o , MMR c ): the instantaneous display on a meter head When the differ- ence between a closing and an opening reading is being discussed, such a difference should be called an IV.
1.8.1.16 net standard volume (NSV): the gross stan- dard volume corrected for nonmerchantable quantities such as sediment and water (CSW).
1.8.1.17 pass:a single movement of the displacer in a prover that activates the start-stop detectors.
1.8.1.18 prover calibration certificate: a document stating the BPV and other physical data required when proving flowmeters (E, Gc, Ga, Gl) The calibration certificate is a written acknowledgment of a proper calibration of a prover between the authorized representatives of the interested parties.
1.8.1.19 proving report: an organized collection of all information (meter, prover, and other), used during meter proving, meter performance verification, and meter factor determination.
1.8.1.20 round trip: the forward (out) and reverse (back) consecutive passes in a bidirectional prover.
1.8.1.21 run, meter proving: one or more consecutive passes, the results of which, when totalized, are deemed sufficient to provide a single value of the meter factor (MF, CMF, MMF) or K-factor (KF, CKF).
1.8.1.22 run, prover calibration: one or more consec- utive passes, the results of which, when totalized, are deemed sufficient to provide a single value of the calibrated prover volume (CPV).
1.8.1.23 U.S gallon (gal): a unit volume equal to 231.0 cubic inches
1.8.1.24 weighted average pressure (PWA): the average liquid pressure at the meter for the ticket period For volumetric methods, the weighted average pressure is the average of the pressure values sampled at uniform flow intervals and is representative of the entire measurement ticket period
Where: n = the number of uniform intervals
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In time-based methods, the weighted average pressure is calculated by summing the pressure values sampled over a specific time interval, multiplying this sum by the corresponding volume or mass for that interval, and then dividing by the total volume measured.
PWA = [SUM (Pi× Vi)]/Vt
1.8.1.25 weighted average temperature (TWA):the average liquid temperature at the meter for the ticket period
For volumetric based methods, the weighted average temperature is the average of the temperature values sampled at uniform flow intervals during the entire measurement ticket period
Where: n = the number of uniform intervals
In time-based methods, the weighted average temperature is calculated by summing the temperature values sampled over a specific time interval, multiplying this sum by the corresponding volume or mass, and then dividing by the total volume measured.
TWA = [SUM (Ti× Vi)]/Vt
Symbols and Abbreviations
While a combination of uppercase, lowercase, and subscripted notation is used in this publication, the uppercase notation may be used for computer programming and other documents as deemed appropriate.
Additional letters may be added to the symbolic notations below for clarity and specificity
SI International system of units (pascal, cubic meter, kilogram, metric system).
USC U.S customary units (inch, pound, cubic inch, traditional system).
ID Inside diameter of prover pipe.
OD Outside diameter of prover pipe.
WT Wall thickness of prover pipe.
API Density of liquid in degrees API gravity units.
API b Base liquid density in degrees API gravity units.
API obs Observed liquid density at base pressure in degrees API gravity units.
DEN Density of liquid in kilogram per cubic meter (kg/M3) units.
DEN b Base liquid density in kilogram per cubic meter (kg/M3) units.
DEN obs Observed liquid density at base pressure in kilogram per cubic meter (kg/M3) units.
RD Density of liquid in relative density.
RD b Base liquid density in relative density.
RD obs Observed liquid density at base pressure in relative density.
RHO Density of liquid in mass per unit volume. RHO b Base density.
RHO obs Observed liquid density at base pressure. RHO p Density of liquid in prover (for prover cali- brations).
RHO tm Density of liquid in test measure (for prover calibrations).
RHO tp Density of liquid at operating temperature and pressure.
Temperature ˚C Celsius temperature scale. ˚F Fahrenheit temperature scale.
T d Temperature of detector mounting shaft or displacer shaft on SVP with external detec- tors.
T obs Observed temperature to determine RHOb
T m Temperature of meter in ˚F or ˚C.
T tm Temperature of test measure in ˚F or ˚C.
T mm Temperature of master meter in ˚F or ˚C.
T p Temperature of prover in ˚F or ˚C.
T mp Temperature of master prover in ˚F or ˚C. TWA Weighted average temperature of liquid for measurement ticket calculations in ˚F or ˚C.
Kilopascals (kPa) are the standard SI units for measuring pressure, with kPa representing absolute pressure and kPa g indicating gauge pressure Additionally, pressure can also be measured in pounds per square inch (psi), where psia refers to absolute pressure in psi and psig denotes gauge pressure in psi.
Pb Base pressure in psi or kPa pressure units.
Pb a Base pressure in absolute pressure units.
Pb g Base pressure in gauge pressure units.
P m Pressure of liquid in meter in gauge pressure units.
P mm Pressure of liquid in master meter in gauge pressure units.
P mp Pressure of liquid in master prover in gauge pressure units.
P p Pressure of liquid in prover in gauge pres- sure units.
6 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
PWA Weighted average pressure of liquid for measurement ticket calculations in gauge pressure units.
Pe Equilibrium vapor pressure of liquid at normal operating conditions in absolute pressure units.
Pe b Equilibrium vapor pressure of liquid at base temperature in absolute pressure units.
Pe m Equilibrium vapor pressure of liquid in meter at proving conditions in absolute pres- sure units.
Pe mm Equilibrium vapor pressure of liquid in master meter in absolute pressure units.
Pe p Equilibrium vapor pressure of liquid in prover at proving conditions in absolute pressure units.
CCF m Combined correction factor for meter at proving conditions
CCF mm Combined correction factor for master meter at proving conditions
CCF mp Combined correction factor for master prover at proving conditions.
CCF p Combined correction factor for prover at proving conditions.
CPL Correction for compressibility of liquid at normal operating conditions (for CMF and ticket calculations).
CPL m Correction for compressibility of liquid in meter at proving conditions.
CPL mm Correction for compressibility of liquid in master meter at proving conditions.
CPL mp Correction for compressibility of liquid in paster prover at proving conditions.
CPL p Correction for compressibility of liquid in prover at proving conditions.
CPS Correction for the effect of pressure on steel (see Appendix A).
CPS m Correction for the effect of pressure on steel test measure.
CPS mp Correction for the effect of pressure on steel master prover.
CPS p Correction for the effect of pressure on steel prover.
CSW Fiscal correction for sediment and water.
CTDW p Correction for the effect of temperature difference of water for prover calibrations.
CTL Correction for the effect of temperature on liquid at normal operating conditions (for ticket calculations).
CTL m Correction for the effect of temperature on liquid in meter at proving conditions.
CTL mm Correction for the effect of temperature on liquid when using a master meter for proving operations.
CTL mp Correction for the effect of temperature on liquid in master prover.
CTL p Correction for the effect of temperature on liquid in prover.
CTS Correction for the effect of temperature on steel (see Appendix A).
CTS m Correction for the effect of temperature on steel test measure.
CTS mp Correction for the effect of temperature on steel master prover.
CTS p Correction for the effect of temperature on steel prover.
CCTS Combined correction for the effect of temper- ature on steel prover and steel test measure.
E Modulus of elasticity of steel prover.
F Compressibility factor of liquid in meter at normal operating conditions (for CMF and ticket calculations).
F m Compressibility factor of liquid in meter at proving conditions.
F mm Compressibility factor of liquid in master meter at proving conditions.
F mp Compressibility factor of liquid in master prover.
F p Compressibility factor of liquid in prover.
Gl Linear coefficient of thermal expansion on displacer shaft or detector mounting.
Ga Area coefficient of thermal expansion of prover chamber.
Gc Cubical coefficient of thermal expansion of prover.
Gcm Cubical coefficient of thermal expansion of test measure or master prover.
MMF start Master meter factor at start of each master meter calibration run.
MMF stop Master meter factor at stop of each master meter calibration run.
MMF avg Average master meter factor for each master meter calibration run.
NKF Nominal K-factor, pulses per unit volume.
KF K-factor, pulses per unit volume.
CKF Composite K-factor, pulses per unit volume.
Volumes BMV Base test measure volume.
BMVa Base test measure volume adjusted for scale reading.
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BPV Base prover volume for prover.
BPV mp Base prover volume for master prover.
GSV Gross standard volume (for ticket calcula- tions).
GSV m Gross standard volume of meter for proving operations.
GSV mm Gross standard volume when using a master meter for proving operations.
GSV mp Gross standard volume of master prover for proving operations.
GSV p Gross standard volume of prover for proving operations.
IV Indicated volume (for ticket calculations).
IV m Indicated volume of meter for proving oper- ations.
IV mm Indicated volume of master meter for proving operations.
ISV m Indicated standard volume of meter for proving operations.
ISV mm Indicated standard volume of master meter for proving operations.
MMR o Opening master meter reading.
MMR c Closing master meter reading.
N Number of whole pulses for a single proving roundtrip.
Ni Number of interpolated pulses for a single proving roundtrip
N avg Average number of pulses for the proving roundtrips that satisfy the repeatability requirements.
NSV Net standard volume (for ticket calcula- tions).
SR Scale reading of test measure.
SRu Upper scale reading of open tank prover.
SRl Lower scale reading of open tank prover.
SWV Sediment and water volume (for ticket calculations).
V b Volume of container at base conditions.
V tp Volume of container at operating tempera- ture and pressure conditions.
WD Waterdraw’s test measure volume adjusted for scale reading and corrected for CTDW and CCTS.
WDz Sum of all test measures’ WD values for a single pass.
WDzb Sum of all test measures’ WDz values for a single pass corrected to Pb.
Liquid Density
The density of a liquid must be determined using appropriate technical standards, correlations, or equations of state, with mutual agreement among all parties involved in the measurement The density can be assessed under both flowing and base conditions through one of three methods: empirical density correlation, an equation of state, or an appropriate technical expression.
The liquid’s flowing density (RHOtp) is determined from the following expression:
RHO tp = RHO b × CTL× CPL and
RHO tp /RHO b = CTL× CPL
To accurately calculate RHO tp, it is essential to know RHO b For recommended liquid versus API correlations, refer to Appendix B—Liquid Density Correlation, which aligns with API’s position paper.
1981 Where an API correlation does not currently exist, the appropriate ASTM standard has been provided to assist the user community.
Derivation of Liquid Base Volume Equations
Determination of Indicated Volume
The IV is the change in meter reading that occurs during a receipt or delivery The word registration, though not preferred, often has the same meaning The IV is obtained by subtracting the Opening Meter Reading (MR o ) from the Closing Meter Reading (MR c ).
Determination of Gross Standard Volume
The GSV is correlated by the following physical expres- sion:
GSV = Mass/RHO b and the mass of the metered quantities by
Mass = IV× MF× RHO tp
As a result, the GSV can be calculated by substituting the various terms to arrive at the following traditional expression:
GSV = IV× CTL× CPL× MF
8 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES or
Note: When using temperature compensated meter readings (MR o , MR c ,
IV), the CTL value shall be set to 1.0000.
Determination of Net Standard Volume
The Net Saleable Volume (NSV) represents the volume of a liquid at its base conditions, excluding nonmerchantable items like sediment and water To calculate NSV, a specific formula is utilized.
NSV = GSV× CSW The correction for sediment and water content (CSW) is explained in the subsequent section.
Determination of S&W Volume
The sediment & water volume (SWV) is a calculated quantity based upon the percent sediment and water
(%S&W) determined by a representative sample of the quantity of liquid being measured It represents the nonhy- drocarbon portion of the liquid and is calculated as follows:
Principal Correction Factors
Liquid Density Correction Factors
Liquid density correction factors are employed to account for changes in density due to the effects of temperature and pressure upon the liquid These correction factors are as follows:
CTL corrects for the effect of temperature on the liquid density
CPL corrects for the effect of compressibility on the liquid density
1.11.1.1 Correction for Effect of Temperature on
When the temperature of a petroleum liquid changes, its density decreases with rising temperatures and increases with falling temperatures This variation in density is directly related to the thermal coefficient of expansion, which depends on the base density (RHO b) and the temperature of the liquid.
The correction factor for temperature's impact on liquid density is known as CTL For the relevant standards regarding the thermal expansion factor of a liquid, refer to Appendix B—Liquid Density Correlation.
When a petroleum liquid experiences a change in pressure, its density will increase with rising pressure and decrease with falling pressure This variation in density is directly related to the liquid's compressibility factor (F), which is influenced by its base density (RHO b) and temperature For detailed standards regarding the compressibility factor, refer to Appendix B—Liquid Density Correlation.
The correction factor for the effect of pressure on the liquid’s density (CPL) can be calculated using the following expression:
CPL = 1/(1 – [P – (Pe a – Pb a )]× [F]) and (Pe a – Pb a ) > 0
Pb a = base pressure, in absolute pressure units.
Pe a = equilibrium vapor pressure at the temperature of the liquid being measured, in absolute pressure units.
P = operating pressure, in gauge pressure units.
The liquid equilibrium vapor pressure (\$P_{e a}\$) is equivalent to the base pressure (\$P_{b a}\$) for liquids with an equilibrium vapor pressure that is less than or equal to atmospheric pressure at the flowing temperature.
Prover and Field Measure Steel Correction Factors
Prover correction factors are utilized to adjust for variations in prover volume caused by temperature and pressure effects on steel.
CTS corrects for thermal expansion and/or contraction of the steel in the prover shell due to the average prover liquid temperature.
CPS corrects for pressure expansion and/or contraction of the steel in the prover shell due to the average prover liquid pressure.
When the volume of the container at base conditions (V b ) is known, the volume at any other temperature and pressure (V tp ) can be calculated from the following equation:
V tp = V b × CTS× CPS Conversely, when the volume of the container at any temperature and pressure (V tp ) is known, the volume at base conditions (V b ) can be calculated by
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1.11.2.1 Correction for the Effect of Temperature on Steel (CTS)
Metal containers, including pipe provers, tank provers, and portable test measures, experience volume changes when subjected to temperature variations This volume change is directly proportional to the cubical coefficient of thermal expansion of the material, regardless of the shape of the prover.
The cubical coefficient of thermal expansion is valid when the calibrated section and its detector switch mountings are constructed of a single material (pipe provers, tank provers, and field measures)
Corrections for Single-Walled Container or Prover
The CTS for pipe provers, open tank provers, and portable test measures assumes a singular construction material and may be calculated from the following:
Gc = Mean coefficient of cubical expansion per degree temperature of the material of which the container is made between T b and T.
T = Mean liquid temperature in the container.
The cubical coefficient of expansion (Gc) for a pipe prover or open tank prover is determined by the materials used in the calibrated section's construction If the coefficient of cubical expansion is not known, the Gc values provided in Table 1 should be utilized.
The cubical coefficient of expansion (Gc) on the Report of
Calibration furnished by the calibrating agency is the one to be used for that individual field measure.
Corrections for Small Volume Provers With External
The cubical coefficient of expansion is essential for calculating the Correction to Standard Temperature (CTS) in pipe and tank provers, as well as field measures However, small volume provers require a modified approach due to their unique design, where the detectors are mounted externally instead of on the prover barrel.
Volume changes caused by temperature variations are determined by the alterations in the area of the prover barrel and the distance between detector positions Although these detectors may sometimes be mounted on carbon or stainless steel, they are more commonly affixed to a special alloy known for its minimal linear coefficient of expansion.
For small volume provers with detectors not positioned in the calibrated section of the pipe, the temperature correction factor (CTS) can be determined using a specific calculation.
Ga = Area thermal coefficient of expansion for prover chamber.
G1 = Linear thermal coefficient of expansion on displacer shaft.
T d = Temperature of the detector mounting shaft or displacer shaft on SVP with external detectors.
T p = Temperature of the prover chamber.
The thermal expansion coefficients, both linear and area, for the materials used in the prover's construction will be applied If the coefficients are not known, the values provided in Table 1 should be utilized.
1.11.2.2 Correction for the Effect of Pressure on
When a metal container, like a conventional pipe prover, tank prover, or test measure, experiences internal pressure, its walls will elastically stretch, resulting in a change in the container's volume.
Corrections for Single-Walled Container or Prover
For practical applications, the correction factor for the impact of internal pressure on the volume of a cylindrical container, known as CPS, can be calculated despite the presence of simplifying assumptions in the equations.
Assuming P b is 0 gauge pressure, the equation simplifies to
Table 1—Coefficients of Thermal Expansion for Steel (Gc,Ga,G1)
Type of Steel Thermal Expansion Coefficient
10 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
P = internal operating pressure of prover, in gauge pressure units
P b = base pressure, in gauge pressure units.
ID = internal diameter of container.
E = modulus of elasticity for container material.
OD = outside diameter of container.
WT = wall thickness of container.
The modulus of elasticity (E) for a pipe prover or open tank prover is determined by the materials used in the construction of the calibrated section If the modulus of elasticity is not specified, the values provided in Table 2 should be utilized.
The modulus of elasticity (E) provided in the Calibration Report from the calibrating agency should be utilized for the specific field measurement If the modulus of elasticity (E) is not available, the values listed in Table 2 should be referenced instead.
Corrections for Double-Walled Container or Prover
Certain provers feature a double wall construction to balance the pressure within the calibrated chamber This design ensures that the inner measuring section experiences no net internal pressure, preventing the walls of the inner chamber from undergoing elastic deformation.
Meter Factors and Composite Meter Factors (MFs, CMFs)
Meter factors (MFs) and composite meter factors (CMFs) are terms to adjust for inaccuracies associated with the meter’s performance as determined at the time of proving.
Unless the meter is equipped with an adjustment that alters its registration to account for the MF, an MF must be applied to the indicated volume of the meter
The MF is determined at the time of proving by the following expression:
The CMF can be applied in scenarios where gravity, temperature, and pressure remain constant during the measurement period, or where any expected variations in these factors lead to unacceptable uncertainties as agreed upon by the involved parties The CMF is calculated at the time of proving using the formula \$MF = \frac{GSV_p}{ISV_m}\$.
Meter Accuracy Factor (MA)
The Meter Accuracy Factor (MA) is crucial for loading rack meters used in refined product applications In truck rack scenarios, meters are adjusted mechanically or electronically during proving to achieve a meter factor close to one This practice streamlines billing and accounting processes related to truck operations in refined product services.
The MA is determined at the time of proving by the following expression:
MA = ISV m / GSV p or the reciprocal of the MF
K-Factors and Composite K-Factors (KFs, CKFs)
K-factors (KFs) and composite K-factors (CKFs) are used in certain applications to remove the necessity of applying meter correction factors to the IV By adjusting the K-factor or CKF during the proving process, the meter is electronically calibrated to maintain a meter factor close to unity.
A new K-factor is determined at the time of proving by the following expression:
The new calibration factor (KF) is calculated using the formula \$\text{New KF} = \frac{\text{Old KF}}{\text{MF}}\$ and is applicable in scenarios where gravity, temperature, and pressure remain relatively constant during the measurement period The updated calibration factor (CKF) is established at the time of proving through this specific expression.
New CKF = (Old CKF)/CMF
Combined Correction Factors (CCF, CCF p , CCF m )
Repeatedly multiplying a large number, such as an IV, by a small correction factor can lead to a loss of precision in calculations Additionally, mathematical errors may arise from sequencing and rounding differences across various machines or software To mitigate these issues, the industry has adopted a method that integrates correction techniques.
Table 2—Modulus of Elasticity for Steel Containers (E)
Type of Steel Modulus of Elasticity
(per psi) (per bar) (per kPa) Mild Carbon 3.00E+07 2.07E+06 2.07E+08
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In this section, we discuss the process of combining multiple correction factors to achieve maximum discrimination levels The method involves calculating a Combined Correction Factor (CCF) through the serial multiplication of individual correction factors, followed by rounding the CCF to the desired number of decimal places.
Three CCFs have been adopted to minimize errors in calculations: a For measurement ticket calculations to determine GSV,
CCF = CTL× CPL× MF or
Note: When using temperature compensated meter readings (MR o , MR c ,
IV), the CTL value shall be set to 1.0000 for CCF measurement ticket calcu- lations.
Note: When using a CMF, the CPL value shall be set to 1.0000 for CCF measurement ticket calculations. b For proving calculations to determine GSV p ,
CCF p = CTS p × CPS p × CTL p × CPL p c For proving calculations to determine ISV m ,
Note: When using temperature compensated meter readings (MR o , MR c ,ISV m ), the CTL value shall be set to 1.0000 for CCF m proving report calculations.
Correction for Sediment and Water (CSW)
Sediment and water are not deemed merchantable components in specific hydrocarbon liquids, including crude oil and certain refined products To account for these nonmerchantable quantities, the adjustment to the gas volume factor (GSV) of the liquid is defined by a specific expression.
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APPENDIX A—CORRECTION FACTORS FOR STEEL
The abbreviated tables contained in this appendix are designed to assist the user in vali- dating computer calculations
14 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
Table A-1—Temperature Correction Factors for Mild Carbon Steel
The temperature correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying table was derived using a specific equation relevant to conventional pipe and open tank provers.
CTS = 1 + [(T – T b ) ắ Gc] a T b = Base temperature in ˚F or ˚C. b Gc = Cubical coefficient of thermal expansion of prover.
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Table A-2—Temperature Correction Factors for 304 Stainless Steel
The temperature correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying table was derived using a specific equation relevant to conventional pipe and open tank provers.
CTS = 1 + [(T – T b ) ắ Gc] a T b = Base temperature in ˚F or ˚C. b Gc = Cubical coefficient of thermal expansion of prover.
16 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
Table A-3—Temperature Correction Factors for 316 Stainless Steel
The temperature correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying table was derived using a specific equation relevant to conventional pipe and open tank provers.
CTS = 1 + [(T – T b ) ắ Gc] a T b = Base temperature in ˚F or ˚C. b Gc = Cubical coefficient of thermal expansion of prover.
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Table A-4—Temperature Correction Factors for 17-4PH Stainless Steel
The temperature correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying table was derived using a specific equation relevant to conventional pipe and open tank provers.
CTS = 1 + [(T – T b ) ắ Gc] a T b = Base temperature in ˚F or ˚C. b Gc = Cubical coefficient of thermal expansion of prover.
18 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
Table A-5—Pressure Correction Factors for Mild Carbon Steel
The pressure correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying tables were derived using a specific equation designed for single-walled containers or provers.
The formula for calculating the CPS (Correction for Pressure and Temperature) is given by \$CPS = 1 + \left[\frac{P \cdot ID}{E \cdot WT}\right\$, where \$OD\$ represents the outside diameter of the prover pipe, \$a_T b\$ denotes the base temperature in either ˚F or ˚C, and \$d WT\$ indicates the wall thickness of the prover pipe Additionally, \$b Gc\$ refers to the cubical coefficient of thermal expansion of the prover, while \$e ID\$ signifies the inside diameter of the prover pipe.
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Table A-6—Pressure Correction Factors for 304 and 316 Stainless Steel
The pressure correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying tables were derived using a specific equation designed for single-walled containers or provers.
CPS = 1 + [(P ắ ID)/(E ắ WT)] c OD= Outside diameter of prover pipe. a T b = Base temperature in ˚F or ˚C d WT= Wall thickness of prover pipe.
20 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES
Table A-7—Pressure Correction Factors for 17-4PH Stainless Steel
The pressure correction for steel values is presented to six decimal places to meet prover calibration standards and aid users in verifying computer calculations The accompanying tables were derived using a specific equation designed for single-walled containers or provers.
The formula for calculating the CPS is given by \$CPS = 1 + \left[\frac{P_{ắ} ID}{E_{ắ} WT}\right]\$, where \$c\$ represents the outside diameter of the prover pipe The base temperature, denoted as \$a_T b\$, can be measured in either degrees Fahrenheit or degrees Celsius Additionally, \$d WT\$ refers to the wall thickness of the prover pipe, while \$b_{Gc}\$ indicates the cubical coefficient of thermal expansion of the prover Lastly, \$e ID\$ represents the inside diameter of the prover pipe.
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The liquid table, found in Table B-1, provides a guide to the appropriate reference for most of the liquids associated with the petroleum and petrochemical industry (RHO b , CTL,
The text following the table describes the recommended references The expertise of a physical properties specialist should be consulted before adopting the recommendations contained in the table.
For some older references, tabular values for RHO b and
CTL cannot be curve fit Therefore, it is recommended that linear interpolation of these tables (between columns and values within a column) be utilized for intermediate calcula- tions.
When using an online density meter, the liquid’s base density (RHO b ) is determined by the following expression:
RHO b = RHO tp /(CTL× CPL)
It is important to note that RHO tp must be known to accu- rately calculate RHO b Also, for low pressure applications,
CPL may be assumed to be 1.0000 if a sensitivity analysis indicates an acceptable level of uncertainty.
Certain liquids have computer subroutines available to adjust to base density following the API MPMS Chapter 11.1 guidelines However, when dealing with high pressures, an iterative method is necessary to determine the base density for fiscal reasons It is advisable to consult the manufacturer regarding elevated pressure conditions.
The computation for correcting from density at flowing conditions (RHO tp ) to density at base conditions (RHO b ) may be carried out continuously if mutually agreed between the parties.
The standards to convert liquid density at observed condi- tions (RHO obs ) to base density (RHO b ) are as follows:
R1 API MPMS Chapter 11.1, Volume X (ANSI/ASTM
The D1250-1980 document includes Tables 5A, 53A, and 23A, which focus on generalized crude oils and JP4 It outlines the procedures for implementation, as well as the rounding and truncating methods used to calculate the Base Density (RHO b ) from the observed data.
Density (RHO obs ) and Observed Temperature (T obs ) at Base
For pressure (P b), Table 5A, applicable at a base temperature of 60˚F, includes generalized crude oils and JP4 with an API@60 gravity range of 0 to 100 For natural or drip gasolines with API@60 gravities exceeding 100, refer to Table 23 of ASTM D1250 (Historical Edition - 1952) Additionally, Table 53A, utilized at a base temperature of 15˚C, encompasses generalized crude oils and JP4 with a DEN b @15 range of 610 to 1075 kg/m³ Furthermore, Table 23A, also at a base temperature of 60˚F, covers generalized crude oils and JP4 with an RD@60 range of 0.6110 to 1.0760.
API MPMS Chapter 11.1, Volume X (ANSI/ASTM D1250-1980) provides guidelines for determining Base Density (RHO b ) from Observed Density (RHO obs ) and Observed Temperature (T obs ) at Base Pressure (P b ) Specifically, Table 5B addresses generalized products, excluding JP4, at a base temperature of 60˚F with an API@60 gravity range of 0 to 85 Additionally, Table 53B is utilized for a base temperature of 15˚C, covering generalized products within a DEN b @15 range of 653.
1075 kg/m3 c Table 23B, used for base temperature of 60˚F, covers generalized products over a RD@60 range of 0.6535 to 1.0760
R3 API MPMS Chapter 11.1, Volume X (ANSI/ASTM D1250-1980), specifically Tables 5D and 53D, provides guidelines for lubricating oils It outlines the procedures for calculating Base Density (RHO b ) from Observed Density (RHO obs ) and Observed Temperature (T obs ) at Base Pressure (P b ) Notably, Table 5D is applicable for a base temperature of 60˚F and addresses lubricating oils with an API@60 gravity range of -10 to.
40 b Table 53D, used for base temperature of 15˚C, covers lubricating oils over a DEN b @15 range of 825 to 1164 kg/m3
R4 ASTM D1250 (Historical Edition - 1952) covers a rela- tive density at 60˚F (RD@60) range of 0.500 to 1.100 Table
23 converts the observed relative density at the observed temperature and equilibrium pressure to the RD@60.
R5 ASTM D1550, used for base temperature of 60˚F, is applicable to both butadiene and butadiene concentrates that contain at least 60 percent butadiene.
The standards that have been developed to determine the CTL values for various liquids are as follows:
C1 API MPMS Chapter 11.1, Volume X (ANSI/ASTM D1250-1980), Tables 6A, 54A, and 24A cover generalized crude oils and JP4 The document specifies the implementa- tion procedures and the rounding and truncating procedures
22 C HAPTER 12—C ALCULATION OF P ETROLEUM Q UANTITIES to determine the CTL from Base Density (RHO b ) and