Search IconMobile Menu Icon

CEESI Uncertainty Analysis Publications

The following are a selection of papers written by CEESI engineers regarding uncertainty analysis. If you would like addition information on this type of meter, or on other flow measurement topics, search the Flow Measurement Technical Library. Please read the CEESI Disclaimer before downloading any CEESI publications.


A User Friendly Approach to Describing Measurement Uncertainty in Industry Standards
Tom Kegel,  2005, CIATEQ

Abstract:
While several well written standards are available, the details of uncertainty analysis remain difficult to apply to flow measurement systems. In an attempt to help the users with flow measurement uncertainty analyses, a different approach is being undertaken for proposed inclusion in several American industry-based standards. These standards are published by the ASME (American Society of Mechanical Engineers), the AGA (American Gas Association) and the API (American Petroleum Institute). The approach is based on building the concepts of uncertainty analysis through a series of examples that gradually increase in complexity. This paper discusses the proposed method for describing uncertainty analysis with an emphasis on support of the United States energy industry.
Go to Download Page


Uncertainty Analysis of Meter Volume Measurements - Part 3, Applications to Systems
Tom Kegel,  2005, CIATEQ

Abstract:
This paper is a continuation of two previous papers on uncertainty analysis1,2. The first paper presented a simplified approach to the uncertainty analysis of a volume measurement based on an ultrasonic or turbine meter. The various components that contribute uncertainty were characterized based on manufacturer’s specifications. The second paper illustrated the interpretation of calibration results for inclusion into the uncertainty analysis. The development incorporated considerable discussion of the impact of systematic and random effects. This paper expands previously developed uncertainty analysis techniques from single to multiple meter based volume measurements. The development includes the concept of correlation and illustrates the effect on the overall measurement uncertainty. A statistical simulation technique is applied to implement the uncertainty analysis.
Go to Download Page


Uncertainty Issues Associated with a Volumetric Primary Flow Standard
Tom Kegel,  2004, Measurement Science Conference

Abstract:
A project has been initiated to upgrade a volumetric primary flow standard that has been operating since 1970. Planned improvements include new instrumentation, improved startup flow capacity, analysis of the diverter valve system and additional tank volume data. A new uncertainty analysis is being developed in conjunction with these efforts. This paper concerns that analysis, it is divided into two major sections. The first provides a review of uncertainty components described in previous publications. The second section is a discussion of the uncertainty in temperature measurement.
Go to Download Page


Uncertainty and Traceability for the CEESI Iowa Natural Gas Facility
Tom Kegel and Aaron Johnson,  2004, Measurement Science Conference

Abstract:
This paper presents an uncertainty analysis for the CEESI Iowa natural gas calibration facility. The facility calibrates flow meters up to flows of 10.7 actual m3/s, at nominal pressures of 7174 kPa. Flow meters are calibrated by a set of nine turbine meter standards that are ultimately traceable to NIST. The analysis shows that the facility can achieve an uncertainty of 0.30% at a 95% confidence level.
Go to Download Page


Uncertainty Analysis of a Wet Gas Test Facility
Tom Kegel,  2003, National Conference of Standards Laboratories (NCSL)

Abstract:
A wet gas flow facility has been operational at the CEESI Colorado location since 1999. The flowing fluids are gas and liquid phase mixtures of natural gas components. For most of the testing the gas phase has been “pipeline grade” natural gas and the liquid has been pure decane. The facility operates over a pressure range from 1.4 to 8.3 MPa (200 to 1200 psi). The dry gas velocity ranges up to 27 m/s (90 ft/s) in a 100 mm (4 in) pipe and the liquid flowrate ranges up to 164 kg/min (360 lb/min). This paper describes the components that contribute uncertainty to wet gas measurements.

Dry gas volume flowrate is measured with a turbine meter that has been calibrated in air over a 0.7 to 4.1 MPa (100 to 700 psi) pressure range. The gas density is determined using an equation of state as a function of pressure, temperature and gas composition, the composition is measured with a gas chromatograph. A subsonic venturi is used as a check standard for the gas mass flowrate. The liquid mass flowrate is measured with one of two coriolis meters depending on the flowrate magnitude. The uncertainty analysis integrates effects due to the gas and liquid mass flowrate instrumentation, equation of state and possible phase changes.
Go to Download Page


Flow Measurement Uncertainty - Analysis Based on Field Grade Components
Tom Kegel,  2003, 4th CIATEQ Seminar on Advanced Flow Measurement

Abstract:
This paper provides a guide to estimating the uncertainty of a flow measurement made with field grade instruments. It is applicable to calibrated or uncalibrated turbine or ultrasonic based measurements. Pressure and temperature measurements contribute uncertainty, the uncertainty components of each instrument are described. A set of typical manufacturer’s specifications are used as an example. The effects of ambient temperature on both measurements are described.

A flow computer acquires signals from the pressure and temperature transducers and converts the readings into engineering units. A gas chromatograph and the equation of state contribute uncertainty to the determination of compressibility under flowing base conditions. The components that contribute uncertainty are described and typical values are proposed.

The process of combining uncertainty components is illustrated based on hypothetical values. The concepts of sensitivity coefficient, expanded uncertainty and coverage factor are described. The data are organized such that the relative contributions of the components can be readily compared. The value of this organizational structure is illustrated by comparing calibrated and uncalibrated turbine meters.

The paper concludes with a brief discussion of advanced topics. These include topics from flow measurement, instrument calibration and measurement uncertainty.
Go to Download Page


Uncertainty Analysis of an Ultrasonic Meter Calibration Process
Tom Kegel,  2002, AGA Operations Conference

Abstract:
In March of 1999 CEESI completed construction of a natural gas flow calibration facility located in Clear Lake, Iowa. The uncertainty associated with the process of calibrating a meter in that facility has recently been estimated to be +-0.23% at a 95% level of confidence. This paper describes the two part analysis leading to that value. The first part is based on manufacturer’s specifications while the second part is based on results from a Measurement Assurance Program.
Go to Download Page


Uncertainty Analysis of an Equation of State for Dry Air
Tom Kegel,  2002, 48th International Instrumentation Symposium

Abstract:
Process measurements of pressure and temperature are often made to calculate thermodynamic properties from an equation of state. While the pressure and temperature measurements are generally accounted for in an uncertainty analysis, the uncertainty associated with the state equation is often unknown. This paper proposes an analysis process for determining the uncertainty of the state equation. The method is applied to the specific case of calculating the density of air. The analysis is expanded to include the effect of correlation, two methods to quantify correlation are proposed. Finally, the uncertainty analysis is expanded to include additional thermodynamic properties.
Go to Download Page


Uncertainty Analysis of a Volumetric Primary Standard
Tom Kegel,  2002, 5th International Symposium on Fluid Flow Measurement

Abstract:
In 1969 CEESI began operation of a volumetric primary calibration system for use with compressible fluids. Efforts are underway to expand the existing uncertainty analysis based on new data and a review of the original results. Four issues involved with that uncertainty analysis are discussed in some detail in this paper. The first consists of a more rigorous analysis of the original volume determination process. Second, the newest dry air equation of state is applied to the limited pressure and temperature range. The third subject is a model of the diverter valve used to begin and end the calibration process. Finally, the unique aspects of propagating uncertainty components associated with density are considered.
Go to Download Page


Uncertainty Analysis of a Large Scale Calibration Facility
Tom Kegel,  2002, 5th International Symposium on Fluid Flow Measurement

Abstract:
In March of 1999 CEESI completed construction of a natural gas calibration facility located in Clear Lake, Iowa. The facility is designed for the calibration of large (up to 30", 760 mm) high pressure (1200 psi, 830 bar) natural gas meters. The facility has three test sections, 20" (508 mm), 24" (610 mm), and 30" (760 mm) in diameter. The flow to a test section is measured with an array of ten 12" (472 mm) turbine meters. A broad range of flowrates can be achieved by flowing simultaneously through multiple meters. Efforts are underway to expand upon the uncertainty analysis performed when the facility was built, this paper discusses a number of issues associated with that effort. The discussion begins with a review of the initial calibration of the flow standards. The discussion continues with three programs designed to maintain traceability and reduce uncertainty. The first is statistical process control based on ultrasonic meter check standards. A new program, turbine swap testing, is described and preliminary results are presented. The third involves applying statistical process control techniques to pressure and temperature measurement. The discussion concludes by proposing a unique approach to propagating uncertainty components.
Go to Download Page


Updated Uncertainty Analysis for a Flowmeter Calibration Process Part 1: Transfer Standards
Tom Kegel,  2001, 47th International Instrumentation Symposium

Abstract:
A transfer standard for flowmeter calibration provides traceability to a primary standard. It is typically used for most commercial calibrations because it represents an economically attractive alternative to a primary system. A set of critical flow venturi (CFV) transfer standards have been maintained in calibration at CEESI for the past 35 years. The uncertainty in mass flowrate has been estimated to be +-0.5% at 95% level of confidence based on analysis of the components that contribute uncertainty. This paper presents analysis of historical data that supports a lower estimate of uncertainty.
Go to Download Page


Updated Uncertainty Analysis for a Flowmeter Calibration Process Part 2: Primary Systems
Tom Kegel,  2001, 47th International Instrumentation Symposium

Abstract:
A primary flow calibration system provides traceability to NIST through direct measurements of mass and time. Two primary systems have been in continuous use at CEESI for the past 35 years. The uncertainties in mass flowrate have been estimated to be +-0.1% at 95% level of confidence based on analysis of the components that contribute uncertainty. This paper presents evidence confirming this level of uncertainty based on the analysis of historical data.
Go to Download Page


Updating the Uncertainty Analysis for a Flow Calibration Laboratory
Tom Kegel,  2001, Measurement Science Conference

Abstract:
For over thirty years CEESI has maintained the same values of uncertainties for the mass flowrate of air. The uncertainty for one data point from a primary standard has been +-0.10% at a 95% level of confidence. The primary standards are used to calibrate critical flow venturi (CFV) secondary standards. The uncertainty for one data point from a secondary standard has been +-0.50% at a 95% level of confidence. A hybrid calibration involves a mix of primary and secondary data points, the uncertainty over a flowrate range of a hybrid calibration has been either +-0.10% or +-0.25% at a 95% level of confidence.

This paper describes part of the process of updating the traditional uncertainty analysis. The primary systems are no longer treated as a group; unique uncertainty values are determined for each system. The CFV secondary standards are also treated independently, the individual values are determined based on historical calibration data. For both primary and secondary calibrations, uncertainties are determined as functions of flowrate or Reynolds number.
Go to Download Page


Measurement Uncertainty Considerations When Using an Array of Critical Flow Venturies
Tom Kegel, Charles Britton, and Richard Caron,  2000, 46th International Instrumentation Symposium

Abstract:
The critical flow venturi (CFV) is an excellent device for generating a known measured flowrate. The CFV exhibits a nominally linear relationship between inlet pressure and mass flowrate. A particular flowrate can be established by applying the proper value of inlet pressure. The range of available inlet pressure values will limit the range of flowrates that can be generated. For applications where the desired flowrate rangeability is greater than the available pressure range an array of CFVs can be used. There is concern that the use of multiple CFVs will result in greater uncertainty than that associated with the use of a single CFV. This paper describes a test program that has been implemented to identify whether this additional uncertainty is present.
Go to Download Page


Uncertainty Issues Associated With a Very Large Capacity Flow Calibration Facility
Tom Kegel,  2000, Measurement Science Conference

Abstract:
In the spring of 1999, CEESI began operation of a natural gas calibration facility located in Iowa with a maximum flow capability in excess of 2000 pounds per second. The flow standard is a parallel array of ten turbine meters. The traceability to NIST is achieved through the CEESI Colorado facility. This paper discusses aspects of the flow measurement traceability methodology and associated uncertainty analysis.
Go to Download Page


A Study of the Repeatability and Reproducibility of the Critical Flow Venturi
Tom Kegel,  1999, 4th International Symposium on Fluid Flow Measurement

Abstract:
The critical flow venturi (CFV) has long been recognized as a high quality gas flow calibration artifact. A program is underway to compile data to be used in determining the intrinsic repeatability and reproducibility of a CFV. This paper describes the initial results of the program, it is divided into three parts. First, primary calibration data from a single CFV are tracked over a 30 year period. Second, results of a test program are presented with the objective of classifying short and long term random effects. Third, results from two test programs are presented with the objective of identifying the source of random effects.
Go to Download Page


A Study of the Repeatability and Reproducibility of the Critical Flow Venturi
Tom Kegel,  1999, 4th International Symposium on Fluid Flow Measurement

Abstract:
The critical flow venturi (CFV) has long been recognized as a high quality gas flow calibration artifact. A program is underway to compile data to be used in determining the intrinsic repeatability and reproducibility of a CFV. This paper describes the initial results of the program, it is divided into three parts. First, primary calibration data from a single CFV are tracked over a 30 year period. Second, results of a test program are presented with the objective of classifying short and long term random effects. Third, results from two test programs are presented with the objective of identifying the source of random effects.
Go to Download Page


Uncertainty Analysis for the CEESI Ventura High Flow Test Facility
Tom Kegel,  1999, 4th International Symposium on Fluid Flow Measurement

Abstract:
In March of 1999 CEESI completed construction of a natural gas calibration facility located in Clear Lake, Iowa. This facility is specifically designed for the calibration of high flowrate custody transfer meters. The calibration of these flowmeter must be made using a method that is traceable to NIST with an uncertainty analysis of that traceability. This paper describes certain aspects of the traceability methodology and uncertainty analysis.
Go to Download Page


Basic Measurement Uncertainty
Tom Kegel,  1996, 71st International School of Hydrocarbon Measurement

Abstract:
When a measurement is made there are two important values associated with the result of the measurement process. The first is the numerical value of the variable being measured, the second is the uncertainty associated with that numerical value. This paper describes an analysis procedure to determine the measurement uncertainty by: 1. Presenting a simplified step by step procedure. 2. Illustrating the use of the procedure to a typical measurement process with real world problems. 3. Briefly discussing some of the more complex aspects of uncertainty analysis.
Go to Download Page


A Novel Primary System for Compressible Flow Calibration: Uncertainty Analysis for the Preliminary Design
Tom Kegel,  1995, 41st International Instrumentation Symposium

Abstract:
The operation of a primary system for compressible flow calibration is typically based on either a gravimetric or volumetric method of mass determination. The gravimetric method provides direct determination of mass while the volumetric method utilizes measurements if density and volume. This paper describes the preliminary design of a primary system that features both gravimetric and volumetric mass determination. The emphasis is on the presentation of an uncertainty analysis procedure to be used for preliminary design designs.
Go to Download Page


Uncertainty Analysis of a Volumetric Primary Standard for Compressible Flow Measurement
Tom Kegel,  1995, 3rd. International Symposium on Fluid Flow Measurement

Abstract:
Primary flow calibration systems are based on measurements of mass and time that yield mass flowrate. One type of system for primary calibration using a compressible fluid involves determination of the mass from values of fluid density and storage tank volume. This paper presents a complete uncertainty analysis of such a system.
Go to Download Page


Uncertainty Analysis of a Compressible Flowmeter Calibration Process
Tom Kegel,  1994, ASME Fluids Engineering Division

Abstract:
This paper presents an uncertainty analysis of the process of calibrating a critical flow venturi with a primary flow standard using dry compressed air. The primary flow standard provides traceability to NIST through measurements of mass and time. The critical flow venturi is being calibrated foe use as a transfer standard. The uncertainty of the calibration process at a 95% level of confidence is estimated to be ±0.038%, data are presented that support this estimate.
Go to Download Page


Uncertainty Analysis of a Sonic Nozzle Based Flowmeter Calibration
Tom Kegel,  1994, National Conference of Standards Laboratories Annual Workshop and Symposium

Abstract:
This paper presents a complete uncertainty analysis for a particular type of flowmeter calibration. This calibration involves air as the fluid and utilizes a sonic nozzle as a transfer standard for mass flowrate. The uncertainty analysis includes the traceability of pressure, temperature and mass flowrate measurements as well as calibration process considerations. Typical numerical data are presented.
Go to Download Page


Uncertainty Analysis of a Gravimetric Primary Standard
Tom Kegel,  1993, National Conference of Standards Laboratories Annual Workshop and Symposium

Abstract:
This paper describes the uncertainty analysis of a primary calibration system for determining the mass flowrate of a compressible fluid at elevated pressure levels. The mass flowrate is determined based on direct measurements of mass and time. The range in expanded uncertainty is estimated to be 44 - 150 ppm at a 95% level of confidence, data are presented that support this estimate.
Go to Download Page


Correlation of Hydrogen and Air Flow in Critical Flow Nozzles, Part 1: Primary Calibration Facility
Tom Kegel,  1992, 1992 Conference on Advanced Earth-to-Orbit Propulsion Technology

Abstract:
Operations of the Space Shuttle Main Engine (SSME) Test Bed requires accurate measurement of high flowrates of gaseous hydrogen, a critical flow venturi (CFV) is proposed to provide this measurement. Calibration of the CFV in a primary facility is costly, the cost can be reduced significantly if the meter is calibrated in air rather than gaseous hydrogen. he goal of this project is to determine correlating parameter that enable the nozzle to be calibrated in air and then used to measure the flow conditions expected is the SSME Test Bed. This paper consists of a primary calibration facility is described. This facility will be used to develop the correlating parameters.
Go to Download Page


CEESI © 2017
CEESI Logo © 2017