FACILITIES AND FLUID METERING TRACEABILITY AT
INTRODUCTION
Standards. Flowrate standards could be significantly simplified if the fundamental bases of these measurements were as simple as those for mass, length, etc. These systems of measurement are based upon discrete standards* or artifacts. For example, the platinum kilogram known as “K-20” is the ultimate artifact to provide the fundamental basis for mass measurement in the U.S. and the platinum meter bar (or its modern-day wavelength equivalent) is the ultimate artifact to provide the fundamental basis for length measurement.
Identity Standards. These mass and length artifacts can be considered “identity” standards because under the appropriate conditions of use they define the basic quantity in their respective measurement systems.
However, for flow rate measurements of fluids—i.e., liquids or gases, there does not exist an identity standard such as a gallon per minute, a liter per second, or a kilogram per hour. To supply the fundamental basis upon which to establish a flow measurement system, a “derived” standard is needed.
Derived Standards for Flow. For gas flow measurements—as needed to form the basis of a national reference system—calibration facilities spanning a range of fluid and flow conditions are maintained by NBS for use by industry and others. These facilities consist usually of:
(1) a source of flow—generally a compressor with appropriate auxiliary equipment or a regulated, pressurized tank of gas,
(2) a test section into which the meter and its adjacent piping can be installed so that the flow and fluid conditions into it duplicate those expected where the meter will actually be used,
(3) a flow determination system having the required level of performance and appropriate proof of this to specify and assure the desired metering performance of the devices in question.
Calibration systems are generally categorized according to the type of flow determination scheme used.
Several of these schemes will be described below.
Flow Determination Systems. The heart of the gas flowmeter calibration facility is the flow determination system. This generally uses a timed collection of the gas which flows through the meter being calibrated.
The amount of the gas collected is determined by gravi metric or volumetric techniques. This collected gas is converted to mass flowrate using the collection time; the volumetric flowrate through the meter can be determined using the pertinent thermodynamic properties measured at the meter. This system can be made to perform at a high level of performance to determine the bulk flow rate of gas.
Levels of Performance. Measurement systems can be characterized via their precision and accuracy.
These are briefly defined as follows:*
Precision – the degree—generally expressed as a percent—to which successive determinations of the same quantity duplicate each other. “Precision” is sometimes further subdivided into
“reproducibility”—which involves “how closely will successive determinations duplicate each other” or “repeatability”—which involves “how closely can successive determinations be made to duplicate each other”.
*The term standard is used to refer to “paper” standards which are documents; it is also used to refer to reference facilities and equipment; it is also used to refer to the specific materials needed to transfer measurement quality from or between facilities. These specific materials are referred to in what follows as “artifacts”.
Accuracy – the degree—generally expressed as a percent—to which a measured result approximates the true value.
These characteristics apply to measurements made by flowmeters and to measurements made using calibration facilities.
Facility Performance. For gas flow calibration facilities, the precision can be evaluated from the appropriate error budget and from the precision of the component measurements that constitute the system.
Difficulty is encountered when facility accuracy is to be quantified because the true value of the gas flowrate is not easily obtained. To estimate possible systematic offsets from true value, approximations—
generally very conservative, are frequently used. Alternatively, and more preferably, a realistic and highly defensible traceability scheme either is available or can be generated and is appropriately used to document the systematic offset of a calibration facility.
Traceability. Traceability is defined many ways by many people, see Appendix 1. Conventional calibration procedures can establish traceability of types 1 and/or 3.
Conventional Calibration Procedures. With conventional calibration programs, a testing laboratory or a meter manufacturer or a meter user might own and routinely use a master meter technique to assess the flowrate measurement performance of the laboratory. To do this, the master meter might be sent yearly to NBS for a calibration in the appropriate NBS flow facility. This done, the meter would be returned to the laboratory with a report on its performance in the NBS facility. The meter would be placed into the respective facility in the laboratory and then calibrated. The relative performance of these calibrations would hopefully compare very favorably and thereby document the closeness of agreement between the laboratory’s facility and NBS. This procedure—while widely used at the present time—can leave a considerable number of factors affecting measurement completely unassessed. Traceability of type 4 (see Appendix 1) might be established for a flowmeter calibration laboratory in the following manner. If calibrated weights (for example from a state office of weights and measures) were used to check a scale system and if a timing standard were used to check the lab’s timing system, then traceability—type 4 could be asserted for the lab’s weigh-time system. However, the overall ability of the lab to calibrate a flowmeter can be quite incomplete. For such reasons, it is widely believed that type 2 traceability is preferred. This type 2 traceability can be established and maintained via flow measurement assurance programs—i.e., flow MAPs.
Flow MAPs. In the case of flow MAPs, a procedure different from the conventional calibration one is used, see [1–4].* This involves NBS (or an initiating laboratory) sending a very reliable and well characterized artifact package (i.e., tandem meter arrangements consisting of two meters in series) to the laboratory in question with the request for a calibration of the device(s) according to tightly specified and prearranged conditions. The results—which would contain the effects of all the lab’s routine calibration procedures—its facilities, its operating conditions, its personnel, and its techniques for calculating final results from raw data—are then sent to NBS. These can be objectively (and informedly) compared to NBS results or, more preferably, to similar results from a number of other comparable labs which have performed the same tests in a “round-robin” set of these calibrations. In these comparisons, NBS results are also incorporated as one of the participants. The results show quantitatively, the agreement (or disagreement) among the participants’ results. Algorithms have been developed to handle these results, see [5–8]. Fig. 1 shows a comparison of conventional calibration procedures and those that can occur with MAPs. The comparison shows that the crucial advantages of the MAP program are that: (1)all aspects of the
*A number of useful definitions are given in the Glossary in Appendix 1 . NATIONAL BUREAU OF STANDARDS
laboratory’s measurement processes are checked, and (2) there is a “feedback” and, if necessary, a “follow- up” activity that can make improvements, etc. These follow-up activities are directed either at the lab’s procedures or at its calibration procedures and facilities, depending upon the results of the algorithms that can be applied to the round-robin data.
Basic Calibration Procedures. Calibrations are usually performed using a facility that includes a source of flow, the meter and connecting piping, and a flow determination system, all connected in series. A typical system is illustrated in Fig. 2. Control volumes, see [9], a, b, c are shown for a meter, connecting pipe and calibrator volumes, respectively. The volumes are separated by imaginary control surfaces, 1, 2, 3 and 4.
For reasons to be discussed, inlet piping to the metering element should be specified and should provide a suitable and reproducible flow pattern at the inlet to the metering element, and this pipe is considered herein as a part of the meter and volume a. Depending on the type of calibrator, control surface 4 of volume c may be a moving piston, the stationary end of a tank, etc. A description of calibration strategy follows, see [10–12].
Conservation of Mass Equation. A calibration usually requires a determination of mass rate of flow (or sometimes volume rate) through the meter. An application of the conservation of mass equation illustrates some of the problems involved. The equation as applied to a flow system of a fixed control volume V enclosed within a surface A can be written in vector form as, see [9]
*Bracketed integers refer to references given below.
FIGURE 1. CONVENTIONAL CALIBRATION VS. MAP COMPARISON.
(1) where, in compatible units M is the substantial time derivative of the mass in the control volume, p is the mass density, ∂p/∂t represents the partial derivative of fluid density p with respect to time, is vector FIGURE 2. TYPICAL CALIBRATION FACILITY.
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velocity of the fluid and is the control surface element of area with a direction taken outward and normal to surface A. The first term on the right hand side of (1) represents an integration covering total volume V to find the rate of accumulation of mass, ∂m/∂t, in volume V if density p is not constant. The second term on the right represents net mass rate of flow through the control volume surfaces. Application of Eq. (1) to each of the control volumes a, b and c of Fig. 2 gives three equations, which when added together gives mass flowrate as
(2) where subscripts 1 and 4 represent surfaces illustrated in Fig. 2, subscript n represents the normal component of velocity at the surface, and subscripts, a, b, and c represent the respective control volumes.
Calibration Facilities at NBS. Calibration facilities are available at NBS for offering calibration service for meters that flow gas,* see [13]. These are performed using air or other gases. Capabilities are shown in the chart shown in Fig. 3. Dashed lines in 3(a) indicate planned extensions of rate. Estimated systematic errors for the calibrations as plotted in 3(a) will be discussed in more detail in other parts of this paper.
Typical reference flowmeters calibrated may add from 0.05 to 0.3% uncertainty to the systematic error shown as a result of imprecise meter readout and possible meter and flow instabilities under field conditions.
Gas Flow: Static Procedure. A “P, V, T, t” (pressure, volume, temperature and time) tank is used as the NBS’ primary standard for high rate gas flow, see Fig. 4. Filtered and dried air (dew point of about −50 °C at 8.5 atmospheres absolute pressure) at rates up to 85 m3/min (3000 scfm) are the original design conditions for this system. The tank contains approximately 28 m3 (1000 ft3) and is used for measurement of air flow rate via the temporal increase in gas density in the constant volume tank. The measurements are called “static” as both volume and density changes can be measured at presumably stationary conditions.
Dynamics are involved only in opening and closing motions of the diversion valves which are timed to give the collection interval. Collection volume capacity is derived from weighed gaseous nitrogen fillings of the tank in conjunction with density as determined from temperature and pressure measurements. Results from separate fillings of the tank with gas indicate that a volume uncertainty of 0.01% can be achieved. Gas temperature in the tank is measured with 10 thermistors that are calibrated against a platinum resistance thermometer which was calibrated by NBS’ Temperature Section. Two calibrated thermistors are located on each of 5 horizontal concentric circles distributed vertically so that the average temperature of the gas is accurately measured. A fan is installed to stir the air in the tank to remove stratification effects. Thermistor elevations are shown in Fig. 4. These temperature sensors, in conjunction with others for measurement of tank metal temperature, and a pressure gage provide information to derive collected gas density and an estimate of its uncertainty. Although the environment of this large tank may not be well controlled, its small surface to volume ratio and use of the circulation fan permit the volume to be derived with an acceptable uncertainty. Using this facility, NBS sonic nozzles are proved and then used as transfer standards to calibrate meters flowing air.
Conservation of mass principles, as applied to this measurement system for a finite measurement interval Δt, can be written,
(3)
*“Special Test” facilities exist at NBS in Boulder, CO. These use cryogenic fluids. A description of these facilities can be found in [14]. In addition, low flow rate helium permeation leaks testing capabilities will be available at NBS in 1986.
where, in compatible units: pc represents density of the fluid in the collection tank volume Vc, with errors represented by a leak term and by an undetected tank-volume change ΔVc. Examples for these errors are, respectively, condensation of vapor in volumes a or b which could appear as a leak, and change of Vc as caused by use of the tank at other than calibration conditions. Vb can be much smaller than Vc to make any error in measurement of Δpb of insignificant consequence. Error in measurement of Vc is related to uncertainties in measured temperature, pressure and mass, perhaps combining to be between 0.02 and 0.05%
as indicated by experiments. When used as a calibration device, the same uncertainties are introduced again, except that uncertainty of mass is replaced by that of published values of super-compressibility factors Z=(P/
pRT) used in the gas law for derivation of pc. Uncertainty in Z enters if either the gas state or the gas itself is different for calibration of the tank and calibration of a meter. If uncertainty of Z and that of weighed FIGURE 3(a). NBS GAS FLOW CALIBRATION FACILITY CAPABILITIES.
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mass are comparable (or both insignificant) total uncertainty can be in the range 0.04 to 0.10% without consideration of an uncertainty in Δt.
Gas Flow: Dynamic Procedure. Filtered dried air (dew point about −40 °C at 35 atmospheres absolute pressure) is measured at rates up to 1.4 m3/min (50 cfm) with piston and with bell-type provers arrangements such as those sketched in Figs. 5 and 6. Motion of the mercury-sealed piston in its vertical glass tube is timed (after an initial acceleration period) with a timer actuated by two photo sensors when their light beams are interrupted by the piston, see Fig. 5. The light beams that traverse the glass tube are placed a known, vertical distance apart, and each is constricted to about 0.01 cm. in the direction of piston travel. Vertical motion of the bell in its annular bath of sealing liquid is timed by similar switches actuated successively by the vertical motion of the bell, see Fig. 6. Interval diameter measurements are used (via calibrated calipers or via strapping techniques with an NBS calibrated tape) to derive volume per unit of distance traveled for both provers, additional measurements being required to account for displacement motion of the sealing liquid in the bell-type prover, see [12].
Careful attention to numerous details is necessary to avoid measurement difficulties. These arise from small rates of flow and small collected volumes, from considerations involving dynamics of the measurement process, and from difficulty in making meaningful gas temperature measurements in small gas FIGURE 3(b). TABULATED SUMMARY OF NBS GAS FLOW CALIBRATION FACILITY CHARACTERISTICS.
flow systems. A nearly constant laboratory temperature, both spacewise and timewise, is used in conjunction with sufficient piping upstream from the meter and calibrator to bring gas temperature to that of the calibration system, meter and laboratory. This not only reduces temperature measurement problems but prevents heat transfer in the meter and prover—a very important requirement. Thermal insulation and/or heat exchangers are also used and are recommended for difficult environments to assure equal meter and gas temperatures.
Other difficulties mentioned which cause errors can be illustrated with use of Eq. (2). This can be written for the bell prover arrangement, for a finite calibration interval Δt, as
(4) where, in compatible units: piΔVc represents the mass of gas collected in the prover during its stroke of volume ΔVc as based on density pi at initiation of collection, with system gas density pe existing at termination of the calibration period. Volumes Va and Vb represent not only meter and connecting pipe volumes, respectively, but also gas volume in such things as instrument lines, and any volume collected in FIGURE 4. NBS’ LARGE AIR FLOW CALIBRATION FACILITY’S P, V, T TANK.
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the prover during its acceleration period. The last term on the right represents an error caused by a system volume change, e.g., when a pressure change affects liquid level in a manometer or sealing liquid level in a bell prover. Undetected density change (pe−pi) is an error that can receive significant multiplication whenever system volume (Va+Vb) is significant compared to ΔVc (as frequently prevails in low flowrate measurements). The last error mentioned in (4) should not be admissible; but leaks as represented by , even though demonstrated as insignificant compared to piΔVc, can be disastrous if located at a pressure tap.
A leak at this location can invalidate measured pressures used to describe meter performance, and preventive tests against such leaks always are made.
Eq. (4) also can be used as a basis for discussion of both systematic and random errors involved in flowrate measurements using these provers. Systematic errors may be considered as characteristics of instruments ordinarily used for measurement piΔVc/Δt. Calibration and reading errors of the instruments, not their dynamic response errors, are summarized below:*
Volume 0.02 to 0.05%
Pressure 0.02
FIGURE 5. SKETCH OF PISTON PROVER ARRANGEMENT.
Temperature 0.03
Timer, clock 0.005
Timer, switching 0.06
These combine to form a possible overall systematic error in the range 0.075 to 0.165%. More reliable and credible bounds to the systematic error can be established via MAP programs. Some of the observed imprecision of rates as evaluated by repeated measurements with these provers can be regarded as connected with the other three terms on the right side of equation (4) and with sensitivity and repeatability of the flowmeter under test. Two terms in (4), (pe−pi) and Δ (Va+Vb) are connected with dynamics of prover motion as affected by its design, by the procedure used, by dynamic response of the instruments, etc.
Environment also affects precision through changes of ambient pressure and temperature, the latter causing heat transfer. Combining the above uncertainties, estimated standard deviation for a flowrate determination is generally between ± 0.1 to ± 0.2% when testing better meters.
FIGURE 6. SKETCH OF BELL PROVER ARRANGEMENT.
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Once these necessary quantifications are completed, it remains to assess the bias, or systematic errors in laboratory measurement capabilities. This can be done via estimating but it is better achieved via traceability established via flow MAP’S—i.e., round robin testing. This topic is described and discussed below.
Flow Measurement Traceability. To establish traceability of the type 2 variety (see Appendix 1) a test program must be devised so that:
(1) high confidence can be placed in the artifact package—the meters assembled and the specifics of the procedures, check-points, responses to anticipated anomalies, etc.,
(2) the data base produced is adequate to the task of clearly evaluating the significant components of the systems that participate, and
(3) the algorithm for processing the data and producing the results is an unbiased and clear procedure that is adequate to this task.
Artifact confidence is established via calibration testing over an extended period of time for the kind of conditions that will be used in the round robin. This testing should occur in the initiating laboratory and it should establish a credible background data base for the units being tested. Specifically, high competence can be attained by calibrating two (2) meters in series according to tightly specified conditions. This type of configuration is shown in Fig. 7. Pre-testing of these configurations gives expected values for the respective meter factors as well as for the relative performance of the meters—i.e., the ratio of their outputs.
*These values should be considered as reasonable estimates. Currently, efforts are underway at NBS to re-evaluate the performance of all the calibration facilities that are used to offer calibration services, see [10, 13].
FIGURE 7. SKETCH OF TANDEM METER CONFIGURATIONS.