Baker R.C. Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications

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4.6 IN SITU CALIBRATION

LEVEL

MEASURE

Figure 4.20. Diagram of a suitable system for a drop test.

METER

PIT

VALVE

d. Satisfactory means of communication between the person who is taking the

level measurements and the person who is taking the volumetric readings on

the meter. Of course, this process may be automated.

Typical uncertainty for such a test may be

Strapping tables (say

1:10,000

dimensional precision) 0.02%

Level measurement (say 2 mm in 10 cm) 2.0%

Timing errors for rate (say 0.2 s in 100 s) 0.2%

Within this group of errors, although the volume of the reservoir may be affected by

tank supports, etc., the level is likely to be predominant. The measurement of level,

often in places with poor accessibility, small changes, and surface waves, may result

in such an error, and the preceding example may be overly optimistic for some sites.

Taking the root of the sum of the squares of these errors gives

2.01%,

which may be

optimistic.

In Situ Measurement of Meter Dimensions (Dry Calibration)

By measuring the dimensions of a differential pressure flowmeter, it may be possible

to deduce the performance. If the measurements confirm that the design meets the

ISO requirements, then the flow rate should be predictable with an uncertainty of

about

1.0-2.5%.

The term dry

calibration

was particularly coined for the electromagnetic flowme-

ter where it is possible to measure the magnetic field strength and the meter bore and

so deduce the meter performance (Al-Rabeh and Baker 1986). Although the methods

have increased in sophistication, it has been found to be not a very satisfactory ap-

proach except under very carefully controlled conditions. However, an uncertainty

of order 5% may be achievable. This will, of course, require checking all secondary

instrumentation as well as measurements of the meter geometry.

The use of retrofitted ultrasonic transducers also depends on the measurement of

pipe dimensions and the positions of the transducers. There

not enough experience

on whether this may offer genuine calibration in an in situ mode.

88 CALIBRATION

Clamp-on Ultrasonic Flowmeters

The possibility of using clamp-on transit-time ultrasonic meters is being explored.

Apart from the inherent uncertainties of using such meters on pipework of unknown

condition,

it is

also essential

avoid installations that are seriously affected

upstream pipe fittings. These meters are discussed in more detail in Chapter 13.

Probes

Probes will be covered in Chapter 18. However, the use of probes for in situ calibra-

tion is common, and a few points need to be made here.

• If

single-point measurement is required, the reader

referred to Table 2.2 where

it is shown that, for a well-developed turbulent profile, if the probe is placed near

the three-quarter radius position (0.76 x radius from the pipe axis), the velocity

at that point is approximately equal to the mean velocity in the pipe. However,

this is

region of strong shear and turbulence, and incorrect positioning of the

probe may result in measurement errors. If the probe is positioned on the axis of

the pipe, the actual positioning is less critical, but the velocity at that point is not

proportional to the mean velocity in the pipe as the Reynolds number changes.

Allowing for

probe calibration

±1% uncertainty, the best that

likely

be achieved

for

the total flow

is of

order 3% and may be much poorer than

this.

•

the velocity profile across the pipe

required, then multiple measurements

will be necessary. These can be equally spaced, but to obtain mean velocity in the

pipe

may be quicker and preferable to use an integration method that selects

fewer positions, which may or may not be equally weighted (cf. ISO 1977b, 1988

and also list of standards). The log linear positioning of measurements (with each

measurement equally weighted) follows:

Number of points

radially

Position,

0.359

0.310

0.958

0.278

0.847

0.253

0.773

r/R

0.730

0.632

0.566

0.962

0.517

0.850

0.936

0.766

0.695

0.635

0.973

Salami (1971) recommended that at least six traverse points on each of six radii

were needed

keep errors down

0.5% for nonaxisymmetric profiles.

assume that the profile

axisymmetric, then we may take one diameter and

select the number

points according

the time available. The specification

of the positions, the recording of the data from the probe, and the calculation

of the mean flow in the pipe are often done today by a portable flow computer

designed for the purpose. We shall also need a value of the pipe internal diameter

(ID).

For further information, the reader is referred to the standards. Realistically

we are unlikely to achieve an uncertainty of better than 3%.

4.6 IN SITU CALIBRATION 89

• The act of inserting a probe will alter the flow in the pipe, and the probe's re-

sponse will vary with insertion position. This is mentioned in Chapter 18, but

the manufacturer of the probe will need to supply detailed information.

Tracers

Tracer methods for obtaining flow in an unknown system are an elegant and attrac-

tive approach, but they have a disadvantage. Those undertaking them really need

extensive experience; otherwise, the resulting accuracy may not be very high. The

method can conveniently be categorized as constant rate injection, sudden injec-

tion, or time of transit.

In the constant rate method, a solution of the tracer material in the same fluid

as that in the main stream is injected from a branch pipe, which has a valve, at a

known rate q

to the line (Figure 4.21). The concentration in the injected stream

Q is known; the concentration in the main stream, if the tracer material happens

to be present, is measured as C

; and, far enough downstream, the concentration

resulting from the injection and thorough mixing C

is also measured. The equation

that gives conservation of tracer material and hence the volumetric flow rate in the

line q

+ q

) (4.1)

and rewriting this to obtain the unknown flow rate in the line we have

qv =

qvi

^Z^L

(4.2)

For this method to be successful, we do not need to know the size of pipe, but we

do need to ensure that all the tracer material goes downstream, and that there is a

genuine steady state, without accumulation of tracer in trap areas in the pipework.

It is probably necessary for the upstream concentration C

to be less than 15% of

the downstream concentration after injection C

. Clearly the tracer must be such as

can be injected into the line without any health or environmental problems, and it

must be cheap enough to use in continuous injection. If

make the assumption, to

obtain an idea of the accuracy, that Q » C

> C

, then with a high quality flowmeter

for the injection and a precise concentration in the injected flow, the downstream

value C

is likely to be the least reliable of the dominant measurements and will affect

the accuracy. Hermant (1962) in the discussion of his paper appears to claim

±1%

the uncertainty compared with use of current meters. Clayton et

al.

(1962a, b), using

a radioactive tracer, were able to claim better than

for the method including using

a portable system. They suggested that 110-220D should be allowed for mixing.

Figure

4.21.

Constant rate injection method (dilution method).

90 CALIBRATION

Qmean

Figure 4.22. Concentration variation downstream

with sudden injection method (integration).

In the sudden injection method (integra-

tion),

one known amount of V is injected

with a known concentration Q, and the

variation in the downstream concentration

is measured with time as in Figure 4.22.

If this curve is integrated, and we assume

that the flow rate is constant during the

measurement period, we obtain the total of

tracer passing, or the mean over the mea-

suring period. Thus

/o(C

- C

) dt

(4.3)

(4.4)

where C

ean is the mean concentration measured downstream. In addition to the

constraints for the constant rate method, the accuracy of sampling the concentra-

tion is likely to be lower because instantaneous measurements will be needed and

the accuracy of the concentration sensor will introduce uncertainty. However, the

amount of tracer used will be less, which may, therefore, allow a wider choice of

tracer, (cf. Spragg and Seatonberry 1975).

In addition to these two methods, it may be possible to sense the passing of tracer

at two points in the line, or, indeed, the variation in some naturally occurring com-

ponent that might allow a correlation method to be used. It should be remembered

that, in this case, the measure will be of velocity and not necessarily of volumetric

flow (cf. Aston and Evans 1975 who estimated likely uncertainties within ±1% for

steady flows and ±2% for normally fluctuating flows).

Scott (1982) also described the Allen salt-velocity method, which measures the

time of transit between two stations between which the volume of the pipe is known.

Again he mentions the need to inject the tracer explosively, in this case a minimal

amount of brine, and the requirement for a sensitive detection system. The marker

point as the brine passed each station was taken as the midpoint of the half height

trace [Figure 4.23 (cf. Hooper 1962 and Clayton et al. 1962b who suggested uncer-

tainties of order 1%)].

Various tracers have been used. For the constant rate method, sample analy-

sis is likely to be the most accurate method of obtaining C

and C

, the values of

concentration. In the case of sudden injection, a continuous detector will be needed.

Examples follow:

Main fluid

Water

Other liquids

Liquids or gases

Gases

Tracer

Brine

Dyes or chemicals

Temperature

Radioactivity

Detector

Electrical conductivity

Color or light sensing

Temperature sensor

Scintillation or geiger counter

O, He, methane Infrared spectrometer

4.7 CALIBRATION UNCERTAINTY 91

TRACER

INJECTION

ELECTRODE

FLOW

_JL

ELECTRODE

(a)

CONCENTRATION

OF TRACER

HALF HEIGHT

OF TRACES

/ \

MID

POINT

TIME

(b)

TRANSIT

TIME

Figure 4.23. The Allen salt-velocity method for time of transit between two stations: (a) Pipe for

which volume is known; (b) Marker points as the brine passes each station (after Scott 1982).

4.7 CALIBRATION UNCERTAINTY

Mattingly (1990/1) gives a very useful run down of calibration uncertainty. Before

the facility is built, the uncertainty can be estimated. For a static gravimetric liquid

facility,

(4.5)

where q

is the volumetric flow rate, M

is the net mass of liquid collected, p is the

liquid density, and t is the collection time. The uncertainties (cf. Equation 1.A.7 for

alternative symbols) can be combined as

1/2

(4.6)

(4.7)

By inserting percentages of reading, an initial estimate can be obtained. This

presupposes that Equation (4.5) is correct. However, other factors are likely to be in-

volved. At the National Institute of Standards and Technology (NIST), Gaithersburg,

Maryland, for liquid flow, the three values to 3 standard deviations were

— = 0.02% — = 0.01%

P t

and combine to

±0.03%

for Equation (4.6) and ±0.05% for Equation (4.7). For gas,

the volume was 0.04%, density pressure effects were

0.13%,

temperature effects were

0.05%,

and collection time for the device was 0.01% and for switching was 0.02%,

giving totals of ±0.15% and ±0.25%, respectively. The next stage is to obtain data

92 CALIBRATION

from the facility, and the third stage is to obtain systematic errors from round-

robin tests. These round-robin tests are known as Measurement Assurance Programs

(MAPs). The systematic error is either root-sum-squared with the random error or,

preferably, obtained by straight addition.

A satisfactory transfer standard is formed by using two meters, often turbines,

with a flow conditioner placed between them in a tandem configuration (Figure

4.17), as already mentioned for laboratory flow facilities. Adequacy of the data is es-

tablished by specifying the number of repeat calibrations done for each flow rate and

meter configuration. These will ensure statistical significance. The Youden (1959)

procedure is recommended (Chapter 1).

4.8 TRACEABILITY AND ACCURACY OF CALIBRATION FACILITIES

For a calibration to be acceptable, the ultimate source of the measurement must

be known, and the calibration must be traceable to that standard, as in Figure 4.4.

Laboratories holding national standards exist in several countries (Benard 1988), and

the address of the nearest should be available from national government information

or from laboratories such as:

Country Laboratory

United Kingdom National Engineering Laboratory, East Kilbride,

Scotland

United States of America National Institute of Standards and Technology,

Gaithersburg, MD

National standards should themselves be traceable back to more fundamental

measures of mass, time, and length. As a result of this, a traceability chain is formed.

Each link is formed from a facility, or a flowmeter calibrated on a facility or against

a flowmeter of lower uncertainty. The chain needs to be rechecked with sufficient

frequency to ensure continuing confidence.

It should also be clear that, if a transfer standard with an uncertainty of, say,

±0.25%

is used to calibrate a flowmeter, the uncertainty in the flow rate measure-

ment made by that flowmeter will be greater than ±0.25% due to additional random

errors in the flowmeter.

Harrison (1978b) clarified the meaning of traceability with the following three

points:

a. Each standard used for calibration purposes has itself been calibrated against a

standard of higher quality up to the level at which the higher-quality instrument

is the accepted national standard. This is usually a unique item held in a national

standards laboratory, but it could, in some

cases,

be a local standard of equivalent

quality built and operated to a national specification and confirmed as operating

to that specification.

The frequency of such calibration, which is dependent on the type, quality,

stability, use, and environment of the lower-quality standard, is sufficient to

4.9 CHAPTER CONCLUSIONS 93

establish reasonable confidence that its value will not move outside the limits

of its specification between successive calibrations.

c. The calibration of any instrument against a standard is valid in exact terms only

at the time of calibration and its performance thereafter must be inferred from

a knowledge of the factors mentioned in b.

The standards for mass and time are national, derived from equivalent interna-

tional standards. The international one for mass is in Paris and for time is based on

a fundamental frequency, which is in turn broadcast nationally.

Thus calibration uncertainties achievable at present appear to be: for liquids

about 0.1% and for gases 0.2-0.3% or possibly better. When total mass or volume,

rather than flow rate, is required, these values may be improved. On the other hand,

in situ calibration is likely to be at best 2% and often 5% or lower and should be seen

as a last resort in most cases. The exception is where a meter installation is equipped

with off-takes so that a high quality transfer standard prover or meter can be coupled

in series and will result in an accuracy approaching that of a dedicated facility (cf.

Johnson et al. 1989 for further useful discussion of component uncertainties for a

gas facility).

4.9 CHAPTER CONCLUSIONS

For most readers, the essential value of this chapter will be knowledge of calibration

methods and accuracy levels, as well as signposts pointing to where to obtain further

detailed information.

For those in the business of designing, installing, and commissioning flow cali-

bration facilities, there are some fundamental questions to be addressed, not all of

which may, yet, be answerable. This chapter has attempted to flag some of these

questions and to point to relevant literature. Some of these questions concern:

• limits of accuracy for a meter in a turbulent flow;

• limits of accuracy for a test stand;

• the nature of flow diversion and its repeatability;

• the design of provers and the interpolation of pulse trains;

• ultimate in situ accuracy including

• more user-friendly tracer methods,

• more experience with retrofitted ultrasonic meters,

• improved confidence in clamp-on ultrasonic meters,

• improved probe measurements;

• theoretical optimum accuracy

traced from national standards and round-robin

meter exchange.

Because, therefore, existing methods may not meet all needs (Paton 1988), new

developments continue to appear. One relatively recent development, which is now

a standard instrument, is the piston prover. Another development that appeared a

few years ago is the gyroscopic load cell, which has been applied to the weighing of

94 CALIBRATION

collection tanks in some calibration laboratories (cf. Bigneirs 1996b proposal for a

positive displacement gas flow standard).

For low gas flows (0.05-5 ml/s), Robinson et al. (1986) suggested

• laminar flowmeters,

• bubble flow calibration (see Section 4.4.6), and

• critical flow venturi nozzle

and achieved agreement of within 1% between laminar and bubble methods. How-

ever, the bubble method, too, has its potential errors due to detergent build-up.

Finally, we may question whether there are other factors resulting from environ-

ment, impurities, or other components in the fluid that may affect the calibration

of certain flowmeter types or the behavior of the test stand.

CHAPTER

Orifice Plate Meters

5.1 INTRODUCTION

The orifice plate flowmeter, the most common of the differential pressure (DP)

flowmeter family, is also the most common industrial flowmeter. It is apparently

simple to construct, being made of a metal plate with an orifice that is inserted be-

tween flanges with pressure tappings formed in the wall of the pipe. It has a great

weight of experience to confirm its operation. However, it is far more difficult to con-

struct than appears at first sight, and the flow through the instrument is complex.

Some key features of the geometry of the orifice and of the flow through it

are shown in Figure 5.1. The behavior of the orifice plate may be predicted, but

the predictions derive from experimental observation and data. The inlet flow will

usually be turbulent and will approach the orifice plate where an upstream pressure

tapping (one diameter before the orifice plate) will measure the pressure at the wall,

that is in this case the static pressure. (Flange and corner tappings will be discussed

later).

The pressure across the pipe will have a constant time-mean value because the

only velocity across the pipe is due to turbulent eddies. The flow close to the orifice

plate will converge toward the orifice hole, possibly causing a recirculation vortex

around the outside corner of the wall and orifice plate. The inward momentum of the

flow at the orifice hole will continue downstream of the hole, so that the submerged

jet coming out of the hole will reduce to a smaller cross-section than the hole, which

is known as the vena contracta, the narrowest point of the submerged jet. Outside

this submerged jet is another larger recirculation zone, and the downstream pressure

tapping (the one after the orifice) set in the wall or in the corner by the orifice plate

senses the pressure in the vena contracta across this recirculation zone. Downstream

of this point, diffusion takes place with considerable total pressure loss.

The data on which the orifice predictions are based may be presented in three

ways (cf. Miller 1996):

The most accurate method is to use a discharge coefficient-Reynolds number

curve for the required geometry, which includes all dimensional effects and other

influences.

To reduce the number of curves, a datum curve is used in conjunction with cor-

rection factor curves. This was essentially the procedure adopted for the British

Standard 1042: Part 1: 1964.

For convenience with the advent of modern flow computers, the data are reduced

to a best fit equation. This is essentially the procedure with the most recent

ORIFICE PLATE METERS

Pressure

tapping

Pressure

tapping

Inlet

profile

Recirculation

Poor

diffusion

Plate

Poor

pressure

recovery

Figure 5.1. Diagram to show geometry and flow patterns in the orifice plate flowmeter.

versions of the International Standard, and its form will be dealt with in the

following pages.

The most common orifice plate is a metal disk spanning the pipe with a precisely

machined hole in the center of the plate; it is usually mounted between flanges on

the abutting pipes, with pressure tappings fitted in precisely defined positions and to

precise finishes. The differential pressure is measured by manometer, Bourdon tube,

or a pressure transducer, and the flow is deduced from the equations and probably

computed using a flow computer.

The importance of the orifice is its simplicity and predictability, but to achieve

high accuracy it is essential that the detailed design of the meter is the same as that

from which the original data were obtained, and that the flow profile entering the

meter is also the same. To ensure that the details are correct, the national and inter-

national standards lay down the precise requirements for constructing, installing,

and operating the orifice meter. It must be stressed that departing from the standard

requirements removes the predictability and prevents the standard from being used

to obtain the flow prediction.

In this chapter, I have sought to avoid duplicating the standards or the very

thorough presentation of Miller (1996) and instead have attempted to present recent

published information on the performance of the meter. It is, therefore, essential

that the reader have a copy of the relevant standards from which to work and, in

particular, ISO 5167-1

(BS

EN ISO 5167-1). The reader is also strongly advised to seek

out a copy of Miller (1996). Access to Bean (1971), Spink (1978), Danen (1985), and

Spitzer (1991) may also be useful because all have extremely valuable information