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

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4.2 APPROACHES TO CALIBRATION

CALCULATION OF UNCERTAINTY BUDGETS

Test Rig:- 8 Tonnes [Low Fiowrate]

Date:-

21.05.97

Measurement quantity:-

Mass

Flowrate:-

Target Weight:-

Typical Density:-

Diversion Time:-

4000

998.0000

667

l/s

kp/m

sees

Symbol

S°

(Wx)

U(Wx)

Source of uncertainty

Calibration of standard weights

Discrimination of weighscaie

Linearity of weighscaie

Hysteresis of weighscaie

Temperature stability of weighscaie

Repeatability of weighscaie

Combined uncertainty

Expanded uncertainty

Value

±Q

1000

100

200

1000

Probability

Distribution

normal

rectangular

normal

rectangular

normal

normal (k=2)

Divisor

2.0

1.73

2.0

1.73

2.0

1.0

U;(W

)

±g

578

116

500

775

1550

Density (densitometer method)

Symbol

DTX

(Dx)

U(Dx)

Source of uncertainty

Calibration of Density Transducer

Temperature compensation

Pressure compensation

Long term stability

Combined uncertainty

Expanded uncertainty

Value

±kq/m

0.200

0.025

0.005

0.200

Probability

Distribution

normal

rectangular

normal

normal (k=2)

Divisor

2.0

1.73

1.0

Ui(D

)

±ko/rn

0.100

0.014

0.003

0.116

0.154

0.307

Time

Symbol

T~DIV

(Tx)

U(Tx)

Source of uncertainty

Calibration of Timer

Discrimination of Timer display

Temperature stability of Timer

Diverter operation

Combined uncertainty

Expanded uncertainty

Value

0.001 %

0.1 ms

0.001 %

126 ms

Probability

Distribution

normal

rectangular

normal

normal (k=2)

Divisor

2.0

1.73

1.0

u,(T

)

sees

0.003

0.000

0.004

0.073

0.146

Summary - Fiowrate measurement

Symbol

(FLOWl

U(FLOW)

Source of uncertainty

Combined uncertainty (FLOW)

Expanded uncertainty (FLOW)

Probability

Distribution

normal

normal (k=2)

Uj(FLOW)

±l/s

0.0016

0.0032

Ui(FLOW)

±%

0.027

0.054

Summary

Quantity passed measurement

Symbol

(FLOW)

U(FLOW)

Source

uncertainty

Combined uncertainty (QUANTITY)

Expanded uncertainty (QUANTITY)

Probability

Distribution

normal

(k=2)

Uj(FLOW)

±l/s

0.0015

0.0030

Uj(FLOW)

±%

0.025

0.049

Figure 4.3. Example of calculation of uncertainty budgets in flow rate measurement. Note that

the symbols, not included in the nomenclature of this book, are defined in the table. Summa-

tion of uncertainties is by means of root-sum-squares. (Reproduced with permission of Danfoss

Flowmetering Ltd.).

CALIBRATION

MASS

DENSITY

TIME

NPL

Stainless steel

Ref, weight STI/831596

Ref. setSTI/831310

Ref. setSTi/852248-860416

South Yorkshire

Trading Standards

NAMAS Laboratory

Measurement uncertainty

+/- 50g/tonne

Cast iron

1000kg weights

DANFOSS

collecting tank

Combined uncertainty

for

MASS measurement

+/-0.02%

NPL

i i

Schlumberger Industries

NAMAS Laboratory

Measurement uncertainty

+/-

0.2

kg/m.3

Schlumberger 7830B

Density transducer

DANFOSS

Densitometer

Combined uncertainty

for

DENSITY measurement

+/- 0.03%

DANFOSS

gravimetric flow

rig

Combined uncertainty

for

measurement

QUANTITY PASSED

Electroservices

(Instruments)

Ltd

NAMAS Laboratory

Measurement uncertainty

+/-1

part

in 10

Philips PM6669

Timer/counter

DANFOSS

Diversion timer

Combined uncertainty

for

TIME measurement

+/- 0.02%

Figure

4.4.

Traceability

measurements made

on a

commercial

test facility. (Reproduced

with permission

Danfoss Flowmetering Ltd.).

Master Meters: For a simple facility to compare two meters, the master meter

offers a suitable transfer standard.

In Situ Calibration: Although there are various ways of calibrating on site, the

ultimate accuracy is usually far less than on a calibration facility, and the skill and

experience needed is greater. It may, therefore, be preferable to use the term in situ

verification.

4.3 LIQUID CALIBRATION FACILITIES 69

Dry Calibration: Dry calibration is not strictly calibration. An orifice meter, if

correctly constructed according to the standards, can be measured, and from the

measurements it should be possible to deduce the flow for a particular pressure

drop.

The same is true of other standard meters such as the venturi, nozzle, and

critical flow venturi nozzle. Other meters are less predictable. No flow test is used,

and so dry

calibration

is something of a misnomer, since we are really talking about

the ability of standards or theory to predict performance. The reader is referred to

the appropriate chapter for the likely predictability of particular flowmeters such

as the electromagnetic and ultrasonic.

4.3 LIQUID CALIBRATION FACILITIES

4.3.1 FLYING START AND STOP

Figure 4.5(a) shows the outline of such a facility, which is most commonly used for

water. This is known as the static weighing method because the water is diverted

into a tank for a fixed period, and the tank can then be measured with the water

static in the tank. In its ideal form, there would be a header tank of large enough size

so that change in level was negligible.

header tank, with a weir to retain constant

head, is shown in Figure 4.5(b). The flow from this, by gravity, would pass through

the flowmeter under test and thence to a control valve before discharging into a

diverter valve. This valve would either allow the flow to drop into a weighing tank

or into the sump tank. Water in the weighing tank would be drained into the sump

tank once the weight had been taken. The beauty of this design is that the flow

would be extremely steady due to the header tank and errors would be restricted to

the measurement of the time during which the flow was diverted into the weighing

tank and to the weight

itself.

Figure 4.6 shows a diagram of the diversion process and

the source of timing error. Mattingly (1982) elaborates on the error, and the reader

is referred to the original article for full details.

The essential problem is that it is physically impossible to divert the flow to

and from the weighing tank instantaneously. The time at which the diversion takes

place is, therefore, not at a precise moment, and the changing flow is illustrated in

Figure 4.6. The timer is set to start when volume a equals volume b. This is when

the lost water shown by volume b is just balanced by the gained water in volume

a, which passed before timing began. The same compromise is needed at the end

of the timing period with c equal to d. The setting is often, but not necessarily, the

same at the beginning and end of the diversion (cf. Buttle and Kimpton 1989 for

the design of a diverter).

In order to check the validity of this compromise method, one test is to divert

many times after short periods, comparing the result with one diversion over

period

equal to the total of the short runs. This will tend to emphasize the errors in the

diversion, and an adjustment can be made to minimize them. However, there may

be variation in the diversion flow depending on flow rate, and this will require a

more sophisticated compensation method.

It is reasonable to assume that the time measurement can now be several orders

of accuracy higher than the other measured quantities. The errors will therefore

CALIBRATION

HEADER

TANK

OVER FLOW

LINE

CALMING

BAFFLES

CONTROL

VALVE

FLOWMETER

UNDER

TEST

DIVERTER

VALVE

(a)

CALMING

BAFFLES

OVER FLOW

TO SUMP

TO CALIBRATION

LINE

(b)

FROM

SUMP

Figure 4.5. Flying start and stop liquid flow calibration facility with static weighing: (a) Outline

diagram; (b) Typical constant head tank design (after Harrison 1978a).

4.3 LIQUID CALIBRATION FACILITIES

TIME

Figure 4.6. Diagram of the flow division for a diverter valve in a flying start and stop facility

(after Harrison 1978a).

come from the weight measurements and the setting of the diverter. Scott (1975a)

suggests that the true weight of water is about

1/1,000

greater than the apparent

weight. For very accurate weighing, therefore, the upthrust due to immersion of

steel test weights and the water in the weigh tanks in air will need to be allowed for.

The typical overall accuracy of such a facility is currently of order

0.1%

(cf. Kinghorn

et al. 1981 in which the U.K. primary standard is described and an uncertainty of

0.1%

or better is claimed).

One variant on the weighing method is to use a dynamic weighing system where

the flow enters the one tank, and a fast drain is available in this tank. The flow enter-

ing the empty tank rises in the tank, and the weight is measured (usually electroni-

cally) at the start of flowmeter output measurement. At the point at which sufficient

water has been collected, the second weight is measured, and the drain valve is

opened. Pursley (1986) advises that the tank should have vertical sides and that the

liquid jet should enter vertically. There are problems with the dynamic nature of this

at high flow rates: Does the inertia of the weighing tank affect the measurement?

Does the jet momentum have any effect?

Another variant is known as the substitution weighing method. At the start, the

weighing machine has the nearly empty tank and a calibrated weight of the same

value as the liquid that will enter the weigh tank. The weight is removed, and the wa-

ter is allowed to enter until the balance is restored. If standing start and stop is used,

then the final balance can be perfected with additional small weights (Pursley 1986).

Gyroscopic weighing cells have been applied in recent years to increase the per-

formance, but load cells may offer an adequate alternative.

In practice, it is often inconvenient to use a header tank and necessary, therefore,

to use some means (a pump) for recycling the liquid. This in turn is likely to make

it more difficult to ensure that the flow is absolutely steady.

Scott (1975a) encouraged protection of the calibration weights and their integrity

by keeping them in soft material.

CALIBRATION

4.3.2 STANDING START AND STOP

The standing start and stop amounts to allowing fluid to pass through the meter for

a fixed time and then comparing the total registered by a reference meter with the

amount collected. The amount collected could be measured either as a volume or a

weight. The problem with this method is that the meter must follow the changing

flow rate accurately, and many meters are unable to do so. Figure 4.7 is a diagram

to indicate the variation between the meter's response and the actual changing flow

rate.

Each meter will differ according to how it measures the varying flow. There will,

therefore, be an error in the measurement in most cases, particularly if the meter is

of poor accuracy at low flows.

For standing start and stop, it is clearly essential to be sure that the same amount

of fluid has passed through the meter as arrives in the mass or volume measur-

ing tank. This usually requires particular attention to the design of weirs and sight

glasses, which confirm that the level in the tank is the same both before and after

the run and that the flow stops quickly. Examples of weirs are shown in Figures

4.8(a, b). It also requires care to ensure that valves do not leak. The block and bleed

is one system to achieve this [Figure 4.8(c)].

A typical measuring vessel for volumetric measurement is shown in Figure 4.9.

The vessel is calibrated using weighed quantities of distilled water at a known tem-

perature. The top and bottom of the vessel are of small diameter so that small volume

changes cause measurable level changes compared with the large volume contained

in the center portion of the vessel. The initial fluid level is usually fixed by a weir

and sight glass. The fluid is then allowed to enter the vessel and is stopped when

it rises into the narrow top section. Against this, there is either a calibrated sight

glass or a means to measure the surface level to obtain the final volume. It has been

found that the vessel will need to be filled and emptied three or four times before it

has wetted sufficiently on the inner surface to ensure that a consistent and correct

reading is obtained. When a consistent reading is obtained, the value can be used

to calibrate the flowmeter.

FLOW

RATE

CONSTANT

FLOW RATE

U^^ FLOW DUE TO

VALVE OPENING ^

FLOW DUE TO

VALVE CLOSING

^ METER INDICATION

ON START UP

METER INDICATION '

AT END OF RUN

TIME

VALVE STARTS

TO OPEN

VALVE STARTS

TO CLOSE

Figure 4.7. Discrepancy between changing flow rate and the meter's response.

4.3 LIQUID CALIBRATION FACILITIES

SIGHT

GLASS

INLET TO

VOLUMETRIC

VESSEL

MINOR

WEIR

SYPHON-

BREAKER

HOSE

MAJOR

WEIR

SIGHT

GLASS

DRAIN

(a)

FLOWS

TO WEIGH

TANK

(b)

FLOW

OUT

(c)

Figure

4.8.

Examples of

weirs,

swan

necks,

and block-and-bleed valves in calibration (after

NEL).

(a) Arrangement for precise starting level for volumetric tank, (b) Arrangement for standing start

and stop gravimetric system, (c) Block-and-bleed valving system.

The viscosity of the liquid will also affect the emptying of the vessel, and as a

result Pursley (1986) recommends a maximum viscosity of 5 cSt for this calibration

method.

Proving vessels of this type are used to calibrate meters to uncertainties of

±0.1%

for custody transfer of hydrocarbon liquids. A typical vessel could have a capacity

of 500 liters. Such vessels, of various sizes, have been used for a variety of liquids

including foods.

Another type of volumetric facility uses the falling head method. A tall tank is

filled with liquid. The liquid is allowed to flow through an outlet pipe to a flowmeter.

CALIBRATION

SCALE -*•

BREAK

SYPHON

WEIR

MAJOR

WEIR

SIGHT

GLASS

DRAIN

Figure 4.9. Volumetric proving vessel for standing

start and stop calibrations (after NEL).

The volume between two level switches is

known, and the meter is calibrated against

this volume. The disadvantage of this

method is that the flow rate may change

slightly as the head falls.

4.3.3 LARGE PIPE PROVERS

Figure 4.10(a) shows a typical design of

prover, and Figure 4.10(b) is a photograph

commercial system. The prover consists

of a carefully constructed length of pipe.

In a bidirectional prover, the sphere passes

both ways. A sphere is projected into the

pipe,

and its passage is recorded past two set

points where there are detectors. When it

passes the first, the meter-pulsed output is

counted until the sphere passes the second,

and the total number of pulses is obtained.

The volume swept is known, and the time

taken is recorded. With this data, the flow per pulse can be checked with the prover

volume, and the actual flow rate can be obtained. Unidirectional provers are also

available. Instruments of this type are commonly included in hydrocarbon metering

stations, where oil and hydrocarbon products are transshipped, and fiscal and cus-

tody transfer requirements come into play. Figure 4.10(b), a photograph of a prover,

shows the valving arrangements to bring the prover into play. Figure 4.10(a) also

shows the separate flanged connections for use when the prover is being calibrated.

This may be done by connecting up a mobile proving vessel or transfer standard

flowmeter. The calculation of the internal volume of the prover by measurement,

even if the accuracy is achievable, would seem unlikely to be an economical method

(cf. Paulsen 1991 on prover ball material problems and materials).

Claims are made that these devices can achieve uncertainties of the order 0.1%

(or less) with calibration.

4.3.4 COMPACT PROVERS

The large bulk of the pipe prover, which leads to weight (e.g., in oil platform instal-

lations) and space considerations, and also the amount of liquid needed to complete

the calibration have led to the design of very compact piston provers [Figure 4.11

(a)].

These devices still depend on the swept volume of a tube but use a piston moving

over a much shorter distance. Figures 4.11(b)-(d) show the stages in the measure-

ment cycle. Thus, with great manufacturing precision, it appears that the perfor-

mance of these compact provers can rival that of the large pipe prover. Compact

provers will, certainly, target the same level of accuracy as pipe provers in order to

provide a realistic alternative.

One problem that arises in the use of these compact prover results is the small

amount of fluid that passes. Thus, if a flowmeter produces a pulse for a certain

volume of fluid passed, the number of pulses resulting from the fluid passed by a

compact prover may be very low, causing a discrimination error. This has led to

4.3 LIQUID CALIBRATION FACILITIES 75

SPHERE

DETECTORS

TO CONNECT

A CALIBRATION

DEVICE

FLOW

OUT

METER

PROVER

TO BE

BY-PASS CALIBRATED

VALVE

(a)

Figure 4.10. Large pipe provers:

(a)

Schematic

of bidirectional prover (after NEL);

(b) Pho-

tograph

of a

bidirectional prover (reproduced

with permission of Daniel Europe Ltd.).

Mobil OSO Nigeria Coodftnsaifl Meiering Sy«t«m

(b)

special techniques

overcome

the

problem, such

pulse interpolation (Furness

and Jelffs 1991)

order

achieve

the

required 0.01% resolution (based

10,000

pulses

for the

pipe prover). Reid

and

Pursley (1986) used

double chronometry

method

for

pulse interpolation [Figure 4.12(a)].

As the

first prover volume switch

is activated,

two

timers

are

started.

The

first timer

(A)

runs

for the

full period

76 CALIBRATION

ACTUATOR

CYLINDER

NITROGEN

HYDRAULIC

FLUID

HYDRAULIC

MOTOR & PUMP

OPTICAL

SWITCHES

ACTUATOR

PISTON

PNEUMATIC

SPRING

PLENUM

PISTON

POPPET VALVE

(CLOSED)

(a)

HYDRAULIC

RESERVOIR

Start of Run

Optical Switch

EndofRun

Upstream or Standby

Position Optical Switch

Optical Switch

Poppet Valve (Open)

Spring

Plenum

Pressure

(b)

Downstream

Outlet

Actuator

Piston

Hydraulic

Solenoid

(Closed)

Prover Piston

- Upstream Fluid Inlet

Figure 4.11. Compact prover (reproduced with permission of Fisher-Rosemount

Ltd.):

(a) Prin-

cipal components; (b) Standby mode; (c) Start of run; (d) End of run.

the piston movement, from activation of the first prover volume switch until the

second prover volume switch is activated (volume D). The second timer runs until

the first turbine pulse and starts again at the second prover volume switch, running

until the subsequent turbine pulse. Alternatively, the second timer (B) runs from the

first turbine pulse after the first volume switch until the first pulse after the second

volume switch (C pulses in total). Thus the full time, the number of pulses, and the

fractional period between pulses are all obtained. The turbine pulses per unit volume

K can be found by multiplying (Time A/Time B) by the total pulses C and dividing

by the displacer volume D [Figure 4.12(b)].

An advantage of the compact prover (Furness and Jelffs 1991), especially for

meters delivering products to ships, is that it can be easily cleaned between grades