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

Подождите немного. Документ загружается.

5.9 ACCURACY UNDER NORMAL OPERATION 117

good predictions using wet gas. Majeed and Aswad (1989) appear to have achieved

agreement between measured and predicted flows based on a correlation by Ashford-

Pierce when using oil field data. They included a computer listing.

5.9 ACCURACY UNDER NORMAL OPERATION

To achieve the accuracy set out in the standards, it is necessary to construct and

install the meter to the detailed specification of the standards.

From the equation

the standard provides a formula for the total uncertainty (cf. Equations 1.A.7 and

7.17 for alternative symbols) in the mass flow rate:

where a, (=CE) the flow coefficient, has now been eliminated. To obtain the overall

uncertainty, the uncertainty in each term is obtained and combined according to

Equation (5.26).

It is instructive to put some values into this equation. Let us set out some values

and the likely errors in them:

Parameter

€

Value

100 mm

50 mm

0.5

0.6051

1.0328

1,000 kg/m

Uncertainty %

0.2

0.1

0.5

negligible

0.1

Comment

Will depend on pipe

specification.

Machine to 0.002 in. or 50 /mi.

Equal to d/D.

From ISO formula or table

(value of

is assumed, but

iteration is normally required).

Incompressible liquid.

Possible variation due to

temperature or purity.

Ap 31.54 kPa 1

From these values, we obtain

= 9.75 kg/s (Re = 1.24 x 10

)

{

1 1/2

(0.5)

+ (0)

+ (0.133)

(0.2)

+ (2.133)

(0.1)

+ -(I)

+ -(0.1

4 4

= 0.89%

118 ORIFICE PLATE METERS

The estimate of uncertainty for gas metering is likely to be considerably larger than

this figure. In a paper describing the specification, installation, commissioning,

and maintenance of typical orifice metering stations for the British Gas national

high pressure transmission system, with flows up to 1.4 x 10

std m

/h at pres-

sures up to 69 bar, Jepson and Chamberlain (1977) concluded that, to achieve

uncertainty of less than ±2%, a very rigorous checking procedure was needed

to ensure that the complete measuring system remained in specification all the

time.

Miller (1996) provided a number of special corrections: for steam quality with

gas-liquid flows, for saturated liquids with up to 10% saturated vapor, for drain

and vent holes, for water vapor, and for indicated differential when the pressure-

measuring device is at a different elevation to the differential pressure device and

the pressure lines are filled with fluid of a different density.

Ting and Shen (1989) commented that the majority of natural gas flow measure-

ments in the United States were determined by orifice meters. They led a systematic

study of measurement by 152.4-mm (6-in.), 101.6-mm (4-in.), and 50.8-mm (2-in.)

meters in the Reynolds number range 1 million to 9 million.

Ting and Shen used Honeywell smart static and differential pressure trans-

ducers, which had microprocessor-based built-in pressure and temperature com-

pensation, higher span-turndown ratio, improved accuracy, and easy rangeabil-

ity. Bias was quoted as better than ±0.15% for differential pressure and preci-

sion as ±0.015%. A precision aneroid barometer of 0.1% full-scale uncertainty

was used for atmospheric pressure. Careful calibration of these instruments took

place, and the paper implied careful experimentation, the only weakness be-

ing that the definition of the inlet pipework was not entirely clear. Their tests

showed that the 101.6- and 50.8-mm orifice discharge coefficients agreed with

the ANSI and ISO standards within the estimated uncertainty levels of 0.35%

with 95% confidence level. However, the 152.4-mm meter agreed for low and

medium beta ratio, but for a beta ratio of 0.74, ANSI and ISO gave a discharge

coefficient about 2% low. Their plots also, helpfully, show the divergence be-

tween the two previous standards, which is not more than about 0.2% over the

range.

5.10 INDUSTRIALLY CONSTRUCTED DESIGNS

Orifice Plates

Orifice plates can be obtained from various manufacturers machined to the

requirements of ISO 5167 (BS 1042) in stainless steel 316, 321, 304, Hastelloy, tanta-

lum, Inconel, and plastics such as polytetrafluoroethylene (PTFE), polyvinylchloride

(PVC),

and polyvinylidene fluoride

(PVDF).

Also available are orifices that are remov-

able from the holding

ring,

with integral gaskets that maybe spiral wound in stainless

steel or of

PTFE

or graphite filled. Size availability extends beyond the common stan-

dard's range going down to a 25-mm bore or less. The orifices will then be stamped

permanently with detailed information (e.g., tag number, pipe size, rating, orifice

5.11 PRESSURE CONNECTIONS 119

diameter, material), usually on the up-

stream side. (Figure 5.14). The information

will also state which is the upstream side of

the plate.

Orifice Plate Carrier Assemblies

Some examples of orifice carrier assemblies

are shown in Figure 5.15(a). The materials

of construction are generally carbon steels,

but stainless steels and duplex steels can be

provided. Carriers can be split ring or one

piece integral design.

Orifice Metering Run Assemblies

Orifice metering run assemblies are con-

structed to the appropriate standards and

may incorporate flange tappings [Figure

5.15(b)]. Although plates are relatively easy

to install and remove, there are occasions

when a plate needs to be inspected without

disrupting the flow or depressurizing the

line.

For this reason, at least one manufac-

turer (Figure 5.16) has developed a system

for removing and replacing plates without

shutting the line down. This consists of a

means for sliding the orifice plate in and

out, possibly with a rack and pinion mech-

anism, and a dual chamber pressure sealing

. ,., ., , . . , Figure 5.14. To indicate the main features of indus-

system while the plate is removed. , .

, ' ,

. , , .

. .

J r

trial orifice plates (reproduced with permission of

Daniel Europe Ltd.).

Sizing

The plate manufacturer may offer a sizing service based on a computer program that

undertakes the iteration and optimization, an otherwise laborious procedure.

5.11 PRESSURE CONNECTIONS

Tapping Orientation

The tapping positions should be such that any unwanted component of the line

fluid or any second phase in the line fluid will not enter the pressure tapping of the

impulse line or become trapped in the impulse line connections. For vertical lines,

any position is satisfactory (Miller 1996). Where the line is not vertical, the following

recommendations should be noted to reduce the chances of accidental blockage (BS

1042:

Part 1: 1964 and Miller 1996):

• For liquids, within an angle of 45° above or below the horizontal;

120 ORIFICE PLATE METERS

Figure 5.15. Commercial orifice plate assem-

blies (reproduced with permission of Elsag

Bailey-Bush Beach Engineering Division): (a)

Carriers; (b) Metering runs.

Z- Gaskets

Orifice Flanges

to ANSI

16.36

Gaskets

Orifice Flanges

to ANSI B16.36

• For dry gases, between the horizontal and vertical upward with a sugges-

tion that for clean noncondensible gases the tapping should be in a vertical

position;

• For moist gases, between an angle of 30° above the horizontal and vertically

upward; and

• For steam and other vapors, horizontal only.

These requirements are illustrated in Figure 5.17. Where a drain hole is provided

through the orifice plate, the single tapping should be orientated so that it

between

90° and 180° to the position of the drain hole.

The standard also recommends that, where there is a danger of blockage, provi-

sion should be made for rodding out the tapping from outside the line.

5.11 PRESSURE CONNECTIONS 121

FRONT PARTIAL SECTIONAL ELEVATION

SIDE SECTIONAL ELEVATION

Figure 5.16. Commercial system for removing and replacing plates while on line (reproduced

with permission of Daniel Europe Ltd.).

Piezometer Ring Arrangements

In pipe lines of 150 mm (6 in.) or greater,

or in lines where one hole may become

blocked, it may be useful to use a piezome-

ter ring, as shown in Figure 5.18. In the pres-

ence of steam or other vapor flows where

condensation may occur, a piezometer ring

may form an unwanted trap for condensate.

The manifold cross-section should always

be equal to or greater than the total area

of the individual tappings which it serves.

The triple T arrangement may be preferred,

and, in any case, traps for condensate and

adequate bleed points should be provided.

In laboratory applications, the use of trans-

parent tubing is recommended.

Layout of Impulse Lines

It should be remembered that, even though

the simple arrangement of manometer

leads,

with the same fluid in each, results in

a deflection, the same as that which would

occur for direct connection to the meter

±45° Sector

Tapping

Normal

clean

liquids

Tapping

Clean noncondensible

gases

Tapping

Vapors and

condensible gases

Figure 5.17. Diagram to show positioning of the pres-

sure tapping for nonvertical lines.

122

ORIFICE PLATE METERS

Pressure

tappings

Pressure

tappings

Figure 5.18. Diagram to show piezometer ring con-

nections: (a) Conventional; (b) Triple T.

line,

any variation in the connecting fluid

due to air, etc., can cause variation in den-

sity and a difference in the pressure across

each line. The effects to be guarded against

are (BS 1042: Part 1: 1964):

• Temperature difference between the

lines leading to a density difference;

• Discontinuity in the impulse line fluid

due to a second component, be that

solid, liquid, or gas; and

• Blockage of any sort including solidifi-

cation of the impulse fluid.

The impulse lines should be as short as

possible, at the same temperature (which

may require lagging together), and at a suf-

ficient gradient to allow drainage, etc., as

required.

Miller (1996) should be consulted for

detailed guidance on impulse lines, sealant

liquids, and transmitter positions. A typ-

ical arrangement for steam is shown in

Figure 5.19.

5.12 PRESSURE MEASUREMENT

The main methods used for pressure measurement are described in Noltingk (1988)

and are manometers, mechanical devices that deflect under pressure, and electrome-

chanical pressure transducers.

A MANOMETER

In a manometer, the height of a column of liquid provides a measure of the pressure

in a liquid or gas.

B MECHANICAL DEVICES THAT DEFLECT UNDER PRESSURE

One such device is the Bourdon tube, which has a flattened tube wound into an

arc.

The tube unwinds under pressure. Another design uses diaphragm elements

made up from pairs of corrugated disks with spacing rings welded at the central

hole.

Pressure will cause the assembly to elongate, and this will in turn be used

as a method of registering the pressure change. Other devices based on expanding

bellows or diaphragm elements are also used.

C ELECTROMECHANICAL PRESSURE TRANSDUCERS

This is the most important and accurate device for the future and is in a state of

continual development. Various methods have been used to obtain an electrical

signal from a mechanical deflection. Some of these are capacitance transducers,

5.12 PRESSURE MEASUREMENT

123

Condensate level ^

Flow

Temperature Transmitter

Mains Supply

Figure 5.19. Installation for steam (reproduced with permission of Spirax-Sarco Ltd.). [Note:

Tappings are often on the same side of the pipe.]

piezoresistive strain gauges, and piezoelectric and resonant devices. In one design,

pressure applied to a diaphragm causes it to deflect and to exert a force on a can-

tilever beam that has a strain gauge bonded to it and that provides an electrical

signal. Smart devices can provide condition monitoring, self-diagnosis of temper-

ature, memory, and reference voltages and will provide ranging and temperature

compensation. Measurement uncertainty can be as low as, or lower than, 0.1% of

span. Regular recalibration at 1- to 6-month intervals is recommended.

124

ORIFICE PLATE METERS

READOUT

ELECTRONICS

Figure 5.20. Typical example of the installation of a density measuring cell in

an orifice metering line (courtesy of the Roxboro Group PLC).

5.13 TEMPERATURE AND DENSITY MEASUREMENT

Methods of temperature and density measurement are described by Noltingk (1988).

A typical installation arrangement for a density cell in a metering line is shown

in Figure 5.20. The cell is arranged to project into the line so that it is at the gas

temperature, and the gas is extracted from the line, passed through the cell, and

returned to the line.

5.14 FLOW COMPUTERS

Flow computers are microcomputers programmed to obtain flow from sensors mea-

suring differential pressure, pressure, temperature, density, or other parameters, and

are of particular importance in the calculation of the orifice plate flows. When used

with smart transmitters, they may offer on-line optimization of differential pressure

measurement. They contain stored information on the conversion of frequency and

analogue signals to actual units, and they contain algorithms for interpreting den-

sity, etc.

Taha (1994) described electronic circuitry to obtain mass flow from an orifice

plate with differential pressure, pressure, and temperature sensing.

5.15 DETAILED STUDIES OF FLOW THROUGH THE ORIFICE

PLATE,

BOTH EXPERIMENTAL AND COMPUTATIONAL

An early study of flow through an orifice plate using laser doppler techniques was

reported by Bates (1981) for a BS 1042 orifice plate with fi = 0.5 in the range of

5.15 STUDIES OF FLOW THROUGH THE ORIFICE PLATE

125

Reynolds number 67,600-183,000. The shape of the profiles upstream at 0.535D

and 0.32D show no recirculation zone in the plate corner, but this may be because

the region of any such recirculation is closer to the plate than was investigated.

Downstream at 0.5D the recirculation region has a zero velocity point at about 25%

radius in from the pipe wall, and this moves to about the 20% radius position at

0.9D downstream.

Morrison et al. (1990b) reviewed past work on flow patterns in orifice meters,

both theoretical and experimental. They used a laser doppler anemometer (LDA) to

obtain detailed flows in an orifice. They also obtained (Morrison et al. 1990a) wall

pressure distributions, and some of these are shown in Figure 5.21(a) for a p = 0.5 at

Re = 122,800 both for conditioned flow and for three angles of swirl. Figure 5.21(a)

shows the pipe wall pressure distributions with a minimum pressure at about D/2

downstream of the orifice plate. Note that data were not obtained between 0.125D

upstream and 0.25D downstream of the plate. Figure 5.21(b) shows the variation of

the velocity on the centerline of the orifice meter, the high peak value at the vena

contracta, and possibly a suggestion of poor diffusion.

All conditions

xlD

Diameters

from

orifice

plate

1.0

0.5

(b)

xlD

Figure 5.21. Experimental curves (after Morrison et al. 1990a, 1990b). (a) Pres-

sure distributions for conditioned flow and for three angles of swirl from pipe

wall tappings for an orifice with p = 0.5 and Re = 122,800. (b) Center-

line velocity distribution using a laser doppler anemometer for an orifice with

£ = 0.5 and Re = 18,400.

126

ORIFICE PLATE METERS

0.615

0.610

0.605

0.600

0.595

Reader-Harris

Computed values

for smooth pipe

Stolz

Figure 5.22. Computed values of discharge coefficient C, for an orifice with

ft = 0.7, corner tappings, and smooth pipe (after Reader-Harris 1989).

Erdal and Andersson (1997) provided a brief review of some computational fluid

dynamics (CFD) work. They emphasized the sensitivity to the use of a particu-

lar code (cf. Spencer et al. 1995). Davis and Mattingly (1997) claimed agreement

between computed and experimental discharge coefficients to within about 4% for

p in the range 0.4-0.7 and

between 10

and 10

. Sheikholeslami et al. (1988) and

Barry et al. (1992) claimed an agreement of about 2%. Patel and Sheikholeslami

(1986) computed the discharge coefficient for Re = 2,500,000 with p = 0.4 to

within 1.5%.

Reader-Harris and Keegans (1986) and Reader-Harris (1989) claimed that dis-

charge coefficients could be calculated to within 0.64%. Figure 5.22 shows some

of Reader-Harris's computations using the

—

e turbulence model with a computer

package (QUICK). In Figure 5.22, computed results for a smooth pipe and a p = 0.7

are compared with the equation in the standard at that date (Stolz) and with an

improved equation (cf. Reader-Harris and Sattary 1990) from which the current ISO

equation has developed. Where two symbols occur at one value of Reynolds number,

the higher is for the more refined grid. Reader-Harris only considered that he had

obtained independence from grid size for Re > 3 x 10

. His results appear to give

encouraging agreement with the modified equation.

Spearman et al. (1991) described laser doppler velocimeter (LDV) measurements

downstream of a Mitsubishi flow conditioner and of an orifice plate in a combined

package.

Erdal and Andersson (1997) indicated the problems which still exist in obtain-

ing adequate modeling of the flow through an orifice plate. They commented that

the predictions revealed the need for considerable expertise and care before results,

especially for pressure drop, could be predicted with confidence.