Badger Meter 340, 340LW, 340N2 Service Manual

Badger® Meter Accuracy Models 340, 340LW, and 340N2, Series 1550 and 2300

Btu Meter System Accuracy

Technical

Brief

The purpose of this technical brief is to explain the basis of the statement of accuracy for the Badger Meter Series 2300, 1550 and 340 Btu meters. On the basis of tests and theoretical analysis, these meters are stated to be accurate within ± 0.48%. The balance of this note justiﬁ es the claim, and provides information on the effects of the accuracy of the sensors used for input to the meters.

A method of speciﬁ cation of Btu meter accuracy has not as yet been determined by any recognized body, and such speciﬁ cation is currently reported by the various manufacturers of this type of instrument as their best estimate of the performance of the various proprietary designs they offer. The ﬁ nal accuracy of the meter is af- fected by the installation of the individual input sensor components and by the parameters under which they operate, and indeed may be dependent on the conﬁ guration of ancillary systems to which they are connected. Any instrument accuracy claim by any supplier of Btu measuring systems should be carefully studied by the potential user, to reach a clear understanding of the basis of the such claims.

The energy content in any ﬂ uid system is a function of the pressure and temperature of the ﬂ uid being monitored. The rate of energy pumped into a heated volume or out of a refrigerated volume, is a function of the difference in pressure and temperature between the inlet conditions and the outlet conditions, and of the ﬂ uid velocity. The function of a Btu meter is to transform these measurable phenomena, into a rate of energy transfer, e.g. Btu/minute.

Most commercially available Btu meters function by combining either volumetric or mass ﬂ ow rate transducer output with outputs from two temperature transducers, one located at the entrance to the metered volume and one at the exit. The effect of pressure on variation in isothermal energy content is under ± ¼% in the temperature region from 50°F to 150°F at pressures below saturation pressure at the given temperature. Thus for operation in this range, the energy content with variations in pressure is usually neglected. Errors caused by not compensating for the effect of pressure on speciﬁ c enthalpy increase rapidly as operating temperature approaches 32°F.

to raise the temperature of one pound (mass) of water exactly 1°F, without regard to the variation in mass density of water with temperature. Thus, a 1°F temperature rise for 1 gallon of water is, in these terms, 8.337 Btu. This assumption can result in large errors over relatively low temperature differentials when the water is at high input temperatures. For example, in a 50 psia (35.3 psig) system operating at 220 °F inlet and 210°F outlet, this assumption has a built-in error of 3.3%, before any consideration is given to calculation errors in the meter software, in A to D conversion of the temperature sensor signal, and in basic sensor calibration errors.

ERROR SOURCES

Errors in any non-pressure compensated Btu meter installation are the result of:

1. Built in systematic errors in the basic meter. These include: a. Method of compensation for changes in density of

the metered ﬂ uid that are temperature and pressure dependent.

b. Conversion errors in relating temperature sensor

output to Temperature. (The effect of this error in the Btu calculation in a condition of low temperature difference (∆T) between the inlet and outlet temperature sensors can be an error source, but such errors are normally far smaller than errors resulting from the basic errors in sensor calibration.)

c. Conversion errors in relating ﬂ ow signal input to a

calculated ﬂ ow rate.

2. Basic errors in transducer calibration and installation. These

include:

a. Flow meter calibration error b. Temperature sensor calibration error c. Installation wiring for temperature sensors

Error analysis has been performed on each of the above sources with the following results.

This basic data input, from the ﬂ ow rate and temperature transducers, is manipulated mathematically to provide a rate of energy transfer within the monitored volume. While the effect of pressure on energy content is not monitored, an average value of Btu per pound mass is used in the calculations as a means of compensation of the pressure effect. This simpliﬁ cation results in some loss in accuracy in the instrument reading as discussed above. The actual error will vary depending on the method used by the instrument manufacturer to compensate for this unavoidable simpliﬁ cation required by using temperature transducers only.

Many Btu meters using volumetric ﬂ ow rate sensors take an even more simplistic approach, assuming that 1 Btu is the heat required

BadgerMeter, Inc.

1. Systematic errors in the Btu meter:

a. Compensation for density changes:

The Series 340, 1550 and 2300 Series Badger Meter Btu meters convert the volumetric ﬂ ow rate entering the metered area to an enthalpy ﬂ ow rate by converting the volumetric rate at operating temperature, to a mass ﬂ ow rate based on the speciﬁ c density of the ﬂ uid at the incoming temperature. The resulting mass ﬂ ow rate is then converted to an incoming Btu (enthalpic) rate by using an adjusted average speciﬁ c enthalpy of water over the temperature range from 32°F to 250°F and the pressure range of 15 to 50 psia. The ﬁ tting constants are derived from ASME Steam Tables, Ed IV, published by the American Society of Mechanical Engineers (1983). Applied to a metered area operating within the range of 32 - 250°F, with a 5 psia DP and a 10°F ∆T between the inlet and outlet, the algorithm as implemented has an inherent error of ± 0.43% maximum over the entire

DTB-051-01

4-09

range. Standard error of the algorithm results based on actual steam table values is 0.237%.

b. A/D Conversion errors, temperature sensors:

By actual test in the Badger Meter laboratories, using a precision resistor decade box to simulate temperature sensor resistance, the following % error data over the input range of 32°F to 250°F data was developed:

THERMISTORS: (used in Badger® Series 2300, 1550, and 340)

10,000Ω @ 25°C (77°F) thermistor temperature transducers are commercially available as ±0.8°F interchangeable devices. Analysis of resistance/temperature data indicates that the error band actually achieved is a smooth non-linear function decreasing from ± 1.01% @ 32°F to ±0.57% @ 212°F and then increasing to ±1.17% @ 250°F.

PLATINUM RTDs: (optional in Series 2300)

0.00385Ω/Ω/°C, 100Ω @ 0°C, RTD transducers are commer-

cially available as conforming to IEC 751. Analysis of resistance/ temperature data indicates that the error band actually achieved is a smooth non-linear function monotonically increasing from ± 0.45°F (1.41 %) @ 32°F to ±0.70°F (0.58%) @ 120°F and then increasing to ± 1.0°F (0.40%) @ 250°F.

c. A/D Conversion errors, ﬂ ow rate calculation:

Flow rate is measured by the internal system clock which is accurate within ±3 microseconds. The usual frequency range for DI sensors is from 3 Hz to 200 Hz, with concomitant periods of 250 milliseconds to 5 milliseconds. The greatest % error thus occurs at the 200 Hz level or ±0.06%. Calculations are carried out to 7 decimal digits for a maximum error of 10

-5

% (0.00001%).

The total basic error of the instrument is found by adding, in quadrature, the individual errors listed above, or ±0.48% for the model described in 1.a above

2. Basic errors in transducer calibration and installation: a. Flowmeter calibration error:

For the purpose of this note, ﬂ owmeter calibration er- ror is the variation from true ﬂ ow rate and that resulting from the use of the calibration constants supplied by the manufacturer. This error affects the reported values of Btu/minute directly, and is independent of the instrument itself. All other things being equal, the % error in ﬂ owmeter calibration produces the same % error in Btu output.

b. Temperature sensor calibration errors:

Temperature sensor calibration error affects the accuracy of the reported energy ﬂ ow, with increasing error as the operating ∆T decreases. For example, in a system operating at a 5°F ∆T using two sensors each with an error of ± 1°F will produce an error of ± 40%. The practice of trimming the paired temperature sensors so that their temperature output is identical at one measurement point can reduce the effect of calibration error, provided that this is done at the mean operating temperature. This zeroing practice could actually increase the error in the readout if performed at temperatures outside the operating range.

NICKEL RTDs: (optional in Series 2300)

A multitude of Nickel RTDs are available, frequently to proprietary designs, although DIN 43760 may govern the basic speciﬁ ca- tions. There is little available information on the temperature/ resistance tolerances achieved with this sensor, and thus little can be said here. The rule of thumb should be to use as precise a sensor as is economical for the installation. (Of course, the same recommendation applies for thermistors and platinum RTDs, as well.) Note that use of nickel RTDs should be referred to the instrument manufacturer, with temperature/resistance data, so that the proper conversion algorithm can be supplied with the delivered instrument.

c. Installation wiring for temperature sensors:

Wiring of the temperature sensors and the ﬂ ow rate transducer should follow the instrument suppliers wiring speciﬁ cations. Generally, for the ﬂ ow rate transducer, shielded twisted pairs of appropriate size should be used with careful attention to any special grounding instructions.

The temperature sensor wiring deserves special attention. Wire sizes appropriate to the basic sensor resistance should be used. Splices in either or both leads from each sensor must be avoided, and termination connections should be carefully used. 100Ω RTDs should be wired to apply at least a 3-wire bridge connection. Thermistors and 1000Ω or higher nickel RTDs are less sensitive to lead resistance. Thermistors are usually wired using a two wire twisted shielded pair. 1000Ω and higher RTDs are usually used to avoid the 3 or 4-wire bridge type of wiring conﬁ guration.

Badger® and Data Industrail® is a registered trademark of Badger Meter, Inc.

Due to continuous research, product improvements and enhancements, Badger Meter reserves the right to change product or system specifications without notice, except to the extent an outstanding contractual obligation exists.

Please see our website at www.badgermeter.com

for specific contacts.

BadgerMeter, Inc.

P.O. Box 581390, Tulsa, Oklahoma 74158 (918) 836-8411 / Fax: (918) 832-9962 www.badgermeter.com