V J: NBS TECHNICAL NOTE 1041

*°*tAU O* *

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Cryogenic Fluids Density

Reference System:

Provisional Accuracy Statement

(1980)
NATIONAL BUREAU OF STANDARDS

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Cryogenic Fluids Density Reference System:

Provisional Accuracy Statement (1980)

J.D. Siegwarth

J.F. LaBrecque

BATJOItAL BUBEA.U OF JTTANDARDB LIBRART JUL 1 3 1981

Hot (LCC --' CtUOO

no. iM\

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

4.,.- ?

"I* ' *J6

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued April 1981
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 1041

Nat. Bur. Stand. (U.S.), Tech. Note 1041, 60 pages (April 1981)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON 1981

For sale by the Superintendent ot Documents, U.S. Government Printing Otfice, Washington, DC. 20402

Price $3.75 (Add 25 percent for other than U.S. mailing)
CONTENTS

I

Page

INTRODUCTION 1

2. DESCRIPTION OF THE IMPROVED DENSITY REFERENCE SYSTEM 3

2.1 Sample Container 4

2.2 Safety Considerations in the DRS Design 8

3. THE DRS DENSIMETER & INSTRUMENTATION 12

3.1 The Reference Densimeter 12

3.1. a The Densimeter with the Original Balance 12

3.1.b Addition of a New Balance 13

3.1.c Calibration of the Balance 16

3.2 Sample Temperature 17

3.3 Sample Vapor Pressure 17

4. MEASUREMENT PROCESS PARAMETERS 18

4.1 Bounds for Systematic Errors 18

4.2 Calculation of Random Uncertainty for DRS 21

4.3 Uncertainty Statement 29

5. MEASUREMENT PROCESS CONTROL 31

6. SUMMARY 32

7. ACKNOWLEDGMENTS 33

8. REFERENCES 33

9. APPENDICES 34

9.1 A Comparison of the DRS Densimeter and an Industrial

Reference Densimeter 34

9.1. a Introduction 34

9.1.b Industrial Reference Densimeter 35

9.1.c Results 38

9.1.d Summary 42

9.1.e References 42

9.2 True Mass of the Silicon Single Crystal 42

9.3 Gas Buoyancy Corrections 45

9.4 Linearity of the Electronic Balance 47

9.5 Weight Certificate 50

9.6 The Change in Volume of the Silicon Crystal for Hydrostatic

Compression and Thermal Contraction 50

9.7 Density of Single-Crystal Silicon 51

m

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM:

Provisional Accuracy Statement (1980)

J. D. Siegwarth and J. F. LaBrecque

National Bureau of Standards

Boulder, Colorado 80303

The improved Density Reference System, the reference densimeter, and the

method of determining sample density are described.

The uncertainty of the density reference system is ± 0.055%. The contribution from the estimated systematic error in density was ± 0.022%. The estimated

uncertainty caused by random error is three times the standard deviation of 0.011%

and is based on sixty-three measurements of the densities of saturated liquid

methane. The total density uncertainty is taken to be the sum of the systematic

3

and random errors. This applies to the density range of 400 to 480 kg/m at

pressures from 0.8 to 4 bar absolute and temperatures between 109 and 128 K. This

3

accuracy statement is expected to apply over ranges of at least 400 to 1000 kg/m

in density, 77 to 300 K in temperature, and 0.8 to 7 bar in pressure though the

accuracy over these ranges has not been verified.

* Compared to the original, this improved density reference system has greater

accuracy, speed, reliability, and flexibility.

Key words: densimeter; density reference system; liquid methane; LNG.

This work sponsored by the Gas Research Institute.

WITIillMMf

1. INTRODUCTION

In an earlier report [1], we described the density reference system (DRS)

used to test some commercially available densimeters in liquefied natural gas

(LNG). These tests involved comparing the density measurement by the densimeter

under test to the density measured by our DRS densimeter in an equilibrated liquid

sample. This earlier report gives an estimate of the uncertainty associated with

a density measurement by the DRS densimeter used as standard for comparison. The

uncertainty of a single determination of the density at the instrument under test

was taken to be ± 0.076%. This includes a systematic error of 0.028% and a

random error of 0.048% which is three times the estimated standard deviation of

0.016%. Four different commercial densimeters were tested and the results reported [2]. The major problem with the commercial densimeters divulged by these

tests and some later measurements was the calibration of the commercial instrument

by the manufacturer. None of the factory calibrations were entirely suitable at

LNG temperatures at the time of these tests.

Because of this calibration problem, we offered a calibration service through

"transfer standards." We calibrate a manufacturer's instrument, which is then

installed in a calibration system at his plant and used to calibrate instruments

he builds. He would then periodically return the transfer standards for recalibration. The process would eventually yield data on the stability as a function

of time of the instruments used as transfer standards. The manufacturer's calibration system and methods can be evaluated by testing in the DRS some of the

instruments calibrated by the manufacturer.

iymiyiwiMHtMmiMiJi''tMJi^uu.^ wmnR
The DRS sample container used in the tests of these first four commercial

densimeters was designed around the densimeters tested. The densimeters in some

cases were specially built. The first version of the DRS was too inflexible to

deal with any design modifications of the commercial densimeters.

A more flexible sample container dewar system has been constructed and is

in current use in densimeter evaluation and calibration work. This DRS design

with a companion liquid sample storage dewar should be suitable for a commercial

calibration facility. We find this sample container more temperature stable

than that of the original DRS. The new DRS is described in more detail in

Section 2.1. Safety considerations made necessary when using combustible gases

are detailed in Section 2.2.

The DRS densimeter has been modified several times before, during and since

the rebuild. Details of these modifications and a shift in the measured density

after the rebuild are discussed in Section 3, along with the other measuring

devices.

In Section 4, the measurement process is discussed. The associated systematic errors are identified, their magnitudes estimated and the overall error

estimate of a density measurement is given. This estimated deviation of the

density for one measurement from the true value is ± .055% for pure methane at

the normal boiling point. The maintenance of this accuracy is discussed in

Section 5.
Since the improved version of the DRS was completed, a number of additional

commercial densimeters have been tested. Each test consisted of a series of

measurements in pure liquid methane, then about 5% propane and 1% to 2% nitrogen

are added to simulate an LNG mixture and another series of measurements was

made. This mixture was used because both propane and nitrogen can be added

without any danger of solids forming in the fill line since both have freezing

points below 110 K. Measurements in an LNG-like fluid permit LNG densimeters to

be tested in a fluid around the temperature and density in which they will be

used. The tests in liquid methane provide a fluid with a known temperature

density relationship, provided 99.97% pure methane is used, to which the DRS

density value can be compared. Also, the methane density data along with the

LNG like-liquid density data provide a much wider range of densities for determining the calibration equation for the instruments under test.

2. DESCRIPTION OF THE IMPROVED DENSITY REFERENCE SYSTEM

This improved DRS operates on the same principle as the original. Densimeters under test are compared to the density reference system densimeter in a

very nearly isothermal liquid sample. The DRS densimeter is an Archimedes type

densimeter consisting of a single crystal silicon float weighed while immersed

in the sample liquid by an electronic balance. Density measurements are made

over an approximately 15°C temperature range along the saturation curve of the

sample liquid. The measurements are made with the sample at equilibrium after a

change of sample temperature has been affected either by a liquid nitrogen

cooling coil or an electrical resistance heater. The sample equilibrium is

obtained by stirring the liquid with a turbine pump. Equilibrium conditions
remain for the period of time required for measurement without stirring because

the heat leak to the sample has been reduced to a small value with radiation

shields and other heat flux interrupting devices.

2.1. Sample Container

A schematic of this improved DRS is shown in Figure 1. The sample container consists of a 25.4 cm OD, 1.6 mm wall stainless steel tube extending

760 mm down from an ambient temperature stainless steel flange to a 3 mm thick

dished bottom head. A similar stainless steel vessel or vacuum jacket 35.6 cm

OD forms an outer wall enclosing the sample container. The space between these

two vessels contains radiation shields and is maintained at a pressure below

-3

10 * pa by an oil diffusion type vacuum pump. All the stainless steel

to stainless steel joints are heliarc welded. All flanges and other gasketed

joints in both the insulating vacuum jacket and sample container employ "0" ring

seals. Unlike the sample container of the original system, which required a low

temperature indium wire vacuum seal to close it, all demountable seals on the

new DRS are located at ambient temperature. A 73 mm high aluminum ring, clamped

between the sample vessel and vacuum jacket flanges provides six 38 mm ID flange

covered access ports into the vacuum space. Through these flanges pass the

liquid nitrogen line to the various cooling coils and the gas vent lines from

these coils shown in Figure 1 and the electrical leads for heaters and thermocouples. The connection to the vacuum pump is also through one of these ports.

All lines and leads are such that they can be readily disconnected to permit the

counterbalanced dewar assembly to be lowered enough that the top flange is below

the bottom of the sample space. The time to disconnect the few lines, remove

the nuts from the twelve 13 mm studs clamping the sample container to the top
Electronic

Balance

Top Flange

Sample mlet —*- \

N 2 Vent—«

LN 2

Inlet —-—

Reference Weight

Heat Exchanger

Vapor

Pressure Bulb

Sample Container

Silicon Crystal

Vapor

Pressure Bulb

Heater

N

£

Vent

Radiation Shields

-Dewar Wall

Cooling Coil

Radiation Shield

Cooling Coil

Sample

Cooling Coll

Liquid Sample

Densimeters

Under Test

Vacuum Jacket

Figure 1. Schematic diagram of the improved Density Reference System.

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flange and lower the dewar is a few minutes. A valve between the vacuum jacket

and the vacuum line disconnect permits the dewar to be lowered without breakinq

/ the insulating vacuum. I

Another 73 mm high aluminum ring is located between top of the sample

container flange and the top cover of the sample container. Again, six flange

covered 3.8 mm diameter access ports provide locations to introduce electrical

leads, the vapor pressure bulb tubes shown in Figure 1 and for pressure gauge

connections. The sample vessel seals are "0" rings. The sample pressure is

maintained above atmospheric pressure in case small leaks are present.

The top plate of the sample container has a port for the DRS densimeter, a

153 mm access port shown in Figure 1 and a port for the stirrer drive shaft (not

shown). The access port flange cover can be modified as required to provide

mountings for various insertion type densimeters. Figure 1 illustrates the

mount for a vibrating cylinder densimeter. An "0" ring sealed gland on the

access flange provides a gas tight stem seal. To avoid a seal on a rotating

shaft, the stirrer drive shaft is coupled magnetically from the exterior to the

interior of the sample chamber.

The evacuated annular space between the sample container and the vacuum

jacket contains all the refrigeration systems used to condense and maintain the

sample at cryogenic temperature. All the refrigeration is supplied from an

adjacent LiL storage dewar through a vacuum insulated transfer line into the LN^

inlet shown in Figure 1. This inlet is connected to all the various cooling

coils and the amount of cooling by each coil is regulated by throttling the

independent hL gas vent lines from the various coils. The coil on the radiation
shield, Figure 1, is vented continuously and the temperature of this polished

copper shield is maintained below the sample temperature. In Figure 1, the

dewar wall cooling coil attached to the shield mounting ring a few centimeters

above the sample level is maintained at a temperature a few degrees above the

sample temperature to minimize the heat conducted down the sample vessel wall.

Within the sample vessel, a copper radiation shield, with an aluminum foil

shield on top, interrupts the heat radiated down from the top of the sample

holder. A second radiation shield is placed a few centimeters above the lower

shield. The operating temperature of the lower shield is normally a few degrees

above the liquid temperature. The cooling coil and heater on the sample vessel,

Figure 1, are used only to change the sample temperature.

The sample is condensed into the DRS from gas bottles using liquid nitrogen

via the counterflow heat exchanger shown in Figure 1. This parallel tube heat

exchanger, composed of two 8 mm I.D. copper tubes about 7 m long soft soldered

together along their length, will condense the 16 liters required in the sample

holder in about an hour. The actual time depends on the LN

? supply rate. Most

joints in these coils and lines are soft soldered and all coils and heaters are

soft soldered to the surfaces to which they transfer heat.

Each time the density of an LNG or methane sample is measured, the temperatures of the sample near the top and bottom are also determined by measuring the

methane vapor pressure in the vapor pressure bulbs shown in Figure 1. The vapor

lines are connected through a selector valve to a quartz spiral Bourdon tube pressure gauge. The temperature difference, AT, measured is nearly always less than

20 mK and usually less than 10 mK. This low temperature gradient is obtained

without the low speed stirring used in the original system [1]. The temperature
drift during the measuring period is comparable in magnitude to AT. Temperatures

of the radiation shields and t^he annular shield support ring, shown in Figure 1,

are monitored by thermocouples to provide information for minimizing the heat

leak to the sample. The temperature and pressure of the gas surrounding the

reference weight are recorded and used to provide the gas buoyancy correction to

this weight reading.

A system of similar design, but perhaps larger, should be suitable for a

manufacturer's calibration facility. To speed up the operation, a manufacturer

could employ additional cryogenic vessels into which he can transfer the calibration liquids. Heated N

? gas or additional electrical heaters can be used to

rapidly warm the sample holder to change densimeters and an LN

? spray nozzle

could be used to rapidly cool the calibration dewar, or the instruments calibrated could be introduced and removed from the top, without warming the whole

dewar. Either way, some modest care is required to ascertain the dewar is

properly purged and inerted before introducing a cryogenic sample.

2.2 Safety Considerations in the DRS Design

Manufacturers of densimeters suitable for cryogenic use have demonstrated

some reluctance to employ calibration methods using cryogenic liquid combustible

gases. In this section, we discuss safety considerations incorporated by NBS

in the DRS.

An experimental system using combustable gases can be made safe by eliminating any opportunity for a combustible mixture of air and the gas to form, or

by eliminating all ignition sources in any area combustible mixtures form. The

8
el iminatiori of combustible mixtures is the preferred way to make a system safe.

Thus, the DRS sample handling system is gas tight and evacuated before introducing the combustible gas. However, should a leak develop in the system or an

accident occur, a combustible mixture could result so ignition sources have been

minimized in the laboratory. Since one can never be assured that ignition

sources are completely eliminated, the probability of a combustible mixture

forming from an accident and the lifetime of such a mixture, if formed, is

minimized by a laboratory exhaust fan. This fan has the capacity to change the

room air about every 12 minutes.

The schematic of the combustible gas handling system for the DRS shown in

Figure 2 illustrates the essential safe handling features. All lines that may

or do involve gas exhausting from the sample container are connected to a stack

that vents above the roof of the building. The sample container, approved for

operating pressures to 10 bar, has a 10 mm ID relief line connected to the vent

with a relief valve set just above the highest operating pressure. In the very

unlikely event that the sample vessel ruptures and dumps the contents of the

sample into the vacuum jacket, a 25 mm diameter relief line ducts the resulting

vapor through a low pressure relief valve to the vent. The vacuum pumps maintaining the insulating vacuum also exhaust to the vent line. The vessel vacuum

pump exhaust is connected to the vent because the system fill procedure requires

the vessel to be evacuated, filled with the sample gas, then evacuated and

filled twice more before condensing the sample. When the tests are completed,

the liquid is blown through valve 5, Figure 2, via evaporating coils. The gas

remaining is pumped out and the sample container is back filled with hL gas

during warmup. This pump also serves to purge the gas sample supply lines when

changing or starting gas supplies. Valve 6, Figure 2, provides a route to

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10
release sample gas into the vent. Check valves could be placed in both the

valve 5 and 6 lines to preclude air entering the sample container if these

valves should be accidentally opened with lower than atmospheric pressure in the

sample container. The solenoid valve 12 prevents complete loss of vacuum in the

event of a power failure.

The liquid sample is often left in the sample container overnight unattended. Liquid nitrogen is passed through the sample and radiation cooling

coils at a rate sufficient to remove the heat leak to the sample. The vapor

pressure is held at about 1% bar absolute by a feedback system that senses this

pressure and supplies sufficient additional heat to the sample heater, Figure 1,

to maintain the set pressure.

Small quantities of gas escaping from the DRS would be swept out of the

room by the ceiling vent fan. To reduce the chances of igniting any larger

spill, mainly "explosion proof" electrical equipment operates in the room during

tests. The stirrer motor case is purged with compressed air. All the electrical

cabinets are enclosed and purged with compressed air. Access to the laboratory

is limited and since the floor is conducting, conducting shoes or ground straps

are used by anyone regularly in the laboratory. A combustion gas detector

connected to a warning horn is located near the DRS.

The vapor pressure bulbs contain less than a liter of STP methane, but this

m result in a very high vapor bulb pressure if not properly vented to the

:orage cylinder during warmup. Two bypass relief valves between the vapor

ilbs and the storage cylinder eliminate this potential hazard.

11
THE DRS DENSIMETER AND INSTRUMENTATION

The DRS densimeter described in the Technical Note 698 [1] has undergone

several modifications since that report was prepared. A major modification

occurred when the electronic balance used to weigh the single crystal was

replaced.

3.1. a. The Densimeter with the Original Balance

Since manually disconnecting and connecting the silicon single crystal and

reference weight caused occasional discontinuities in the electrical balance

reading, pneumatic drive cylinders were connected to both actuators. These

cylinders were mounted on the scale case and were sufficiently slow moving to

gently place the weights on the balance while not shaking the balance mounting.

This modification decreased the scatter of the methane density values determined

by the DRS relative to the Haynes-Hiza [3] density values calculated from the

average sample temperature.

When the sample containment portion of the DRS was reconstructed as described in Section 2, the silicon crystal disconnect mechanism was rebuilt. The

suspension wire in the vapor region was replaced by a 1.6 mm diameter thin wall

stainless tube and the assembly connecting the suspension to the bottom of the

balance was modified. The balance was readjusted for corner load effects.

These adjustments, when properly made, make the balance weight reading independent of the position on the pan a weight is placed.

12
The density of methane in the new sample holder as determined by the DRS

densimeter was offset by approximately 0.07% relative to the Haynes-Hiza [3] and

Goodwin [4] values for the density calculated from average temperature for six

subsequent methane fillings. The vapor bulb positions were altered and the

methane in the bulbs changed without affecting this offset. To ascertain the

pressure gauge had not shifted calibration, it was compared to the barometric

pressure and found to be in agreement. The temperature difference represented

by the difference between the barometric pressure and the vapor pressure gauge

reading amounted to less than 0.01 K. The methane density difference corresponding to 0.01 K is too small for the DRS densimeter to measure. This offset will

be discussed in more detail below.

3.1.b. Addition of a New Balance

Recently an electronic balance with sufficient range to directly weigh the

128 g crystal to 1 mg has become commercially available. This balance has other

advantages; it is more compact and much less sensitive to vibration than the

original balance. It is lightweight and can be transported in any orientation

without securing the moving parts. The DRS densimeter has been rebuilt to

incorporate one of these electronic balances. Conceptually, and in actual

design, this densimeter differs little from the original densimeter. However,

because it has sufficient capacity to weigh the silicon directly, a reference

weight [1] with the attendant buoyancy correction is no longer required. We have

retained the reference weight as a means of calibrating the balance and monitoring the calibration during tests.

13
A suspension system consisting of two cages, one for a reference weight and

one for the silicon crystal, \is attached to the underside of the balance. The

/ reference weight cage is about 20 cm below the balance and in the sample gas

space while the silicon crystal cage is 76 cm below the balance and completely

immersed in the sample liquid. The section of the suspension passing through

the liquid surface is a wire. The suspension is always attached to the balance.

Lifting mechanisms permit the weights to be attached and detached from the

suspension independently. Surface tension effects on the suspension should

cancel since weight off (zero) readings are included in the measurements and

subsequent density calculations.

The liquid density p is now given by the relation (equation 4, Reference 1)

with M replaced by (M -M ): a a ao

1 - (M -M ) a ao

7 ,-.. p " p

s —

M

(1)

s

where p is the silicon density, M is the silicon crystal mass in vacuum, M is

s s a the apparent mass when weighed in the liquid and M is the balance reading with

the crystal and reference weight disconnected. This latter value nearly always

is zero to ± 1 mg as the balance is tared (zeroed) with the silicon crystal

removed before the density readings are taken.

The systematic offset in the observed density of liquid methane compared to

Haynes-Hiza discussed in section 3.1. a remained and even increased slightly with

the introduction of the new balance. The reference 1 data are probably in error

because of an undetected corner loading error in the balance. We cannot directly

confirm this supposition since we cannot recover the old balance adjustment.

14
Because of the way the silicon crystal and the reference weight were

placed on the balance in the original system, any corner loading error must have

had some effect on density measurement. The reference weight was placed on the

pan and the crystal was suspended from a part of the balance assembly well below

the pan. This vertical offset in attachment points probably did not contribute

a systematic error to the density determination, but the relative displacement

in the horizontal plane of the attachment points that existed could affect the

results. We placed 100 g weights on the pan which were weighed relative to a

counterweight such that the balance reading was on scale on the 20 g range of

the balance. However, the pan was only corner load adjusted so 20 g could be

read to within a milligram, thus a mass value error approaching 5 mg at the edge

of the pan was possible for a 100 g weight even for a properly adjusted balance.

The results of a series of tests of the balance indicated some corner loading

error was still present even after the balance was readjusted.

Comparison tests between the DRS densimeter and a silicon crystal densimeter built for a commercial calibration facility showed agreement to about

0.01%. These results are shown in Appendix 9.1 and lend added support to the

contention that the systematic shift in the measured methane densities relative

to the measurements reported in Reference 1 resulted from an error in the adjustment of the original electronic balance.

In some later tests, a third silicon densimeter, the Portable Reference

Densimeter (PRD) was compared to the DRS densimeter in the DRS [5]. The PRD and

DRS densimeters are similar in design, but the silicon single crystal was obtained

from a different source. The density readings were indistinguishable.

15
3. I.e. Calibration of the Balance

Even though the present DRS densimeter no longer requires a reference

weight to determine LNG density, we have retained this weight for calibrating

the balance and monitoring the calibration. The balance is calibrated by

weighing the reference weight in air and adjusting the balance to read the

apparent true mass in air. The reference weight still weighs approximately the

same as the silicon crystal when the latter is submerged in liquid methane.

In the course of taking data at each sample temperature setting, this reference weight is measured and recorded. The apparent mass is corrected for gas

buoyancy and compared to the true mass value. This correction is readily made

for methane or methane-nitrogen samples but not for methane-propane-nitrogen

samples because propane suppresses the methane vapor pressure by an uncertain

amount and because the gas mixture is slow to reach equilibrium. The method of

calculating the buoyancy correction is detailed in Appendix 9.3. The reference

weight is located in a region in which the gas temperature is -10 to -20°C,

which contributes to the buoyancy correction uncertainty in the ternary mixture

even though the gas temperature is measured and applied to the buoyancy calculation.

The reference weight is weighed periodically in air to monitor the balance

calibration. The calibration can be adjusted if needed, or a calibration factor

can be introduced. In the six months of operation, the calibration has not been

adjusted. A calibration correction amounting to 1.7 mg was included in the

calculations for two fillings. For later fillings, a correction was not needed.

The results of monitoring the reference weight during tests are presented in

Section 4.

16
Corner loading errors are unlikely in the new silicon crystal weighing

system since both the reference weight and the silicon weight are suspended

below and placed on the suspension axial to the suspension wire, thereby eliminating essentially all possibility of corner loading errors.

3.2. Sample Temperature

Temperature is measured using vapor pressure thermometers. One thermometer

bulb was located at the bottom of the sample volume and the other near the top.

3 Each thermometer contains a few cm of liquid methane. Pressure communicates

from each thermometer bulb via a 1.6 mm O.D. stainless capillary tubing through a

selector valve to a quartz-spiral bourdon tube pressure gauge. The temperature

range used is 110 K to 126 K. The accuracy of the quartz-spiral gauge is 0.01% of

full-scale pressure as determined by a master piston gauge calibrated by NBS.

This pressure uncertainty is equivalent to 0.01 K at 110 K and 0.003 K at 125 K.

3.3. Sample Vapor Pressure

The liquid sample vapor pressure was measured using a bourdon tube pressure

gauge with a to 4 bar range and an 0.2% of full scale accuracy according to the

manufacturer. The vapor pressure is used only for a small buoyancy correction to

the reference weight and need not be accurately known.

17
4. MEASUREMENT PROCESS PARAMETERS

\

4.1. Bounds for Systematic Errors

The primary sources of uncertainty in the density measurements can be

obtained from examination of the measurement equation. The knowledge of the

basic uncertainties of the separately measured quantities such as the masses and

densities, can be combined to give an estimate of the systematic errors in the

density as measured by the density reference system.

Equation (1), the measurement equation, gives the density p as a function

of several independently measured variables.

P = e<Wao'<VT) - C2)

The temperature is included here because the density at the test densimeter

is the quantity we wish to know and a temperature gradient may exist.

The uncertainty in p, arising from uncertainty in some variable x, for

example, can be evaluated from

6p = || 6x (3)

The total uncertainty in density is taker, to be the square root of the sum of

the squares of the various contributions,

r=^(StiT

18
This is the propagation of error relationship for systematic error when the

variables are independent and the magnitudes of the relative errors are small so

that second order terms are negligible [6].

Table 1. Systematic errors

Variable, x 8p/3x Max Magnitude* 6x Sp/p (%)*

M

s (P-P s )/Ms -0.015 cm" 3 0.0005 0.0019

M

a -ps /M

s -0.0184 cm~ 3 0.001 g ±0.0046

M

ao P

s /Ms 0.0184 cm" 3 0.001 g ±0.0046

p

s P/P s 0.17 6x10 5 g/cm3 ±0.0026

T 8p/aT 0.0016 g/cm3 K 0.05 K ±0.02

total , fi"om ±0.022%

equat ion (4)

*At the smallest measured density, -\-0.4 g/cm3

.

Table 1 is a summary of the most significant contributions to the total

systematic uncertainty in density as estimated from the various contributing

sources. The first column, labelled x, identifies the variable for which the

uncertainty is calculated. The second column is the partial derivative of the

liquid density with respect to the variable of the first column and the third

column gives its maximum magnitude. The column labelled 6x is the estimated

largest error of that variable.

The systematic error, 6x, of M , is estimated from the standard deviation

of the weighings and the uncertainties of the 5 weights used (Appendix 9.2). The

estimate of the systematic error for M and M is the resolution of the electronic J a ao

19
balance or ± 1 mg. The calibration of the electronic balance is monitored by

weighing the reference weight\as discussed earlier which permits holding this

uncertainty within the balance resolution. The error estimate of the silicon

crystal density covers uncertainties due to the temperature and pressure effects

(Appendix 9.6) as well as uncertainties in published densities (Appendix 9.7).

The combined temperature gradients and drift during data acquisition

measured by the vapor pressure thermometers rarely exceed the value of 0.05 K.

We assume for the purposes of error estimation a AT no larger than 0.05 K. This

temperature difference is dependent on the heat input of the instruments under

test and AT is usually less than half this value. A density difference resulting

from this temperature difference can be calculated from the methane properties

[3,4].

Average System

Temperature Ap/p for AT = 0. 05 K

110 K 0.017%

127 K 0.02%

These uncertainties are the same size as claimed for the original DRS and

are most certainly overestimated. To confidently reduce these values, however,

we would prefer to have a more detailed knowledge of the temperature distribution in the sample during a density measurement. Our present accuracy needs do

not warrant increasing the complexity of the system by the addition of more

thermometers. An additional systematic error results from the uncertainty in

the absolute value of T. This is not included in the table since it makes no

20
contribution to the systematic error when densimeters are being compared. When

liquid methane density measurements are being compared with those of other

workers, however, we have a 0.01% contribution to the systematic error at 110 K

that decreases to less than 0.001% at 127 K.

4.2. Calculation of the Random Uncertainty for the DRS

The accuracy and precision of the DRS densimeter is essentially independent

of liquid composition. Its accuracy and precision depend primarily upon the

accuracy and precision of its balance and how well the weight and density of the

silicon crystal are known. The ability to make an accurate reading will, of

course, depend upon conditions within the sample holder. The liquid needs to be

relatively quiet, well mixed and of a fairly uniform temperature in the area in

which the densimeters are being tested. It should be sufficient, then, to test

the DRS densimeter in a liquid whose density is known. Saturated liquid methane

was chosen as its density, as a function of temperature, has been determined by

Goodwin [4] and Haynes and Hiza [3], and it is the major constituent of LNG.

The present evaluation of the improved DRS is based on data taken for

fifteen fillings of the liquid sample holder. Ten of these fillings were made

after the new balance was installed; so we will be looking at the continuity of

the DRS through a balance change.

The major interest in commercial densimeters is their performance in an

LNG-like mixture. We first fill the DRS sample holder with liquid methane, take

a series of measurements over the range of about 110 to 125 K, then add nitrogen

(about 1% to 2%) and propane (about 4% to 6%) to simulate LNG and take another

21
series of measurements in the same temperature range. We then have data comparing the DRS densimeter to the \Haynes-Hiza methane densities and an evaluation of

the densimeter under test in an LNG-like mixture.

We compare the values of density as determined by the Haynes-Hiza method

for saturated liquid methane and the corresponding values determined by the DRS

densimeter. The vapor pressure bulbs, from whose average value the Haynes-Hiza

density is calculated, bracket the volume containing the silicon crystal. The

Haynes-Hiza value, then, is more of an average reading, while the DRS densimeter

registers a point value.

A continuing calibration test of the new DRS balance is made as discussed

in Section 3. I.e. The silicon crystal apparent mass in the sample liquid is

100 g to 107 g for the mixtures being considered, and the mass value of the

reference weight is approximately 103 g. This weight is used before filling the

system, during the density measurements, and after the system is emptied to

determine the calibration of the DRS balance.

Figure 3 is a plot in chronological order of the differences between the

Haynes-Hiza values for saturated liquid methane and the corresponding values

determined by the DRS densimeter. The symbols alternate from filling to filling

to distinguish the separate fillings. The measurements in the first five fillings

counting the groups from the left, were by the old DRS balance after readjusting

it for corner loading. The jump between the fourth and fifth filling is attributed to a change in the calibration of the balance since the densimeter had been

dismantled and reassembled between these fillings.

22
cc

LUD

DCO

-J<ooooIo e

uj/6>i 'saa-HH

<o o

4J HI

U

O co O- C 4-> * = i a a» *->

-O CO «4_ -O C <T3 a> >>+>

4- tO (TJ

COm qj q; e •-» <«

a, o * -£=

4-> <S> o

••-> o

<o £ c <o

i- ii— T3

J- <T3 t- O t—

co

O

I— CO O

.o a> E -c

CO

O)

CO CO 8 c

-C o

CO 0131-

.c i- it3 <1> cr a> r- i.0)

a> >

.C <T3 +>

a> c .C

cj +J

O)3 E

•M

O • oJ- 00

a> en

X3 i— ° >>•«= i— A3

<C 3 U i-

•f- -O O) (1) O U_

CO

C7> C

a; en

+-> c

i_ i—

fO <—

Q--rco .C 3 u o <c

<D

CO

L.

OO 2

a> "a u a> c +>

i- i—

0) 3

•i- (O

f>

O £ C CT> O 3

tO

J= 5-

-4->

O Ol c en O r—

co <3j <D U

i— c

en cj c s-

•i- <*- I- cj_ +> -r- X3 oc <U (O en

i_

•t- a>

co <v 3 Q.

aj

u +-»

v.

C7>

23
The apparent shift occurring after the installation of the new DRS balance

probably results from some remap ning corner loading effects for the old balance

as discussed in Section 3.1.b.

The average difference between the Haynes-Hiza and the DRS densimeter

values using the new balance is approximately 0.09% larger than the 0.01% difference reported in Reference [1]. The difference for the old balance readjusting was approximately 0.07% larger than previously reported [1].

The average difference between the methane densities determined by the

Haynes-Hiza method and those determined by the DRS densimeter show the latter to

be approximately 0.1% lower. That the DRS densimeter is now measuring density

correctly is supported by the data for fillings 11 through 14. The meter under

test for these fillings was also an Archimedes densimeter using a silicon crystal

See Appendix 9.1 for details of this comparison. The average difference between

the corresponding density values given by this meter and the DRS densimeter is

.004% ± .017% (95% C.I), i.e., the density values were not statistically distinguishable. The comparison between the DRS and Portable Reference Densimeter,

to be reported later, also shows the present DRS densimeter to be correctly

measuring the density.

Each time a commercial densimeter was tested in pure methane, data were

taken to permit comparing the DRS measured density to the Haynes-Hiza density

calculated from the average temperature. A series of density measurements with

each liquid sample were taken over a range of temperatures by either heating or

cooling the sample to a target temperature, waiting for equilibrium while

stirring the sample, and taking the desired schedule of readings with the

24
stirrer off. The target temperature was only nominally achieved at equilibrium.

The sample was stirred again and the readings duplicated. The duplicate readings

provided assurance that the DRS and test densimeters had reached equilibrium. A

lack of equilibrium was never noted. The second reading also reduced the chance

of losing a data point through a reading error or a malfunction of a test densimeter, which are often sensitive to bubbles. The temperature drift between the

duplicate sets of readings for the new DRS had a standard deviation of approximately 0.1 K with the second reading averaging 0.05 K higher.

The random errors of the duplicate density values obtained from a densimeter

as described above would be expected to correlate more closely with each other

than with values at different temperatures. In fact, the correlation between

duplicates for the difference between the Haynes-Hiza and DRS densities is about

0.5. A correlation of 1.0 would mean the duplicates provide the same information,

while a correlation of would mean the duplicates provide independent information on the process. Since we have much more data than needed for the error

estimate and the correlation between the duplicate data at each temperature

complicates the analysis, only the first of each duplicate reading has been used

to analyze the DRS.

The model used to analyze the methane data is:

H(T) - YCT)^. - u(T) + a. + e.. (5)

where Y(T).. is the jth density determination by the DRS on the ith methane

filling for temperature T; H(T) is the corresponding density value derived from

the Haynes-Hiza relationship, p(T) represents any systematic difference between

25
the two methods at temperature [T, or. represents a shift in the mean for measurements on the ith filling, and e\ . the random contribution to the jth measurement

made on the ith filling.

The solid diamonds in Figure 3 show the average difference for each filling

and show the shifts, a. in the mean of the Y. . from one fillinq to the next.

Considering the data before the new balance, the only significant shift is

between the 4th and 5th fillings, and this probably resulted from dismantling

the densimeter in between the two fillings. The data taken after the installation of the new balance show the shifts from filling to filling to be rather

small for the first five fillings, but somewhat larger for the last five. The

a. appear to be random in nature and have an estimated standard deviation of

3 3

.013 kg/m (.0031%). A 99% upper confidence bound for this value is .036 kg/m

(0.0082%). What accounts for the shifts in the a. is at present unknown. The

deviations of the measured values of the calibration weight from the true mass

value of 102.9022 g, AW, are shown versus chronological order in Figure 4. A

buoyancy correction must be made to the balance reading to obtain the true mass

value (see Appendix 9.3). The changes in the mean of the observed true mass

values of the calibration weight from filling to filling are statistically significant, but they are not well correlated with the a., and if they were, their

estimated standard deviation could account for only a 0.0020% component in the

variation of the a., leaving additional effects to account for 0.0024%. A difference between the temperature of the liquid at the crystal and the average

temperature given by the two vapor pressure bulbs might also contribute to this

uncertainty if the difference were to persist over the time of the run (filling).

26
1 1 1 1

°°°° s

o t6<D

<

—

o ff o —

—

8

§

*/

_ - 8 ° —

-

8 °o~

o

°^ 8

—- ° 0c*°°

• ••

CO cm

6uj 'AAV

0> f— u «— C C T-

•v- to <*- ^-

V) ID Ol

4-> -O 4->

l/» 1> aizIO c o JC f— iring m

equ

diff

age. o 3 O */> *- "O J~ 0> 0) CM t»- 1— > cc

LU

1- o> •<- 0> 3 C U JZ Q

DC

»o E c

o

o

i i. o j E QJ Q. O

O

QJ 0> (/) *~ 3 -O "O •— c tn

«3 l) (5 C

_i > 3 — i— "O i— o <

E <T3 <U »— 3 > WiCO o

O <*- u E <-

to 3 c_> .c •^ > 3 U

o

o o T3 O "C3 •»- CO _J !-> O to o u s~ ro o z $- «3 o E

O Q.--- T3 o o

o E ovfO O "O

.C O C

Dl Oi C <D X -.-COO.

O) (T3 I- O

o o

5 -c x:

QJ 01 .C CM

Referenc liquid

m

shown

in

ings.

T

o

i-3

27

IIIMIMllMIIIWIlHIIIIIIllPlPllilHI'll
Based on the differences shown in Figure 3, the within filling standard

\ 3 deviation for fillings through the 15th is estimated to be 0.0216 kg/m (.0051%)

I 3 with a 99% upper bound of 0.0277 kg/m (.0065%). This is a conservative estimate.

A least squares lot of the DRS density data for fillings 1 through 5 to the

temperature of the saturated methane after removing the filling-to-filling shifts

results in the equation,

D(T) = 526.935 - 0.410996 T - . 0047017T2

(6)

3 where D(T) is the predicted density in kg/m for T in kelvin. The fit was made

assuming that only the DRS density data were subject to error. However, T being

the average of the upper and lower temperature of the liquid sample, it will

differ from the temperature of the liquid at the densimeter. This assumption is

likely to bias the estimated coefficients in the equation and also the estimated

standard deviation for the DRS values. The residual standard deviation is 0.027

3 kg/m (37 degrees of freedom) and is comparable to the within standard deviation

discussed above. The range for T was 109 K to 128 K. A similar fit for the DRS

density data for fillings 6 through 15 results in the equation:

D(T) = 525.092 - 0.382535T - 0.0048151T2

(7)

3 The residual standard deviation for this fit is 0.019 kg/m (53 degrees of

freedom). The range for T was 109 K to 130 K. The differences between the

predicted values of the two equations over the range 110 K to 130 K is given for

selected temperatures in the table below. The last column of the table gives

3 the differences less the 0.07 kg/m estimated offset between the old balance

values and the new balance values.

28
Temperature Equation 6 Equation 7 Eg. 6 - Eg. 7 Less 0.07

110 424.83 424.75 .08 .01

115 417.49 417.42 .07 .00

118 412.97 412.91 .06 -.01

120 409.91 409.85 .06 -.01

125 402.10 402.04 .06 -.01

130 394.05 393.99 .06 -.01

The percentage deviation, 100 (H(T) - D(T))/D(T), between the Haynes-Hiza

relationship [3] and eguation (7) is shown in Figure 5. The same comparison is also

shown for eguation (7) and the Goodwin results [4].

4.3. Uncertainty Statement

The use of three times the estimated standard deviation is commonly used in

reporting the limits of random error. This derives partly from simplicity and

partly from the fact that if the true standard deviation were being used,

m(T) ± 3 SD

would contain 99% (almost all) of the measured Y(T).., where m(T) is the

systematic error. Section 3.1 gives bounds to this value of ± 0.022%. From

Section 3.2, the filling-to-filling standard deviations 99% upper bound is

3 0.036 kg/m and that for within a filling has a 99% upper bound of

3 0.028 kg/m . Combining these two to obtain an upper bound on the standard

2 deviation of a single determination of Haynes-Hiza minus DRS, we get ((.036)

2 1/2 3 + (.028) ) = .046 kg/m . Although this value contains the uncertainty for

29
to

0) +> a) n

•r- -C E

(

C 4-> II 1-co // D

/ c -c / (O *>—

/

.C to /

4-> O) /

£ -4-> UO

/ c a:

/ -O — o

/

•f— fO

I 3 »-> OJ 1ft crs-r

-CN r— U

k

LU

nd

Goodwin

ed

total

un

.0.055%

for

es

is

0.1%.

CON

o

1-

<

zaa

imat d

± siti ! \l

*" •i- 4-> C C I 1/5 (O (D

co \«o CC O) 0) 1 "O 1^ \o

C -C X —

LU >>l- 3

H V Q.

a: o •— X U) s

.c a: *« c

UJ

O 5

•D, o -C o o

homparison

sured

by

t

rror

is

+

for

the

Go

<_> «c a> o E u »->

1 _T" •r- C

in a> +-> •!-

1

igure o

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sterna

ncerta LJ i

U_ 4J to 3

1 1 oI A1ISN3Q SUQ WOUd 30N3U3ddlQ %

30

*
both density determinations (Haynes-Hiza and DRS), we are assigning all of it to

3

the DRS. The 3a value for this uncertainty is 0.138 kg/m .

3 Transforming the estimated standard deviaton of ± 0.046 kg/m to percent at

3 422.63 kg/m , the normal boiling point density of methane, gives a value of

± 0.011%. The sum of 3 x 0.011% plus 0.022% gives the present estimated limit

of total uncertainty for a single density measurement made on pure methane with

the DRS as ± 0.055%. This uncertainty decreases for LNG mixtures because of the

increased density.

5. MEASUREMENT PROCESS CONTROL

As future measurements are made, the random errors will be continually

monitored and the systematic error estimates will be confirmed experimentally as

described below.

Each time a set of density reference measurements is made using the system,

measurements on at least two separate fillings of pure liquid methane will be

included in the tests. Density measurements will be made at temperatures

around 110 K, 115 K, 120 K and 125 K with some randomness in the order. The

remeasured methane densities will be compared to the Haynes-Hiza results and to

the earlier reference system measurements to determine whether the system has

shifted. This reliability of the system will be checked only in conjunction

with density comparison work rather than periodically because of the expense of

making density measurements. The reference weight, of course, now permits a

continuing monitoring of the balance performance and can provide information to

31
correct any drift within a run. The methane tests will primarily monitor the

silicon crystal itself and the yapor pressure bulb thermometer performances.

For future occasions, the within standard deviations will be compared

statistically to those of previous occasions to test for any change in this

measure of precision. We will also test for the presence of occasion-tooccasion shifts or signs of non-random behavior (e.g., drifting). If there are

no apparent changes, the data from previous occasions will be combined with the

new data to obtain updated estimates. Any statistically verifiable changes in

the DRS process will call for corrective action with respect to the process.

Revised uncertainty statements will be presented as

needed.

6. SUMMARY

The density reference system of the National Bureau of Standards, is

described. The procedure for determining the density from weighing, zeroing and

calibrating the balance and the calculational method is discussed.

The uncertainty of the improved density reference system for pure methane

at the normal boiling point is ± 0.055%. The contribution from the estimated

systematic error in density was ± 0.022%. The estimated uncertainty caused by

random error is three times the standard deviation of 0.011% and is based on

sixty-three measurements of the densities of saturated liquid methane. This

32
total density uncertainty is taken to be the sum of the systematic and random

errors and should vary approximately as p /p where p is the density of normal

boiling point liquid methane and p is the density of the sample liquid.

7. ACKNOWLEDGMENTS

The authors wish to thank W. G. Stewart and J. D. Bruel of this laboratory

for their design work on the DRS densimeter and their help with the rebuilding

of the density reference system.

8. REFERENCES

[1] Siegwarth, J. D. , Younglove, B. A., and LaBrecque, J. F. , Cryogenic Fluids

Density Reference System: Provisional Accuracy Statement. NBS Technical

Note 698, November 1977.

[2] Siegwarth, J. D. , Younglove, B .A., and LaBrecque, J. F. , An Evaluation of

Commercial Densimeters for Use in LNG. NBS Technical Note 697, October

1977.

[3] Haynes, W. M. , Hiza, M. J., Measurements of Orthobaric Liquid Densities of

Methane Ethane, Propane, Isobutane and Normal Butane, J. Chem. Thermodynamics 9, 179, (1977).

33
[4] Goodwin, R. D. , The Thermophysical Properties of Methane, from 90 to 500 K

at Pressures to 700 Bar. \ NBS Technical Note 653, April 1974.

[5] J. D. Siegwarth and J. F. LaBrecque, A Portable Calibration Densimeter

for use in Cryogenic Liquids. NBS Technical Note 1035, to be published.

[6] Cook, N. H. , and Rabinowitz, E. , Physical Measurement and Analysis, AddisonWesley Publishing Co., Inc., 1963.

9. APPENDICES

9.1. A Comparison of the DRS Densimeter and an Industrial Reference

Densimeter

9.1. a. Introduction

An industrial densimeter calibration facility, similar to the Density

Reference System (DRS) of the National Bureau of Standards, is presently under

construction. Like the DRS, the calibration method consists of simultaneous

density measurements of a homogeneous liquified natural gas-like liquid by the

densimeter under test and a reference or calibration densimeter.

The industrial reference densimeter, hereafter referred to as the IR

densimeter, for this industrial facility and the density reference system

densimeter are Archimedes type densimeters. Both densimeters consist of silicon

34
single crystals immersed in the sample fluid and weighed by electronic balances.

The main difference between the densimeters is the choice of electronic balance

as will be discussed below. Neither densimeter requires calibration in a fluid

of known density since the calibration is determined from the weight and volume

of the silicon single crystals. Thus, none of the parameters used to determine

density from the weighing of the crystal are adjustable for either densimeter

and we are comparing the densimeters, rather than calibrating either. In this

appendix, we present the results of a comparison between the DRS and IR densimeters in the Density Reference System. These results show that within the

specified uncertainty of the DRS densimeter, no significant difference exists

between these reference densimeters. However, the accuracy of the calibration

of other densimeters calibrated by the IR densimeter must be based on an analysis

of the accuracy of the whole calibration facility and not just the IR densimeter.

9.1.b. Industrial Reference Densimeter

The method of calculating density from a measurement by the IR densimeter

is similar to the method described in Reference 1 (main text). Because the

conventional read out unit of the electronic balance was replaced by a digital

volt meter to increase sensitivity, the calibration was not adjustable and the

read out did not give grams directly. An additional small brass mass is weighed

to obtain a scale factor. This scale factor is applied to the difference between

the reference weight and the immersed silicon crystal.

The density equation is:

p = (z(M

ao

- M

a

) + M

s

- Mw

Mw

P

g

/pw

)/(M

s /ps

).

35
This equation and the symbols are identical to equation (7) of Reference 1 with

substitution of the gas buoyancy correction; but there, z = 1. Thus M is the

I ao balance reading for the reference weight, M is the reading for the immersed

a silicon single crystal, M and M are the true mass values of the reference

W o weight and silicon crystal and p , p , and p are the densities of the sample

g w s vapor in the vicinity of the reference weight, the reference weight and the

silicon crystal at 110 K respectively. The quantity z has been introduced

because the balance is uncal ibrated. A calibration weight of about 10.3 g is

weighed and this value is divided into the true mass value of the calibration

weight reduced by the amount of the mass of the gas displaced i.e., the apparent

mass value. The value for z was nominally 1.002 in this work. The silicon

apparent mass was read twice. The reference weight apparent mass was recorded

between each weighing M M so four values of M - M were obtained and averaged. A ao a

M

similar procedure was used to weigh the calibration weight in gas.

The true mass values of the weights s M , M , and M , where M is the calibras' w' c' c tion weight used in the calculations, are:

M = 163.7952 g

s s

M = 132.7430 g w

3

M = 10.3172 g

c 3

These values have an uncertainty of about ± 1 mg which produces an uncertainty of 0.003% for liquid methane density. Since these weights were determined on an equal arm balance, no gravitational constant corrections are required.

36
The required densities are:

p s = 2.33078 g/cm3 (silicon at 110 K)

3

p = 8.4 g/cm (Brass at ambient temperature)

W

and p is determined as described in Appendix 9.3.

The weighing was done with an 0.1 mg sensitivity beam balance using a set

of class S weights. The various weights were transposition-weighed, and buoyancy

was corrected. These weights should be periodically checked to assure the

values do not change with use due to chipping, scratching, oxidation, dirt, etc.

Even though the silicon crystal is large and thus provides more sensitivity,

this electronic balance is less sensitive than that in the DRS and the weighing

method is inferior so the measurement uncertainty is greater. The electronic

balance in the IR densimeter is capable of measuring weights of to 400 g, but

its resolution is only ± 10 mg when equipped with the factory readout unit. A

resolution of about 1 mg was sought using a more sensitive digital volt-meter is

substituted for the factory readout. The method of comparing the crystal weight

in liquid to a reference weight was used, though the accuracy of this method

compared to a direct weighing of the crystal was not examined. The direct

weighing method had a disadvantage in these measurements because a capacitor

placed across the analog output of the balance to reduce the noise level resulted

in a long system time constant. The accuracy of the density measurements by the

IR densimeter are also affected by the accuracy of the required gas bouyancy

corrections to the reference weight and the small scale calibration weight. The

method of calculating this buoyancy correction is detailed in Appendix 9.3.

37
9. I.e. Results

The two reference densimeters were compared in four separate fillings.

More of the data were taken in pure methane on the first test because the reference weight came off the manipulator during the LNG tests. The second test was

principally for demonstration so the LNG like mixture data were taken mainly for

the last two tests. On the third test only two methane readings were made.

Figure 9.1 shows the percentage differences

f p TR " pDR<n x 10 ° 6% = i-^ ^^

(%) (9.1)

PDRS

versus run number where P nR c ar>d P TR are the densities measured by the DRS and

IR densimeters respectively. The different symbols in the figure refer to

composition: for methane and A for the LNG-like mixture. The corresponding

solid symbols represent the arithmetic averages of the 6% for the two liquids

from filling to filling. The solid-dot line connects methane averages, and a

dotted line connects the LNG averages.

The most striking feature of Figure 9.1 is that the averages of 6% for the

first two methane tests are higher than for the last two. This is also true

with regard to the LNG tests but to a lesser extent. It is also evident that

for the first two tests the methane averages were higher than the corresponding

LNG averages. We cannot say now whether this pattern is part of the random

changes that can be expected in the operation of this system, or whether there

are some learning effects in the operation of a new densimeter since these are

the first measurements made with this industrial reference densimeter. For the

38
GO

s_

QJ

4-> QJ

<D CD

II II II O

<

<?

oo : O

?>. o

o^

o>

o

o o

o o

^o

i

1 1 r in o

i 1 1 1 1 1 1 r

-8

moinoinomoinoin rsirM OOOOOOOOOOO — — ooo — — ojcsi

-I-o

o

en

a:U

Z>

to

OD

to

in

too

o

cQ

oo

DC

-o

QJ -C

-M

CD

CD

QJ -Q

QJU

C

QJ

QJ

QJCD

to

-t-J c

QJ • U SS- QJ

QJ -Q

Q- E

i— c • rj

QJ (/) s- zs 3 00 en S- i- QJ u_ >

%9 N0I1VIA3Q

39
purposes of this report, the changes in the average values of the 6% from filling

to filling are assumed random. Also the 6% for methane are sufficiently different from those for LNG for the data for the two liquids to be analyzed separately.

Two kinds of random uncertainty are considered in this analysis: random

errors that individually affect the 6% within a filling, and errors which

affect the mean (long term average) of the 6% from filling to filling. The

standard deviation within fillings is designated by o> and that for filling- tofilling by Op. The following table gives estimates of ov, o> and the mean for

three comparisons: p, R versus Pnpc' Puh versus PnRV anc' Pun versus Ptd> where

pHH

is the density of the saturated liquid methane according to the work of

Haynes and Hiza and is based on the average temperature in the sample holder.

The estimates for o> are based on 39 observations, while the estimates for ov

are based on the four averages of the 6% for the four fillings. Percentages are

3 based on normal boiling point of methane of 422.63 kg/m . The analysis of the

methane data shows essentially no difference between the mean for p, R and the mean

for Pn R

r- The within filling standard deviation for 100 (p tr"Pli(j)/Pl|l| 1S

0.01% which is the same value as for the percentage difference for 6%, but the

percentage difference for 100 (Puu~PnDc)/PnDc 1S or| ly na ^ "that, i.e., 0.005%.

This indirect comparison suggests that the within standard deviation for pj R is

significantly larger than for P nRC-- This may be attributable to the types of

weighing systems employed in the two densimeters. Looking at the ov column we

see little difference for the three comparisons. This might indicate that the

magnitude of whatever affects the mean value for one densimeter is the same as

that which affect the other.

40
Table 9.1. Statistical Summary for Percentage Differences for Methane Data (%)

95% Confidence

Estimate Upper 95% Estimate Upper 95% interval for

6% of a

F confidence limit of ov confidence limit mean

P IR~ PDRS

P DRS

xlOO .010 012 0085 034 -.00371.017

P HH~ P DRS

PDRS

xlOO 0051 0063 0063 022 0871.012

p HH" p IR

p

IR

xlOO .010 013 0071 032 0831.015

The estimated values of ov and ov for 6% equation (9.1) in the case of the

LNG-like mixture are, respectively, 0.005% and 0.004%. The first of these

numbers is based on 60 observations and the second on the means of the four

fillings. A 95% upper limit for ov is 0.006% and a 95% upper limit for

a

F is 0.014%. The 95% confidence interval for the mean of the 6% for the four

fillings of LNG is -0.006% 1 .009%. Based on the data for either methane or

LNG, there is no significant offset between the two densimeters.

The measured value of the reference weight, corrected for buoyancy, was

occasionally more than a milligram different during these tests from its

assigned mass value of 102.9022 g. The average value for the methane runs is

0.8 mg higher and that for the LNG runs is 0.5 mg lower than this value. Some

of the deviation is probably due to non-equilibrium in the sample vapor space so

the correction for buoyancy has detectable errors, and there seems to be some

41
error in the buoyancy correction itself. Over the course of the measurements,

the reference weight true mass values show no evidence of change in the calibration of the DRS balance.

9.1.d. Summary

The IR and DRS densimeters agree to within the limits of statistical error.

Except for perhaps a slightly larger random error for the IR densimeter, we see

no practical difference between the two densimeters.

When the IR densimeter is used to calibrate other densimeters in some other

calibration device, other factors besides the reference densimeter uncertainty

are important and may even dominate. For instance, the degree to which the

liquid sample in the calibration system is homogeneous and isothermal during the

comparative density measurement is very important. From the measurements reported here, we can only report an uncertainty relevant to insertion in the DRS.

An uncertainty statement including the system in which the IR densimeter is to

be used is required to estimate the accuracy to which another densimeter may be

calibrated. The portable reference densimeter is available to do this [5].

9. I.e. References

References in section 8.

9.2 True Mass of the Silicon Single Crystal

The weight of the crystal has been determined by weighing the crystal

against a set of class S stainless steel weights on an equal arm balance with a

42

I
0.1 mg resolution. Since the weighings are in air at ambient temperature and

the silicon density is smaller than the weights, an air buoyancy correction is

required. Also, the balance arms are sufficiently unequal so that 0.6 mg must

be added to the measured weight of any object of 130 g mass if weighed only on

the left pan. The 99% confidence interval for the mean of the six weighings of

the silicon crystal in the table below is 127.4351 ± .0003 g. A calibration

certificate for the weights used appears in Appendix 9.5. The sum of the uncertainties of the S weight values for 127.390 g is added to 0.0003 g for a total

silicon mass uncertainty of ±0.0005 g.

Date Silicon Crystal Vacuum Weight

2/2/79* 127.4348

5/7/79* 127.4352

6/15/79 127.4353

8/17/79 127.4352

1/8/80 127.4349

8/22/80 127.4351

Average = 127.4351

^Weighed on left pan only with .0.6 mg added.

The true mass values of the silicon single crystal and the reference

weight measured relative to the NBS standard of mass are shown on the weight

certificate (following page). Our weighings on the equal arm balance at the

Boulder Laboratory are within the estimated uncertainty of the certificate

mass values. The true masses of these two weights will be monitored in the

future using the balance and S weights at Boulder. The Boulder values of

127.4351 g and 102.9022 g for the silicon and reference weight true masses were

used in this report.

43
RWMNK-441

(RKV. u-a)

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON, D.C. KB34

REPORT OF CALIBRATION

January 23, 1981

For: J. D. Siegwarth

Division 773.1

NBS - Boulder

Item: Two (2) Mass Standards

1. Silicon single crystal: 2.329g/cm3

2. Copper reference standard: 8.5g/cm3

The above items have the mass values shown with reference to the NBS

standard of mass. The volume was computed from its mass and above

density.

Mass Uncertainty Volume at 20°C

Item (grams) (grams) (cm3

)

Silicon 127.4345 0.0007 54.7164

Copper 102.9026 0.0007 12.1062

The uncertainty figure is an expression of the overall uncertainty using

three standard deviations as a limit to the effect of random errors of

measurement, the magnitude of systematic errors from known sources being

negligible.

For the Director,

)aniel R. Flynn, Program Manager

Mechanical Production Metrology

CMEPT/NEL

44
9.3 Gas Buoyancy Corrections

The gases used in these tests to make the liquid samples are methane,

nitrogen and propane. Only the first two are ever present in significant amounts

in the vapor space for the mixtures used if the system is at equilibrium. Some

evidence suggests, however, that the propane is not necessarily at equilibrium

when the LNG-like sample is first created. Lack of equilibrium is implied by the

observed mass value of the DRS densimeter calibration monitoring weight which is

located partially inside the dewar where the gas temperature varies between

about -10°C and -30°C. A buoyancy correction using the measured gas temperature

must be applied to this weight and the result compared to the true mass value to

monitor the calibration. When propane is first added, the observed true mass value

is low, which could result from the gas density correction being too

small because propane vapor is present.

The method of determining buoyancy corrections for methane and methane

ntirogen mixtures is straightforward. The density of the methane gas was calculated from the equation of state given in reference 1. This equation is:

P = RD + p a + (higher order terms in p) (1)

where P is the pressure, p is density, R is the gas constant and T is the

2

temperature. The coefficient of the p term is:

a = NJ + N

2

T

1/2

+ N

3 + N4/T + N4

T

2

(2)

For the temperature and pressure range of interest and the accuracy required,

the higher order terms can be neglected.

L
/ The density, p, in moles per liter can be derived from (1) for P in bars

and T in Kelvin with R = .0831434 and:

N., = -1.8439486666 X 10~ 2

N

2 = 1.0510162064

N

3 = -1.6057820303 x 10

N 4 = 8.4844027562 x 10

2

N c = -4.2738409106 x 10

4

5

This relation fits the data of Goodwin [2] in the region of T = 240 to 295

K and P = 1 to 4 bar to better than 0.1%.

When some nitrogen is added to the methane, we assume that the vapor

pressure in excess of the value of pure methane at that temperature (this

value is obtained from the vapor bulb readings) is contributed by the nitrogen

gas and calculate gas density accordingly. The density contributed by the

nitrogen gas is determined from the perfect gas relation, p = (.33694) P/T

(gm/cc), with no virial terms, where P is the partial pressure of nitrogen in

bars and T is temperature in Kelvin. This relation fits the nitrogen tables of

Strobridge [3] to better than 1/2 percent over the required mixture region of 240

to 295 K and 1 to 4 bars vapor pressure.

When propane is added to the mixture, determining the density of the vapor

becomes more difficult since adding propane reduces the partial pressure of

methane. From some earlier density measurements in methane containing 5%

propane, we could estimate the suppression of the methane vapor pressure as a

function of the pure methane vapor pressure Pp H4 to be P = 0.015Pp

H

- - 0.031,

46
where the pressures are in bars and Pp.,. is given by the vapor pressure thermometers. This correction is only an estimate as the methane-propane-nitrogen

mixture used varies somewhat from filling to filling. This correction is

subtracted from the methane partial pressure and added to the nitrogen partial

pressure before calculating the gas buoyancy corrections to the various weights.

The concentration of propane in the vapor we consider negligible.

[1] McCarty, R. D. , A Modified Benedict-Webb-Rubin Equation of State for Methane

Using Recent Experimental Data, Cryogenics 14, 276 (1974).

[2] Goodwin, R. D. , Thermodynamic Properties of Methane from 90 to 50 K at

Pressures to 700 Bar, NBS Technical Note 953, April 1974.

[3] Strobridge, T. R. , The Thermodynamic Properties of Nitrogen from 64 to

300 K between 0.1 and 200 Atmospheres, NBS Technical Note 129, January

1962.

9.4. Linearity of the DRS Electronic Balance

The linearity of the electronic balance was tested by weighing 1,2,2,4, and

100 g class S weights in combination to produce weights of 100, 101, 102, 103,

104, 105, 106 g in random order. These weights well represented the range of

observed mass values encountered in the densimeter runs. In comparing the

certified values of the weights (See Appendix 9.6) to those measured by the DRS

balance, the linearity factor for the DRS values was calculated to be 1.000049

at 100 g with an estimated standard deviation of .000025 (12 degrees of freedom).

47
The 95% confidence interval for this factor is .999995 to 1.000103. Over the six

gram range, the effect may be virtually nothing to .0006 grams. Even the extreme possibility is not large enough to be considered of any real influence in

the density measurements being made with the DRS so no linearity effect is

included in the uncertainty estimate.

48
Appendix 9.5 Weight Calibration Certificate

Richard D Lamm

Governor

Morgan Smith

Commissioner

Donald L.Svedman

Deputy Commissioner

§g}£J

COLORADO DEPARTMENT OF AGRICULTURE

406 STATE SERVICES BUILDING

1525 SHERMAN STREET

DENVER, COLORADO 80203

May 27, 1980

Agricultural Commission

William A Stephens. Gypsun

Chairman

Ben Eastman. Hotchkiss Vice-Chairman

Henry Chnstensen. Roggen

John L Malloy. Denver

Elton Miller. Ft Lupton

Don Moschetti. Center

William H Webster Greeley Clede Widener, Granada

Kenneth G Willmore. Denve

REPORT OF TEST

jWNER: National Bureau of Standards

Thermophysical Properties Div,

Boulder, Colorado

Certification No. 6086

S/N: NBS K-l.

DESCRIPTION: 100 g to 20 mg, Fisher weight kit.

The standards described below have been tested and compared with the

standards of the State of Colorado, and have been found to be within the tolerances

as prescribed by the National Bureau of Standards for Class S weights. The effect

of air bouyancy has been considered negligible.

ITEM APPARENT MASS CORRECTION

mg

UNCERTAINTY

100 gram -0.0069

50 40.1650

20 40.0470

20* 40.0181

10 -0.0225

5 +0.0002

2 40.0809

2* 40.0226

1 40.0398

500 mg 40.0146

200* -0.0044

200: -0.0059

100 -0.0316

50 -0.0041

20 • 40.0089

20: 40.0104

0/T

4^

F H Brzoiacky, Khief Metrologist

Colorado Metrology Laboratory

3125 Wyandot St.

^-nver, Colorado 80211

0.1096

0.0786

0.0217

0.0217

0.0197

0.0131

0.0093

0.0093

0.0090

0.0082

0.0141

0.0141

0.0087

0.0081

0.0079

0.0079

mg

CLASS S ADJUSTMENT TOLERANCE

1.200 mg

0.12

0.074

0.074

0.074

0.054

0.054

0.054

0.054

0.025

0.025

0.025

0.025

0.014

0.014

0.014

THESE CERTIFICATIONS ARE TRACEABLE TO THE

:ATI0NAL BUREAU OF STANDARDS.

ALL CERTIFICATES ISSUED BY THE COLORADO

• 'ARTMENT OF AGRICULTURE-METROLOGY LAB-

?-'.TCRY EXPIRE ONE YEAR FROM THE DATE OF

ISSUANCE.

j
9.6. The Change in Volume of the Silicon Crystal for Hydrostatic Compression

and Thermal Contraction

The buoyant force of the liquid on the silicon crystal will be reduced by

the decrease in volume due to hydrostatic compression. This is described by

V = V (1 - kP)

where V is the volume at the reference pressure, in this case about one atmoso K ' phere or one bar. P would be the pressure in excess of this and k the compressibility;

K V 8P

T

-fi ~1

This correction was found to be negligible since k = 1.01 x 10 bar and

at 110 K and P - 6 bar, —rj = 6 x 10 . In this case k was computed from silicon

data on velocity of sound by McSkimmin [1] using the usual relations for bulk

modulus and elastic constant as evaluated from sound velocities.

The change in volume was computed from the thermal contraction of silicon

values from Gibbons [2]. We have

29

f

" T = (25.5 ± 0.6) x

10" 5

L298

for the change from 298 K to 100 K where L is length. The uncertainty, 0.6 x -5

10 is 3a or 3/2 of Gibbon's probable error of 0.5% multiplied by 3. This

value is essentially unchanged over the temperature interval 100 K to 140 K.

50
AV ,AL,

P

s (100K) = p(298K) (1.000765 ± 0.000018)

[1] McSkimmin, H. J., Measurement of Elastic Constants at Low Temperatures by

Means of Ultrasonic Waves—Data for Silicon and Germanium Single Crystals,

and for Fused Silica, J. Appl. Phys. 24, 988 (1953).

[2] Gibbons, D. F. , Thermal Expansion of Some Crystals with the Diamond

Structure. Phys. Rev. 122, 136 (1958).

9.7 Densities of Single-Crystal Silicon

Densities of Silicon Temperature Preparation Range of p

2.328982* g/cm3 Ambient Grown in vacuum 1. 5 ppm

2.329022* Ambient Grown in Argon 1 ppm

2.32900** 25°C No specified ± 9 ppm

Each are average of 12 measurements, Bowman, Schoonover, and Jones [1].

The density given for the vacuum grown crystal in their introduction

contains a typographical error. Their primary interest was the variability

of the density over each of the sample boules hence they did not specify

precisely the crystal temperatures.

51
** Henins and Bearden [2] measured the density of 18 crystals from four

manufacturers to a precision better than 2 ppm. The density values ranged

from 2.328986 to 2.329021 g/cm5.

{

Based on these density measurements we assume a density halfway between

the extreme values of 2.32900 ± 0.00002 g. The assumed uncertainty in

silicon single crystal density spans this range. When computing p at 100

to 140 K we add the expansion correction uncertainty to this density

uncertainty (Appendix 9.7) and obtain for p ,

p = 2.33078 ± 0.00006 g/cm3

[1] Bowman, H. A., Schoonover, R. M. , and Jones, M. V., Procedure for high

precision density determinations by hydrostatic weighing, J. of Research,

NBS C, 71C 178 (1967).

[2] Henins, I., and Bearden, J. A., Silicon crystal determination of the

absolute scale of x-ray wavelengths, Phys. Rev. 135 , A890 (1964).

52
»>U4A (REV. 9-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-1041

2. Gov't Accession No.I

I. TITLE AND SUBTITLE

Cryogenic Fluids Density Reference System: Provisional

Accuracy Statement (1980)

5. Publication Date April 1981

*.

i "" 11 '

AUTHOR(S)

J. D. Siegwarth and J. F. LaBrecque

8. Performing Organ. Report No.

I. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

$^:.^|e<#fa«lt^e^:tteit Ifow

11. Contract/Grant No.

2. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

Gas Research Institute

8600 West Bryn Mawr Avenue

Chicago, Illinois 60631

13. Type of Report & Period Covered

5. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

6. ABSTRACT (A 200-word or leas tactual summary of most significant information. If document includes a significant biblioilrarthv nr

literature survey, mention it here.) The improved Density Reference System, the reference densimeter, and the method of

determining sample density are described.

The uncertainty of the density reference system is + 0.055%. The contribution from

the estimated systematic error in density was + 0.022%. The estimated uncertainty

caused by random error is three times the standard deviation of 0.011% and is based

on sixty-three measurements of the densities of saturated liquid methane. The

total density uncertainty is taken to be the sum of ^he systematic and random errors

This applies to the density range of 400 to 480 kg/m at pressures from 0.8 to 4 bar

absolute and temperatures between 109 and 128 R\

3

This accuracy statement is expected|

to apply over ranges of at least 400 to 1000 kg/m in density, 77 to 300 K in

temperature, and 0.8 to 7 bar in pressure though the accuracy over these ranges has

not been verified.

Compared to the original , this improved density reference system has greater

accuracy, speed, reliability, and flexibility.

W. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

densimeter; density reference system; liquid methane ; LNG.

US. AVAILABILITY [)pj Unlimited

I I For Official Distribution. Do Not Release to NTIS

[XX 0rder From Sup. of Doc, U.S. Government Printing Office, Washington, DC

20402,

I 1 Order From National Technical Information Service (NTIS), Springfield, I VA. 22161

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