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NBS TECHNICAL NOTE 698

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and

technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the

Office of Experimental Technology Incentives Program.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center for Radiation Research — Laboratory Astrophysics- — Cryogenics 2 — Electromagnetics- — Time and Frequency 3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational insti- tutions, and Government; provides advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials, the Office of Air and Water Measurement, and the following divisions:

Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services developing and promoting the use of avail- able technology; cooperates with public and private organizations in developing technological standards, codes, and test methods; and provides technical advice services, and information to Government agencies and the public. The Institute consists of

the following divisions and centers: Standards Application and Analysis — Electronic Technology — Center for Consumer Product Technology: Product Systems Analysis; Product Engineering — Center for Building Technology: Structures. Materials, and Safety; Building

Environment; Technical Evaluation and Application — Center for Fire Research: Fire Science; Fire Safety Engineering.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment, and serves as the principal focus wthin the executive branch for the development of Federal standards for automatic dat:i processing equipment, techniques, and computer

languages. The Institute consist of the following divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE OF EXPERIMENTAL TECHNOLOGY INCENTIVES PROGRAM seeks to affect public policy and process

to facilitate technological change in the private sector by examining and experimenting with Government policies and practices in order to identify and remove Government-related barriers and to correct inherent market imperfections that impede

the innovation process. THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS; promotes the development of the National Standard Reference Data System and a system of in- formation analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services

to ensure that the NBS staff has optimum accessibility to the scientific information of the world. The Office consists of the following organizational units:

Office of Standard Reference Data — Office of Information Activities — Office of Technical Publications — Library —

Office of International Standards — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

2 Located at Boulder, Colorado 80302.
SJAT10NAI, BUREAU

OF STANDARDS

LIBRARY CRYOGENIC FLUIDS M "** ^^

*H

DENSITY REFERENCE SYSTEM: .^3

PROVISIONAL ACCURACY STATEMENT

1 ecJLj. „, ro. 6 ?W

J.D. Siegwarth

B.A. Younglove

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

and

J.F. LaBrecque

Applied Mathematics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Prepared for:

American Gas Association, Inc. 1515 Wilson Boulevard

Arlington, Virginia 22209

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

November 1977
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 698

Nat. Bur. Stand. (U.S.), Tech. Note 698, 32 pages (November 1977)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1977

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402

Stock No. 003-003-01864-3 Price $1.30 (Add 25 percent additional for other than U.S. mailing)
CONTENTS

Page

1. INTRODUCTION 1

1.1. Symbols ' 2 2. DESCRIPTION OF THE BASIC MEASUREMENT PROCESS 3 2.1 System Description 3 2.2 Density 5

2 .

3

Temperature 7 2.4 Vapor Pressure 8

3

MEASUREMENT PROCESS PARAMETERS 8 3.1 Bounds for Systematic Errors 8 3.2 Random Error from Measurements on Methane 11

3.3 Uncertainty Statement 16

4. MEASUREMENT PROCESS CONTROL 16

5. SUMMARY 18

6. ACKNOWLEDGEMENTS 18

7. REFERENCES 19

8 - APPENDICES 2 8.1. The Change in Volume of the Silicon Crystal from

Hydrostatic Compression and Thermal Contraction . . 20

8.2. Silicon Crystal Weighings in Air 21

8.3. Densities of Single-Crystal Silicon 21

8.4. Weight Certificate 22

8.5. Linearity Check of the Balance 23
CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM:

PROVISIONAL ACCURACY STATEMENT

J. D. Siegwarth, B. A. Younglove

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

and

J. F. LaBrecque

Applied Mathematics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

The density reference system of the Cryogenics Division of the

National Bureau of Standards is described. This system is used in

making density measurements of cryogenic liquids. The methods of com- putation and the accuracy to which the density of the liquid can be

measured are discussed in detail.

At this time the estimate of sample standard deviation for a single

density measurement made using this system is 0.016% (at 422.63 kg/m 3 ).

Using three times this standard deviation as a limit for random error

and using 0.028% as the bound for known sources of possible systematic

error, the uncertainty of a single determination with this system is

± 0.076%. This provisional statement of accuracy applies for the density range 400 to 480 kg/m 3

, pressures from to 3 bar, and temperatures

from 110 K to 125 K. Because of the densimeter design, this accuracy

statement is expected to apply to the density range from 400 to 1000

kg/m 3 and to the temperature range of 77 to 300 K at least, and to

pressures of 7 bar, though these ranges of application have yet to be

verified.

Key Words: Densimeters, density reference system; liquid methane; LNG.
1. INTRODUCTION

The density reference system (DRS) was evolved to determine the uncer- tainty of measurements made by several field type densimeters capable of

operating at cryogenic temperatures in liquefied natural gas (LNG) . The

project was performed under a grant from the American Gas Association, Inc

(A.G.A.) on behalf of its membership.

This system has the capability at present of operating from room temperature to near the boiling point of liquid nitrogen (300 K to 80 K) , and at

pressures of 7 bar (100 psi) to vacuum. In this work densities of 400-480

kg/m 3 were covered.

At this time the value of the standard deviation for a single density

comparison measurement made on this system is 0.016% (at the methane normal

boiling point density of 422.63 kg/m J

)

, based on measurements made using

samples of cryogenic liquids. Using three times this standard deviation as

a limit for the random error, and adding 0.028% as the bound for known

sources of possible systematic error, the uncertainty of a single determination by this system is taken to be + 0.076%.

Density is determined in the DRS by weighing an extremely pure (semiconductor grade) single-crystal of silicon in the liquid whose density is

to be determined. The density of the liquid is calculated from the apparent weight of the silicon submerged in the liquid usinq the Archimedes

principle

It is appropriate that silicon was used in this work as its density

has been recommended by Bowman [1] of NBS as the priraarv standard for solid

densities. His work, which uses Archimedes principle, discusses the sev- eral advantages that this type of silicon has for accurate measurements of

liquid densities: relatively low density (compared to other solids), high

thermal conductivity, low electrical resistance, and low compressibility.

Of course, Bowman's work and others [2] provide accurate values for silicon

density
1.1. Symbols

g acceleration of freely falling body

k compressibility factor

L length

L 2 9 8 length at reference temperature 298 K L length at absolute temperature T

M apparent mass

M apparent mass as read by balance for zero mass load

ao L c J M counterweight mass

c m bouyancy correction to M

M silicon crystal mass

s

J M reference mass standard used to evaluate zpro of balance

w

m bouyancy correction to M w w

P system pressure

T system temperature

V volume of silicon

s

p density of liquid sample

p density of gas (vapor phase in equilibrium with sample liquid)

y

p density of silicon

s

J

p density of brass

w

Y, m ,

.

jth density determination by the DRS on the ith methane filling

(T) l

j

J H, . corresponding density value from average T using Haynes-Hiza

relationship

m ,m\ systematic difference between Y. . and H. .

a. shift in the mean for measurements made on ith filling

l e.

random contribution to jth measurement on ith filling
2. DESCRIPTION OF THE BASIC MEASUREMENT PROCESS

2.1 System Description

The density reference system consists of a vacuum insulated cryogenic

fluid sample container with an integral densimeter. Provision is made to

insert other densimeters into this container so that simultaneous measurements of the density of an isothermal fluid can be made with the reference

and test densimeters. It is desired that the density reference system be

able to test density measurements of other instruments to 0.1%.

The liquid sample, test densimeters, and measuring devices are con- tained in a closed system, as shown schematically in figure 1. An automatic balance is in the upper gas space which is an integral part of the

sample space. From the balance arm is suspended the silicon crystal, whose

apparent mass when immersed is directly related to the liquid density. Two

vapor pressure thermometers are used to measure the liquid temperature at

the top and bottom of the sample. Pressure of the liquid sample is measured by a quartz-spiral bourdon gauge.

Cryogenic temperatures are achieved by flowing cold nitrogen gas

through a coiled tube attached to the outside of the sample holder. These

coils are used to cool the sample, and resistance heaters are used to heat

it when changing temperatures between data points. Each data point is

taken with the sample and container as nearly as possible at isothermal

conditions. During the period of time data are being recorded, the thermal

inertia of the sample is used to keep the temperature constant. The heat

leak to the sample has been minimized by surrounding the sample container

with a nitrogen gas cooled shield. This shield temperature is maintained

near that of the sample by controlling the flow of the nitrogen gas passing

through the shield cooling coil. To obtain temperature equilibrium rapidly

in the 14 liter vessel, a 5-cm diameter turbine pump is used to mix the

sample. The sample fluid is pumped through a 3 . 5-cm diameter intake line

from the bottom of the sample vessel and is exhausted into the top of the

vessel through a discharge line of the same size. This stirrer, capable of

mixing the fluid very rapidly at full speed, is operated at reduced speed

during the actual measurements, since rapid circulation of the fluid sample

affects the densimeter readings. The stirring speed used, is well below

the disturbance threshold.
to o

>-

CO -C c

LU 0)

0> 5

CO

LJ

uOO

>-

ocu

L. k. -D

__ o 0) -a

0)E

«/> c

0)

0)

L.

0) I

0) c

*• c MM Mi

Q

^_ c o a a O > u E E CO

(1)

O

to to w> t— ex.

"tT"

aEo

to ca -a- oou

fi Q_

C o \o o /b 5 B~

<D to

»_ >- 3 0)

to *"

to 0) 2 i

sio a, Q-.C >
2.2. Density

The density reference system densimeter uses the Archimedes principle;

that is, a body immersed wholly or partially in a liquid experiences a lifting force equal to the weight of the fluid displaced. The net force on

the body is the difference between its weight and this buoyant force.

The basic arrangement of the silicon crystal, the weighing balance,

and sample holder can be seen in figure 1. A silicon crystal is weighed

immersed in the test liquid. Its apparent weight is the difference in its

true weight and the buoyant force exerted by the liquid.

M

a

g = (M

s - P V

s )g. (1)

In the following relations we have removed the factor, g, as it is common

in all terms. Solving for density

p = (M

s - M

a

) ^

(2)

Using the measured value for the silicon mass and the value for singlecrystal pure silicon density, p , we have

M = p V

s s s (3)

Combining equations (2) and (3) to eliminate V ,

p = p (1 - M /M : iD Ct O (4)

This is the basic form of the measurement equation. The one actually used

is developed below.

It is desired to weigh the 127 g silicon crystal to about 1 mg. The

electronic balance used weigh the crystal only weighs to 1 mg on a zero to

20 g range. This is sufficient to measure the buoyancy change of the

crystal in the fluids over the density ranges of interest. A counter

weight on the balance beam is adjusted so that the weight reading of the

crystal is less than 20 g for the lowest density liquid. Then equation 2 can be written:

M +M -m = M -pV a c c s s (5)
The M of equation (2) has been replaced by M + M - m where m is the a

J a c c c counterweight buoyancy correction due to the sample vapor which has free

access to the vessel containing the balance. Since M cannot be measured

c directly another weighing is required. Before or after weighing the silicon crystal, the crystal is disconnected and a reference weight M is

olaced on the balance pan. This reference weight is chosen so that it is

approximately two grams heavier than M . This insures that the balance

reading will remain well above g as the balance does not read negative

weights. The balance condition for the electronic balance with only the

reference weight on the pan is;

M + M -m = M -m. (6) ao c c w w

Subtracting equation (5) from (6) and solving for p gives an equation

for p that excludes M and m : c c

M -M + m +M -M s w w ao a ,-,. P = m—7

* ' ' M /p

s s

Like M and m , all other components of the balance and the crystal

suspension are weighed in both measurements and cancel out when equations

(5) and (6) are subtracted.

All the quantities in equation (7) are measured separately from the

density measurements except for m and of course M - M . The density at

room temperature of the gas vapor in the balance volume, p , is calculated

from the vapor pressure of the sample and m

w

is calcuated using the re- lation:

m = M p /p tT . w w g w

The quantity m may be measured by weighing a plastic weight in the gas in

the sample space when the gas composition is unknown.

The measured values of the various masses in equation (7) are:

M = 127.4330 g, P c = 2.33078 gm/cm 3 s s M = 100.9296 g, P t7 = 8.5 gm/cm^ . w w

so equation (7) becomes:

26.5034 + M

aQ

- M

a

+ Pq (11.9) g/cm :

54.674

6
The value for the silicon mass is an average of several weighings in

air, corrected to weight in vacuum (see appendix 8.2)

The density of 2.33078 g/cm 3 has been corrected for thermal contraction to LNG temperatures (appendix 8.3) from the literature values (appendix 8.1) . Pressure dependence of p is negligible (appendix 8.1)

Calibration of the balance .

The linearity was verified using a procedure recommended by the

Statistical Engineering Laboratory of NBS . See appendix 8.5. A continual

check of the calibration was performed using a 5 gram weight. Provision

was made for lowering this calibration weight onto the balance pan by a thermally actuated bi-metallic strip. This allowed a very gentle and

repeatable placement of this weight upon the balance pan.

The calibration of the electronic balance was checked periodically

during the course of the run both while reading the reference weight and

while reading the silicon float weight. The calibration has never required

adjusting

A scale factor correction of 1.0002 has been applied to the scale

readings even though a 99% confidence interval for this scale factor is

1.0002±.00045.

2.3. Temperature

Temperature was measured using vapor pressure thermometers. One

thermometer bulb was located at the bottom of the sample volume and the

other near the top. Each thermometer contains a few cm 3 of liquid methane.

Pressure communicates from the thermometers to a quartz-spiral bourdon tube

pressure gage (200 psi maximum)* via 1/16" O.D. stainless capillary tubing.

The temperature range was 110 K to 126 K. All the quartz-spiral pressure

gages used in this work were calibrated using an air dead weight gage. The

air dead weight gage has an accuracy of ± 0.015%. The accuracy of the

quartz-spiral gages was found to be better than ± 0.015% of full-scale

pressure. This pressure uncertainty is equivalent to 0.03 K at 110 K and

0.01 K at 125 K for the 200 psi gage used to measure the vapor bulb

pressures

1 psi = 6.895 k Pa.
92,np/3!lnT

^

for AT =

P 0.05 K

0.38

0.5

.017%

.02%

Temperature gradients as measured by the vapor pressure thermometers

have shown a median value of 0.06 K with 17% of the measurements larger

than 0.1 K and a maximum gradient of 0.29 K. The densimeters under test

are closer to the DRS density probe than are the two vapor pressure thermometers. It is assumed for the purposes of error estimation that AT is no larger than 0.05 K. The density difference resulting from this temperature difference can be calculated by using methane properties [3,4].

Here we use the dimensionless derivative 9«np/3fnT at saturation:

Average System

Temperature

110 K

127 K

An additional temperature uncertainty, usually less than 30 mK

,

results from the temperature of the sample drifting slightly during the course of a density measurement.

2.4 Vapor Pressure

The liquid sample vapor pressure was measured using a quartz-spiral

bourdon tube pressure gage. Most of the measurements were made using a to 100 psi unit that was calibrated against the air dead weight gage.

3. MEASUREMENT PROCESS PARAMETERS

3.1. 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 (7) , the measurement equation, has the density p as a function of several independently measured variables.

p = p (M ,M ,M ,M , p ,p ) . (8)

s w a ao sw
The uncertainty in p, arising from uncertainty in some variable x, for

example, can be evaluated from

6p = f£_ 6x (9) 6x

or as a dimensionless ratio,

Sp . . 8 £np 6x

p 3£nx x

(10)

which has the advantage of expressing the independent and dependent variables as dimensionless ratios. The total uncertainty in density is taken

to be the square root of the sum of the squares of the various contributions. — = \ y

P ) L 9£np l &x.^ 2 ih

3 1 nx . x . i i (n:

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 [5].

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 total

logarithmic partial derivative of the liquid density with respect to the

variable of the first column and the magnitude. The column labelled 6x/x

is the ratio of the estimated worst possible uncertainty of that variable.

The systematic error, <5x/x, due to mass determinations is estimated

from the uncertainty generated by the balance and weights used to determine

the masses. The estimate of the systematic error of the apparent mass is

the uncertainty of the electronic balance reading as specified by the

manufacturer. Linearity measurements (appendix 8.5) indicate this number

is conservative. The error estimate of the silicon crystal density covers uncertainties due to the temperature and pressure effects (appendix 8.1) as well as uncertainties in published densities (appendix 8.3). The metal

density uncertainties of which M is the dominant term are estimated from w volume and weight. The gas density, required for bouyancy corrections,

contains all gas pressure, temperature and composition uncertainties when

calculated. This quantity is also determined experimentally by weighing a
Table 1. Systematic errors

Variable, x 3£np/9?,nx and max magnitude >x/x 6o/p in %

silicon crystal (p - p)M /pp V

s s s mass

1.6x10 5 ±0.0080

apparent masses M /pV

Tl /pV

ao'

M /22

a M /22

ao7

.001/M.

C .001/M

ao

±0.0046

±0.0046

Silicon density1 M /p V

s s 3.0x10 5 0.003

ref. wt densityJ M p /p pV w g w

2x10 3 006 ±0.0012

gas density M p /p pV w g w2x10 ' .05 ±.01

temperature

gradient

32np/3f.nT . 5 4X10 h ±.02

temperature drift 9Hnp/9.nT

over course of

measurement

4X10 k

t .012

total, from equation (11) 028%

low density weight of known mass and volume in the gas. The only significant uncertainty is then in the balance readings. The uncertainty due to

temperature gradients is discussed in section 2.3. 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 contribution to the systematic error when densimeters are being compared. When density measurements

are being compared with those of other workers; however, there is this

0.01% contribution to the systematic error at the lowest temperature that

decreases to less than 0.001% at the highest temperature.

10
3.2 Random Error from Measurements on Methane

The random error of the density reference system was determined

experimentally by measurements on cryogenic liquids.

In order to observe the DRS over several periods of operation, measurements were taken on saturated liquid methane for five separate fillings

of the system. For these five fillings there was a total of 53 density

measurements. The temperatures at which the saturated methane was measured

were nominally 110 K, 115 K, 120 K, and 126 K. These density measurements

were compared to densities computed from the Haynes-Hiza relation for

density versus temperature for saturated liquid methane [4] . The vapor

pressure measurements were converted to temperature [3] and the resulting

temperature converted to density. The percent deviations of the HaynesHiza values from the DRS are shown in figure 2 in chronological order, in

figure 3 as a function of density, and in figure 4 as a function of temperature .

The model used to analyze the methane data is

H

(T) " Y (T)i 3 = V (T) + a i + S

ij

where Y, mN . . is the jth density determination by the DRS on the ith methane

(T)

j

J J J filling for temperature T; H. . is the corresponding density value derived

from the Haynes-Hiza relationship, p . . represents any systematic difference between the two methods at temperature T, a. 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 sample.

Figure 2, 100* (H-Y) /Y as a function of chronological order, provides a look at shifts, a. , in the mean of the Y. . from one filling to the next,

each filling having a different symbol. The statistical analysis of the

data, however, does not indicate the presence of any shift not accounted

for by the within sample variability of the data.

The percentage differences, plotted in figure 4 as a function of

temperature, show what appears to be a second degree effect. It would not

be surprising to find apparent systematic differences between the two

methods. The DRS data can be reasonably fit as a second order polynomial

in temperature as discussed below; and the Haynes-Hiza relationship relating temperature and density for saturated methane may also be fairly well

11
o

* in

en

4- >•> QJ O 4-

S_ -r-

+-> O C

ro -i- QJ i- +-> "O

OJ (J •!- CL C

E ^ oo

O) 4- r—

-l-J O

ro -Q E E

O oo >,

i. Hi l/l 4- o

ulated densi

t.

fferen

01 U -r- i— oo Q

hi ro o: CD

O <=>

CD en +-> -> c c c: ro -f- <u ,o 3 -S= X) E P C HI ro 2 ai o i_

o

QO

d

sr CXI o O

o o

o

C\J sr o o

o o

CL Z! OO OO a qj a3

•r- S_ QJ

=J S- E

cr o

•r- U QJ i— -C

QJ +->

>5 E *-> o

QJ

QJ 00

O ro r— 4-

SZ -r- O DC i— I

ro QJ (_) QJ > >^

QJ ro

QJ 4- .c -r-

% 'N0I1VIA3Q

12
ro

qj o

+-> O

QJ u

E 3

>, en

T3 +-> c

Qj T- -r-

+-> 1/1 I (0 C i—

i— QJ •!- 3 "D 4- O

CD m

_*: o O QJ

<D CX> QJ ^ c: C 4- >-

03 .- 4- a •!J- h- ai O

c: CL >, CO

LUQ

+-> O

QJ -a

c T- o

i >>

> >, c

QJ to QJ Qlt)

% 'N0I1VIA3C]

13
o

ro

•j -*ro ** ~

t->» <•>- ro"

ro U4***

to * ,,r

CDO

sl- CXJ o o

o o

o CXJ O

Oi % 'N0I1VIA3Q

CD + cvi

c\j

C\J s£

.,00

,,'sl"

..o

CD

o

o

bi

a. +J E -i- O) </> +-> c

cu E ~o o

i- oo

4- enQ o<U en

+J C

ro *- — -a u o

i— Q.

rn </>

i_> aj

LU

or<

enLU

LU

a e

<- o

ZJ Saj -i- m

i a> ti i/i a

.c ai e J-' E 'V

ID Dl-P

.- c o

> •<- c

11 in 3 O 3 <+-

14
represented by a second order polynomial. Therefore, unless the two functions were identical, their difference would also look like a second degree

polynomial—see figure 5. However the differences among the four group means are small enough to be due to the imprecision in the data without

having to resort to systematic difference as an explanation. Hence the

subscript (T) can be dropped from the p , . in the model and an overall mean

|j can be considered. A 99% confidence interval for this systematic difference between the DRS and the Haynes-Hiza determinations is 0.024+0.026

kg/m 3

; i.e., not distinguishable from at the 1% significance level.

On the basis of the data, a new model can be written:

(T)ij (T) = p + e.i]

where p is considered to be small, if not zero. The estimated standard

deviation (SD) of the Y< . . . based on this model is 0.065 kg/m 3 for 52

degrees of freedom (d.f.) . An upper 99% confidence limit for this value is

0.0 84 kg/m 3.

Tests were also made with other liquids: Methane plus 1% nitrogen,

methane plus 2% nitrogen, LNG, LNG plus 2% nitrogen. The LNG mixture con- tained 88^% of CHt, , 6^% C 2 H 6

, 3% C 3 H 8 and 2% n-C^H^. The LNG data covers a density range from 445 to 480 kg/m 3

. The method of least squares was used

to fit each of these four sets of data as functions of temperature. The

estimated deviation obtained from these fits are

liquid standard deviation (kg/mCj + 1% N 2 Ci + 2% N 2 LNG

LNG + 2% No

.075 (II d.f

.066 (6 d.f .

.062 (11 d.f

.052 (5 d.f.'

These estimated standard deviations are not statistically different from

the estimated standard deviation of 0.065 kg/m" (52 d.f.) obtained for the

pure methane data. An estimate for the standard deviation based on the

data for all liquids is 0.065 kg/m i (85 d.f.). The estimated systematic

error applies to these mixtures also.

A least squares fit of the DRS density to the temperature of the

saturated methane resulted in the following equation:

15
D(T) = 533.074 - 0.51138T - 0.0042734T 2

,

where D(T) is the predicted density in kg/m

'

; for T in Kelvin. The residual

standard deviation was 0.065 kg/m 3 (50d.f.). The range for T was 110 K-126

K. The standard deviation for predicted value of D in this temperature

range went from about 0.01 kg/m 3 near the middle to 0.02 kg/m ; at the ends.

The percentage deviation, 100 (H(T) - D(T))/D(T), between the HaynesHiza relationship [4] and the one above is shown in Figure 5. A similar

comparison is also shown for the above relationship and that determined by

Goodwin [3]. In this figure the limits of random error (99% confidence

interval) associated with the empirical fit of the DRS data are shown in

percent as the shaded area. No systematic errors associated with any of

these three methods are included. As can be seen, the percent deviation

for the Haynes-Hiza relationship is almost entirely within the shaded area.

3.3 Uncertainty Statement

The use of three times the estimated standard deviation is commonly

used in reporting the limits of random error. This derives partlv from

simplicity and partly from the fact that if the true standard deviation

were being used,

m

(T)

t 3 SD

would contain 99.7% (almost all) of the measured Y , m . . ., where m, m . is the

(T) i] (T)

systematic difference from the true density. Considering m. . as the

percentage systematic error, section 3.1 gives bounds to this value of

±.028%. Transforming the estimated standard deviation of + 0.065 kg/m" to

percent at 422.63 kg/m 3

, the normal boiling point density of methane, qives

a value of ± 0.016%. The sum of 3 , 0.016% plus 0.028" qives the__ present

estimated limit of total uncertainty for a single density measurement made

on pure methane with the DRS as ±.076%. This uncertainty is smaller for

LNG mixtures because of the increased density.

4. MEASUREMENT PROCESS CONTROL

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

checked and the systematic error estimates will be confirmed experimentally

or the error source eliminated where possible as described below.

16
I

n J IX)

CSJ m

I

I

1

\

i

11

m

\

> V)

c/> ^ 5. OC o ra o cs x

o -a

i/i to

+-> QC E O

cu -m

E CL

CM

1\

<

\

IT)

\

=S O

U CD C 4- o o

03 ro

L/l l—

en s_ o o

I— (_)

QJ S_ r- 4-

QJ T3

\

II V

CM CM PO

% SUQ lAIOUd N0I1VIAHQ

17
Each time a set of density reference measurements are 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. These measurements

will be made at each temperature in random 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.

For these occasions the within standard deviations will be compared

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

measure of precision and the presence of occasion-to-occasion shifts or signs of non-random behavior (e.g., drifting) will be tested. 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.

5 . SUMMARY

The density reference system of the National Bureau of Standards,

Cryogenics Division is described. Since the density determination by the

DRS is basically a weighing process, the details of calculation of this

process are described in detail. The procedure for determining the density

from weighing, zeroing and calibrating the balance is discussed.

The uncertainty of the density reference system is + 0.076%. The

contribution from the estimated systematic error in density was ± 0.028%.

The estimated uncertainty caused by random error is three times the standard deviation of 0.016% and is based on a hundred measurements of the

densities [4] of various cryogenic liquids. The total density uncertainty

was taken to be the sum of the systematic and random errors.

6 . ACKNOWLEDGEMENTS

The authors wish to especially thank Dr. J. C. Holste who contributed

heavily to the construction and start-up of the density reference system.

The authors also wish to thank Janet Donaldson of the NBS Statistical

Engineering Laboratory for her recommendations on the method of acquiring

data from the automatic balance and Milton Loeb for his help with the data

analysis

.

18
7. REFERENCES

[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)

[3] Goodwin, R. D., The thermophysical properties of methane, from 90

to 500 K at pressures to 700 bar, NBS Tech. Note 653, Apr. 1974.

[4] 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).

[5] Cook, N. H., and Rabinowicz, E., Physical Measurement and Analysis,

Addison-Wesley Publishing Co., Inc., 1963.

[6] 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. 2_4, 988

(1953)

[7] Corruccini, R. J. and Gniewek, J. J., "Thermal expansion of technical solids at low temperatures," NBS Monograph 29, May 1961.

19
8. APPENDICES

8.1. The Change in Volume of the Silicon Crystal from Hydrostatic

Compression and Thermal Contraction

The buoyant force of the liquid on the silicon crystal will be re- duced by the decrease in volume due to hydrostatic compression. This is

described by

V = V (1 - kP)

o

where V is the volume at the reference pressure, in this case about one

o

L atmosphere or one bar. P would be the pressure in excess of this and k

the compressibility;

k =

1 8v

V 3P

This correction was found to be negligible since k = 1.01 * 10 ' bar ] and at 110 K and P - 6 bar, -— = 6 * 10 6

. In this case k was computed

from silicon data on velocity of sound by McSkimmin [6] 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 Corruccini and Gniewek [7]. We have

'29 - Lr = 2 5.5 * io 5 '2 9 8

for the change from 298 K to 100 K. This value is essentially unchanged

over the temperature interval 100 K to 140 K.

Av AL

v "

6 L '

232.90 (1.000765) kg/m 3

233.08 kg/m :

20
8.2. Silicon Crystal Weighings in Air

Silicon Weight

Date in Air Temperature Pressure

gram Celsius mm Hg

Silicon Weight

in Vacuum

gram

01-10-74

01-15-74

01-27-74

02-28-74

04-02-74

04-05-74

10-27-74

10-28-75

127.3947

127.3950

127.3941

127.3945

127.3926

127.3941

127.3930

127.3927

21 633

20 631

20 625

21 620

21 628

20 630

23 625

21 620

Average

127.4335

127.4339

127.4335

127.4334

128.4320

127.4338

127.4319

127.4316

127.4330

The estimated uncertainty including uncertainties associated with the

calibration weights is taken to be ±.002 gm.

.3. Densities of Single-Crystal Silicon

Densities of Silicon

2.328932*

2.329021*

2.32904**

Temperature

22-27°C

22-27°C

25°C

Preparation

Grown in Vacuum

Grown in Argon

Not known

Std. Deviation, la

1 ppm

1 ppm

± 9 ppm

* Each are average of 12 measurements, Bowman, Schoonover, and Jones [1] ** An average of about 75 measurements, Henins and Bearden [2]

Reference density for silicon was taken to be 2.3290 at 25°C.

A 14 g portion of the same crystal was weighted in water and in air.

Using average of four weighings in air and water the density computed

at 30°C was p = 2.3291 g/cm 3, as compared to p = 2.3289 from the above

after correction for thermal expansion. This is a difference of about

0.009%. The density used here is 2.3290 gm/cm 3

. The uncertainty, taken

to be ±0.0007 gm/cm 3

, includes the vacuum grown crystal density since

the atmosphere in which this crystal was grown is unknown.

21
4. Weight Certificate

Richard D. Lamm

Governoi

Rov R. Romer Commissioner

Donald L. Svedman

Deputy Commissioner

-HAff*

.OKWH

°»tvno

COLORADO DEPARTMENT OF AGRICULTURE

406 STATE SERVICES BUILDING

1525 SHERMAN STREET

DENVER. COLORADO 80203

June 9, 19?6

REPORT OF TEST

AGRICULTURAL COMMISSION

Clarence Stone, Center Chairman

William A. Stephens, Gypsum

Vice-Chairman

Ben Eastman, Hotchkiss John L. Malloy. Denver

M. C. McCormick. Holly

Elton Miller, Fort Lupton

Kay D. Monson, Fleming

William H. Webster, Greeley

Kenneth G. Wilmore, Denver

OWNER: National Bureau of Standards

Cryogenic Laboratory

Boulder, Colorado

Certification No. 308?

DESCRIPTION: Seven weights from NBS Kit No. 143922

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 UNCERTAINTY CLASS S ADJUSTMENT TOLERANCE

20. gram

20..

10

5

2.2..

1

-0.0080 mg

+0.016

+0.009

-0.0403

+0.0216

+0.0431

+0.0229

.022 mg

.022

.020

.0134

,0134

.0134

,0093

0.074

0.074

0.074

0.054

0.054

0.054

0.054

mg

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.

rVvvA ~i :.:rS F H Brzotidy ,/Metrologist

Test completed June 9, 1976

Colorado Department of Agriculture

Metrology Laboratory

3125 Wyandot Street THESE CERTIFICATIONS ARE TRACEABLE TO THc Denver! Colorado 80211 NATIONAL BUREAU OF STANDARDS.

ALL CERTIFICATION CERTIFICATES ISSUED BY THE COLORADO DEPARTMENT OF A6RICULTURii-\VE!GH,b AND MEASURES-FOR STANDARDS HERE LISlED. EXPIRE AS INDICATED BELOW:

(a) PRIMARY STANDARDS- Five Years After Date or C:r:i^Son

b OFFICE (OR SECONDARY) STANDS - ONE YEAR AFM 0..E

OF CERTIFICATION.

(C ) Working (or Field) Standards - One Year Alter Date of Ceftifc.t.oi.

Baro. Press. 627.0mm

Temp. 23.4°C

Rel. Hum. 45.5%

22
8.5. Linearity Check of the Balance

The linearity of the balance was verified by weighing 1, 2, 2, 5, 10,

and 20 g class S weights (see weight certificate in appendix 8.4) in com- binations to produce weights of 1, 2, 3, 4, 5, 6, . . .20 g in a random

order. These weighings were analyzed by the Statistical Engineering

Laboratory of NBS

Their interpretation was that the residual standard deviation is

0.0009 g based on 36 degrees of freedom. The linearity coefficient was

1.00014.

A summary of these measurements is shown below.

Weight (g) Balance

Reading (g)

Predicted

Reading (g)

Standard Deviation

of predicted Values

(g x 10 3

)

3.9996

15.9981

10.9987

1.9998

6.9992

.9999

8.9990

17.9979

8.9990

18.9978

10.9987

11.9986

14.9982

19.9976

3.9996

12.9985

4.9994

12.9985

.9999

11.9986

18.9978

13.9984

19.9976

3.9995

16.0015

11. .0005

2.000

6.999

0.999

8.9995

18.001

9.000

18.999

11.000

12.0005

15.0015

20.0005

4.000

12.999

5.000

12.9995

1.000

11.999

19.001

14.000

19.998

3.9997

15.9998

10.9997

1.9996

6.9997

0.9996

8.9997

17.9999

8.9998

18.9999

10.9997

11.9998

14.9998

19.9999

3.9997

12.9998

4.9996

12.9998

.9996

11.9998

18.9999

13.9999

19.9999

.27

.19

.14

.25

.16

.27

.14

.23

.14

.25

.14

.14

.18

.27

.21

.15

.19

.15

.27

.14

.25

.16

.27

23
Weight (g) Balance Predicted Standard Deviation

Reading (g) Reading (g) of predicted Values

(q x 10 3

)

17.9979 17.998 17.9999 .23

7.9991 8.000 7.9997 .15

15.9981 16.001 15.9998 .19

1.9998 2.000 1.9996 .25

5.9993 5.999 5.9996 .18

9.9988 10.000 9.9997 .14

14.9982 15.000 14.9998 .18

6.9992 6.9995 6.9997 .16

2.9997 2.9995 2.9996 .23

16.9980 17.0005 16.9999 .21

5.9993 5.999 5.9996 .18

2.9997 2.9995 2.9996 .23

9.9988 10.0005 9.9997 .14

16.9980 16.999 16.9999 .21

7.9991 7.999 7.9997 .15

13.9984 13.998 13.9999 .16

4.9994 4.9995 4.9996 .19

24
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS TN-698

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Cryogenic Fluids Density Reference System: Provisional

Accuracy Statement

5. Publication Date November 1977

6. Performing Organization Code

275.05

7. AUTHOR(S)

J. D. Siegwarth, B. A. Younglove and J. F. LaBrecque

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2757574

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

American Gas Association, Inc.

1515 Wilson Boulevard

Arlington, VA 22209

13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The density reference system of the Cryogenics Division of the National Bureau

of Standards is described. This system is used in making density measurements of

cryogenic liquids. The methods of computation and the accuracy to which the density

of the liquid can be measured are discussed in detail.

At this time the estimate of sample standard deviation for a single density

measurement made using this system is 0.016% (at 422.63 kg/m 3

) . using three times thi

standard deviation as a limit for random error and using 0.028% as the bound for knoi\ sources of possible systematic error, the uncertainty of a single determination with

this system is + 0.076%. This statement of accuracy applies for the density range

400 to 480 kg/mT, pressures from to 3 bar, and temperatures from 110 K to 125 K. Because of the densimeter design, this accuracy statement is expected to apply to

the density range from 400 to 1000 kg/m 3 and to the temperature range of 77 to 300 K at least, and to pressures of 7 bar, though these ranges of application have yet

to be verified.

17. 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)

Densimeters; density reference system; liquid methane; LNG.

18. AVAILABILITY (~x)>t!nlimited

"2 For Official Distribution. Do Not Release to NTIS

|a| Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13- 46 : 598

1 ! Order From National Technical Information Service (NTIS)

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19. SECURITY CLASS

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21. NO. OF PAGES

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