NBSIR 77-852

FILE CO

DO NOT REM

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM:

PROVISIONAL ACCURACY STATEMENT

B.A. Younglove

J.D. Siegwarth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder , Colorado 80302

January 1977

Prepared for:

American Gas Association, Inc. 1515 Wilson Boulevard

Arlington, Virginia 22209
m
NBSIR 77-852

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM:

PROVISIONAL ACCURACY STATEMENT

B.A. Younglove

J.D. Siegwarth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder , Colorado 80302

January 1977

Prepared for:

American Gas Association, Inc. 1515 Wilson Boulevard

Arlington, Virginia 22209

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

CONTENTS

Page

1. INTRODUCTION 1 1.1. Symbols 2

2. DESCRIPTION OF THE BASIC MEASUREMENT PROCESS 4 2.1. Density 4 2.2. Pressure 10

2.3. Temperature 10

2.4. Composition 11

3. MEASUREMENT PROCESS PARAMETERS 12

3.1. Bounds for Systematic Errors 12

3.2. Random Error from Measurements on Methane 15

3.3. Uncertainty Statement 16

4. MEASUREMENT PROCESS CONTROL 16

5. SUMMARY 19

6. ACKNOWLEDGEMENTS 19

7. REFERENCES 2 0

8. Appendices 21

8.1. The Change in Volume of the Silicon Crystal from

Hydrostatic Compression and Temperature 22

8.2. Silicon Crystal Weighings in Air 23

8.3. Densities of Single-Crystal Silicon 24

8.4. Weight Certificate 25

8.5. Linearity Check of the Balance 27

iii

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM: PROVISIONAL ACCURACY STATEMENT

B. A. Younglove and J. D. Siegwarth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

The measurement capability of the density reference system

(DRS) of the National Bureau of Standards, Cryogenics Division, is

described. This system measures density, pressure, and temperature

of LNG mixtures for the purpose of testing densimeters which are contained in the liquid sample. Sample composition is determined

by weighing the gas samples separately before condensing them into

the sample. The DRS measures density by weighing a single-crystal

of silicon immersed in the LNG mixture. This process is described

and the equations used in the computation of density are discussed.

At this time the estimate of sample standard deviation for

a single density measurement made on this system is + 0.062% (at

0.4 g/cc). Using three times this standard deviation as a limit

for random error and adding + 0.026% as an upper bound for known

sources of possible systematic error, the uncertainty of a single

determination by this system is + 0.21%. This statement of accuracy applies for the density range 380 to 430 kg/m^ and 1200 to

1400 kg/m\ pressures to 7 bar, and temperatures from 80 K to 140 K,

This statement is expected to be correct in the intermediate density

range and for all temperatures up to 300 K. Measurement uncertainties for temperature, pressure, and composition are discussed. Comparison of measurements for liquid argon

densities with the results of other laboratories is given.

Key words: Densimeters; density reference system; liquid methane;

LNG.

1. INTRODUCTION

The density reference system (DRS) was evolved to determine the uncertainty 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 we covered densities

3 of 390-500 kg/m , a range normally found in LNG work. Some additional density measurements were made on liquid argon. Only methane density measurements were used in the determination of the system uncertainty.

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

density measurement made on this system is + 0.062% (at 0.4 g/cc), based on measurements made using samples of liquid methane (99.97%). Using three
times the standard deviation as a limit for the random error, and adding 0.026%

as an upper bound for known sources of possible systematic error, the uncer- tainty of a single determination by this system is + 0.21%.

Density is determined in the DRS by weighing an extremely pure (semiconduc

tor grade) single-crystal of silicon in the liquid whose density is to be deter

mined. The density of the liquid is calculated from the apparent weight of the

silicon submerged in the liquid using 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 primary standard for solid densities. His work which uses Archimedes principle discusses the several

advantages that this type of silicon has for accurate measurements of liquid

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

conductivity, reasonably 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 a freely falling body

k compressibility factor

L length

^29S length at reference temperature 298 K

L^j^ length at absolute temperature T

M apparent mass

M^j^ apparent mass as read by balance during calibration

M apparent mass as read by balance for zero mass load

ao

M.^ buoy mass, silicon crystal + tungsten wire + stainless steel wire

iminersed in liquid

Mj_^g apparent mass of buoy in gas

Mj^^ apparent mass of buoy in liquid

M counterweight mass

c

^ M^^ apparent mass of counterweight in gas

hanger mass

Mj^g apparent mass of hanger in gas

calibration mass

Mj^g apparent mass of calibration mass in gas

:,; ,, range mass apparent mass of range mass in gas

2
silicon crystal mass replacement mass standard used to evaluate zero of balance

apparent mass of replacement mass in gas

M.^ hanger mass, brass part

M2 hanger mass, stainless steel wire part

M2 hanger mass, stainless steel wire, that part of located in liquid

hanger mass , tungsten wire part

P system pressure

T system temperature

V volume of buoy

V volume of silicon

s AMa apparent mass less zero mass reading of DRS balance

6 density difference between DRS density and a reference density

e density variation in 6 from the average value of 6 , for a methane

sample

n density variation in 6 from a methane sample to an average methane

sample

p density of liquid sample

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

y

Pj^ density of reference methane liquid

Pg density of silicon

p-|^ density of brass

P2 density of stainless steel

p^ density of tungsten

a standard deviation

standard deviation of e standard deviation of n

y density difference bias

3
2. DESCRIPTION OF THE BASIC MEASUREMENT PROCESS

2.1. Density

The density reference system determines density via the Archimedes principle, which is that a body submerged wholly or partially in a liquid is buoyed

by a force equal to the weight of the fluid displaced. The net force on the

object is the difference between its weight and the buoyant force.

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

sample holder can be seen in figure 1. Figures 2 and 3 are photographs of the

partially disassembled reference system. 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 g = (M - pV )g. (1)

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

all terms. Solving for density

P = (M^ - M^) ^. (2)

s Using the measured value for the silicon mass and the value for single-crystal

pure silicon density, p^, we have

M = p V . (3) s s s Combining equations (2) and (3) to eliminate ,

p = p^ (1 - M /M ) , (4) o do

This is the basic form of the measurement equation. The one actually used is more elaborate and is developed in the following sections.

Density from actual readings using a balance .

In practice we measure density using an automatic balance. This balance

uses magnetic force to achieve balance. It has the advantage of speed and

convenience of operation. On one side of the balance we have a movable counterweight which can be initially adjusted to put the system in balance. Ordinarily one would adjust its moment arm to precisely balance the system. Here

we leave a slight unbalance so that the automatic system will always react in one direction initially. For purpose of clarity we take the small initial

unbalance of the system as being M^, however this will subtract out subsequently

as seen below. The force generated by the magnetic balancing system is con- sidered to be an equivalant mass M (or apparent mass), and is the reading of

the automatic balance. Here we have

M+M = M+M, +M^„. (5) a eg rg hg b£

4

Figure 2. Density Reference System showing small sample holder.

6
Figure 3. Partially disassembled Density Reference System.

7
Notice that is now M^^, as we have a buoyant effect of the gas pushing

upwards on the masses in the gas.

The value of was chosen for a given M^^ and to be large enough to

give a reading on-scale (0 to 20 grams) for the automatic balance for the

range of densities of LNG under consideration. When more dense liquids were

measured, for example liquid argon, a heavier range weight was used.

Zeroing the balance . Experience with the balance showed that the zero would change although the

calibration did not. In order to zero the balance the silicon crystal and its

wire hanger and brass support piece were lifted off manually via a mechanical

contrivance that could be operated outside the enclosure through a sliding vacuum seal.

This decrease in weight was compensated for by placing the weight on

the balance pan, again with a mechanical device such that

-

. M+M^M+M (6) ao eg rg wg

where M^^ is the zero reading of the balance. Here the range weight is still

on the pan as before. Since this measuremient occurs just before the measurement described by equation (5) then we may subtract out M^^ and M^^ giving

a ao hg bZ wg

or

Calibration of the balance.

AM = M, + M, „ - M . (V: a hg b£- wg

The linearity was verified using a procedure recommmended by the Statistical Engineering Laboratory of NBS . See appendix 8.5. A continual check

of the calibration was performed using a 10 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 precise method of

placing this weight onto the balance pan.

The calibration was checked under the zero check procedure. Immediately

after checking the zero, as described by equation (6), the calibration weight,

M^, was placed on the balance pan so that the apparent mass (the M^^ in

equation (6)) is now M , , M,+M = M +M +M, . (7a; ak eg rg wg kg

Subtracting equation (6) from (7a),

M - - M = M, . (7b) ak ao kg

8
As long as equation (7b) holds, no adjustment was needed for the balance.

In practice it was found that adjustment of the balance was rarely needed.

The measurement equation . As in equation (4), the final measurement equation can be put in the form

p = Pg(l - f (M^,M2,...p^,P2..-)) (8)

where the independent variables are all known. In actual practice the hanger

M.^, consisted of a brass part (M-j^,p-|^) and a stainless steel wire suspended from

this brass hanger (M2,p2)« However, part of the stainless steel wire was immersed in the liquid. The part in the gas is M2 - and the part in the liquid

M,. = + M2 - (9)

is M^. Therefore,

and,

hg 1 2 3 g (10)

Also the mass M, breaks down into b

b s 3

4

where is a short length of tungsten wire (M^,p^) wrapped around the silicon

crystal (M^,p^) so we have

M, „ = M + + M. - p hi s 3 4

^

1 M, ± + ^ + -A (11)

Putting these relations into equation (7)

AM = M-, + M_ - - p a 1 2 3 g

+ M + + M. - p s 3 4

^

M^^ ^ ^2 - ^3

Pi P2

M

+ -1 + -i

M

- M + p — w g p^

(12)

P =

+ + M2 + - - AM^ - Pg [ (M^ - M^)/p^ + (M2 - ^2^/02^^

(jr7p7~r"M^7^~r~M^7^p (13)

the form of equation (8) may be obtained by factoring out p^ and Mj_^ to obtain

1 + M + M + M. - M - AM p —W^ - M^ t(^l - ^w^/Pl ^ (^2 - ^3^/^21

P = P^ ^ M-^ mS • ^^'^

1 + -1 + -± -±

P2 P4

9
The following are the measured values of the masses used in equation (13).

Literature values of the densities were used, the possible effect this could

have on measurement accuracy is discussed below.

M-. = 127.4330 g, p = 2 . 33078 g/cm^ the silicon crystal.

"s ' s

h ~ ------ ^2

3 = 4.2441 g, = 8.5 g/cm the brass hanger.

= 0.2121 g, p^ = 7.9 g/cm^ the stainless steel suspension wire.

M- = 0.026 g stainless steel suspension

wire submerged in liquid.

3 M,^ = 0.055g, p^ - 18.8 g/cm the tungsten wire tied about

the silicon crystal.

= 100.9296 g the brass replacement weight.

The denominator of equation (13), ^^/P^ + ^3/'^2 ^4'^'^4 total volume of

the submerged material. From the above it is

V = 54 . 674 + 0. 00329 + 0. 00293 cm"^ V = 54 . 680 cm"^.

The total equation (13) becomes

31.0146 - AM + p (11.351)

a g / 3

P = 54 . 6802 ^''^^ •

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

corrected to weight in vacuum. (See appendix 8.2, page 23).

3 The density of silicon of 2,33078 g/cm 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).

2.2. Pressure

The system pressure was measured using a quartz-spiral bourdon

tube. During the first series of measurements (data taken before December

1975), the system used a 500 psi* gage, the data after that used a 200 psi

gage. The calibration of all pressure gages used was checked at this laboratory using an air-dead weight gage, which is accurate to 0.015%, with

the accuracy traceable to NBS. Pressure uncertainty was found to be within

the 0.015% of full scale pressure specified by the manufacturer.

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

3 the top. Each thermometer contains about 5 cm of liquid methane. Pressure

* 1 psi = 6.895 k Pa.

10
communicates from the thermometers to a quartz-spiral bourdon tube (100 psi

maximum) via 1/16" O.D. stainless capillary tubing. The temperature range

was 100 K to 140 K. Sensitivity and precision of this device is the same as specified for the gages in section 2.2. This pressure uncertainty is equivalent to 0.03 K at 100 K and 0.003 K at 140 K for the 100 psi gage used to

measure vapor pressure.

Temperature gradients as measured by the vapor pressure thermometers were

generally 0.030 K and on rare occasions approached 0.3 K. The density difference

resulting from this temperature difference can be calculated by using methane

properties [3,4]. Here we can use the dimensionless derivative d?-np/dilnT at

saturation

Average System Ap ^ ^^^3 ^ Temperature d£np/d&nT p 110 K 0.38 0.0038%

140 K 0.26 0.0026%

In the worst instance the difference was only 0.04%. The densimeters under

test were actually physically closer to the DRS density probe (the silicon

crystal) than were the two vapor pressure thermometers, implying a lower density

difference.

2.4. Composition

When mixtures were used for the density measurements, the compositions

(mole fractions) were determined by accurate measurement of the mass of the

separate constituents and subsequently applying corrections for the effect of

gas phase to the total system composition to obtain liquid phase compositions.

The samples were weighed in metal cylinders. After transfer to the DRS

cryostat, the cylinders were again weighed and the amount transferred computed

from the difference.

The balance used for this purpose is a high-resolution and high-capacity

balance (resolution better than 0.01 g, with maximum capacity of 20 kg).

Class S weights were used (see appendix 8.4).

Upon condensation in the cryostat the sample separates into a liquid

and gas phase. The volume of the gas phase was two to four times the volume

of the liquid. The large volume of the gas phase was required to house the

automatic balance used in weighing the silicon crystal which measured the

liquid density.

The composition of the liquid phase was calculated from the total composition by subtracting the amount of the vapor phase. The total composition is

that computed from the amounts of sample gas transferred into the system. If

the composition of the gas and liquid phase were the same, then the liquid

composition would be the same as the total composition.

11
For mixtures of methane with ethane, propane and butane the vapor phase

was assumed to be methane. The vapor phase densities in the balance volume

sample chamber and interconnecting tube are computed from a virial equation

of state [3] using the system pressure and temperatures. The calculated

quantities of methane are then subtracted from the total amount of methane

in the system and the result is used to compute the liquid phase composition.

For mixtures with nitrogen, the vapor phase is assumed to be methane and

nitrogen. The densities of the vapor phase were computed from a mixture virial

equation which included terms to the second virial coefficient. Since this

equation used the mixture second virial coefficient, it was computed from the

second virial coefficients of the pure components and the interaction second

virial coefficient for the mixture, as well as the vapor phase compositions.

The vapor phase compositions were estimated from phase-equilibria data for

methane-nitrogen of this laboratory [5] using enhancement factors. The re- sulting computation of vapor densities allows a first estimate of the amount

of nitrogen and methane in the vapor phase. From this, a corresponding first

estimate of the liquid phase composition is made. The estimate is improved by

iterating the computation using the results of the preceding evaluation.

In the instance of a binary mixture the composition could be computed

from another approach. Dielectric constant density measurements of the liquid

and with the assumption that the polarizability of the methane-nitrogen mixture could be computed from ideal mixing, allows one to compute the mole fraction

of the binary mixture. Agreement between the calculation described in the

above paragraphs and the dielectric constant calculation was found to be about

0.2 to 0.4 mole percent when the nitrogen composition was less than 2 mole

percent

Because of the additional uncertainties of mixtures discussed above, only

pure methane results were used in the random error determination.

3. MEASUREMENT PROCESS PARAMETERS

3.1. Bounds for Systematic Errors

A listing of the primary sources of uncertainty in density measurement

can be obtained from examination of the measurement equation. If one has

knowledge of the basic uncertainties of the separately measured quantities

such as the masses and densities, then these can be combined to give an estimate of the systematic errors in the density as measured by the density

reference system.

However, until experimental evidence of the actual effect is obtained

by introducing an offset in these factors, both singly and jointly, this

analysis is just that, an estimate of undemonstrated validity.

12
Equation (13), the measurement equation, has the density c as a f\inction

of several independent variables.

p = p(M^,M^,M2,M3,M^,M^,iM^,o^,c^,=2,c.,) . (15)

The uncertainty in c, arising frora -uncertainty in c^, for example, can be

evaluated from

So =

op

or as a dinensionless ratio,

6p = 1^ (16)

s

5p _ J Xnc

p ~ o£nPg (17)

which has the advantage of expressing the independent and dependent variables

as dimensionless ratios. The total uncertainty in density is the square root

of the sum of the squares of the various contributions.

r-- cx.>2 1/2

a/.nx. x.

1 1

(18)

This is the propagation of error relationship for systematic error [6] when the

variables are independent and the magnitudes of the relative errors are s-all

so that second order terms are negligible.

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. The column labelled cx/x is the ratio of the estimated worst possible

uncertainty of that variable.

The systematic error, cx/x, due to mass determinations is estimated from

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

r.asses. The estimate of the systematic error of the apparent -ass 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 volume and v;eight. The aas w

density is required for bouyancy corrections, contains all gas pressure,

temperature and composition uncerrainties and is the leading sysrenatic error

for mixtures containing LN2. The uncertainties 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 m.akes no contribution zo the systematic error when densimeters are

13
being compared. When density measurements are being compared with those of

other workers, however, there is an 0.01% maximum contribution to the systematic

error at the lowest temperature that decreases to less than 0.001% at the

highest temperatures.

Table 1. Systematic errors. Variable, x 8£p/9£nx 6x:/x 6p/p in %

silicon crystal (Ps

- p)M^/pPgV 9 1

6 X

_ 10 5 + 0. 0062 mass

bras'? hanapr ^1 P ) M, /PPn V. . 1 . g 1 1

8 X 10 12 . 4 X 10~ 4 + 0 . 0043 mass

steel wire mass p )M_/pp_V..8.

g 2' 2 9 X 10" 4

4 . 7 X 10" 3 + 0. 00042

steel wire mass { C\ n gJii2/PP2 0 X 10 53 . Q0 X 10 4 in liquid

p )./dp .V. . 5

g 4 4

5 2 tungsten wire (P , - 4 X 10" 1. 8 X 10~ —

ma s s apparent mass AM /pV

a

1

0 X 10~ 4 + 0 . 010

silicon density M /p V

s s 1. 6 X 10" + 0 . 0016

metal densities (M^ - ^w^Pg/PlP^--2- 0 X 10" 3 2. 3 X 10" 2 + 0 . 0046

gas density . Pg((^l - ^w^/Pl ^

/O^) /qV. .2. 2 X 10" 3 1. 0 X 10" 1*

+ 0 . 022

1 4 temperature d£np/d2,nT 3. 8 X 10" 1. 0 X 10" + 0. 0038

gradient

Total, from equation (18) ... + 0., 026 5,

The large uncertainty for gas density results from the large uncertainty of

the methane-nitrogen vapor densities. The uncertainty due to gas density is

only 0.002% for methane and the total from equation (18) is + 0.014%.

Some of the systematic errors listed above will be eliminated in

future measurements. By moving the point the silicon float disconnects

from the balance down into the liquid such that the float disconnects from

all suspension hardware, all systematic errors associated with the brass

hanger and the steel and tungsten hanger wires will be eliminated. The un- certainty of the silicon mass was determined from the uncertainty of the

measuring weights and the density uncertainty comes from literature values

of the density. The uncertainty in apparent mass is due to the balance and

has been determined experimentally (see appendix 8.2). The temperature

gradient was measured to determine that uncertainty. Only the uncertainty

due to the density of the replacement weight and the gas density correction

has yet to be examined experimentally. This can be done by using a more

dense mass for the replacement weight. However, any effect due to changing

14
this weight should be very small compared to the random error. If any change

ir. -he esrir.ated systematic error is warranted after experimentally checking

fcr replace-er.r -•reight buoyancy effects, this correction will be made in

the updated uncer-air.-y s-::atements

3.2. Random Error frcr. "easurenents on Methane

The rar.dor. error of the density reference system was determined experirr.er.rallv hv measuremer.-s cn licuid methane.

Dens^-y -.easure-er.rs or. pure -ethane vrere co-pared to densities computed

fro- the Hayr.es-rliza rela-ior. for density versus ter.perature for saturated

liquid -erhar.e [4] . The vapor pressure -.easurenents were converted to temcerauure ]3' and the resulting te—perature converted to densities as described,

The presen- esuir.a-es of the precision fcr density detenrdnations made

using uhe TR5 are based on measurements of the density of eight different

samples (fillings) of liquid methane. For the eight samples there was a total

cf seventy-one density measurements of saturated methane in the temperature

range 100 K to 140 K — for the last four samples the temperatures were 110 K,

125 K, and 140 K.

Tne mc ue _ usee ~o analyze "cne m.e"c.nane ua~a is

y(T)ij ^(T) ^(T) + ^ij

where v _,, . . is the ~th densitv determination bv the DRS on the ith methane

sample for temperature _ ; H^ry^j is uhe corresponding density value derived

from: the Haynes-Hiza relationship, - ^rj.^ represents the long term relative

bias, IS -he random, contribution to all measurements m;ade using the ith

sample, and e, ^ is uhe random, contribution to the jth measurem.ent m.ade on

-he urh sam.ple. The =-andard deviation (SD) for the a. is called the between

sample ST, and uhe ST fcr -he e^ ^ is called the within sample SD. The SD of

measuremen-s v . . is -he scuare root of the s-um of the sauares of these

There were sevenuy-one leasr squares estim.aues of the e^ ^ for the

liquid meuhane m.easurem.enus . The variability among the estim;ate samples -- uhe las- -wenry--wo, e.g. — is less -han am.ong the preceeding forty-nine.

The ccinr es-im.a-e fcr -he within SD for the first six samples is +_ 0. 074%

using 400 kg/m"^ as reference," and uhat for the last two is + 0.034%. The

corresponding 99% confidence intervals are (0.057, 0.101) and (0.024, 0.055).

This change in variability is attributed to the cleaning of the knife edges

cn -he T?.S ' s balance. The pcin- estimate for the between samples SD fcr

the eigh- samples is - 0.052%, a 99% confidence interval is (0.029, 0.13).

The cleaning cf rhe knife edges has net effecred this component of the

variabilirv. The estima-ed ST fcr a sincrle m.easurement m.ade on the DRS

15
previous to the cleaning of the balance is + 0.090%. For measurements made

after that time the SD is estimated to be + 0.062%.

Only the within SD ' s after the knife edges were cleaned are taken to

correctly reflect the precision of the within sample density measurements.

A comparison of these data with the Haynes-Hiza densities is shown in Figure

4 as well as a comparison to the work of Goodwin [3].

For the methane data the DRS measurements of density shows a bias with

the Haynes-Hiza relationship which is a linear function of density. For

a density of 0.38 g/cc the bias is -0.062% with an estimated SD of 0.021%;

a 99% confidence interval is (-0.12%, -0.006%). For a density of 0.43 g/cc

the bias is -0.11% with an estimated SD of 0.018%; a 99% confidence interval

is (-0.16%, -0.062%)

Figure 5 shows a comparison of densities for two samples of liquid argon

as measured by the density reference system to those measured by the HaynesHiza apparatus, as well as other laboratories as indicated in the caption.

As can be seen in this figure, the agreement with Haynes and Hiza is generally

within 0.1%.

3.3. Uncertainty Statement

While the use of three times the estimated SD is commonly used -in re- porting the limits of random error, because of the small number of observations (eight) relating to the sample-to-sample error, the limits using

3 X 0.062% will provide a 98% confidence interval rather than one of 99%.

When the samples of liquid methane measured by the DRS exceed fifteen, the

use of the factor 3 will give confidence intervals of better than 99%. The

limit of possible sources of systematic error has been judged to be + 0.026%

(see section 3). This systematic limit of 0.026% plus 3 x 0,062% gives the

present estimated limit of total uncertainty for a single density measurement made on the DRS as + 0.21%.

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.

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, 125 K, 130 K and 140 K. Three measurements will be made

at each temperature in random order. The remeasured methane densities can

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

16
0.1

LIQUID METHANE

7Z -0.1

t

i

Haynes and Hiza

DRS

Goodwin

0.38 0.39 0.40 0.41 0.42

DENSITY, g/cm3

Figure 4. Liquid methane density results of this work relative to the work

of Haynes, et al.[4]. The data are the 22 points taken after the

knife edges were cleaned.

17
Figure 5. Liquid argon densities of other workers compared to a least squares

fit to this work.

o Younglove, this work. Pan, et al. [14]. o Haynes and Hiza [9]. V Goldman and Serase [15]. e Chui and Canf ield [10]

Saji and Kobayashi [16].

+ Van Itterbeek and Verbeke Mathias, et al. [17].

[11]. « Street and Staveley [18]. A Terry, et al. [12], Dobrovolskli and Golubev [19]

Gosman, et al. [13].

18
work rather than periodically because of the expense of making density measurements.

For these occasions the within SD ' s will be compared statistically to

those of previous occasions for any change in this measure of precision,

and the occasion-to-occasion shifts, (see 3.2), will be tested for any

change in their variability or for signs of non-random behavior (e.g., drifting). If there is no apparent change, 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. A revised uncertainty statement will be presented

as further calibration measurements are completed.

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 + 0.21%. The contribution

from the estimated systematic error in density was + 0.026%. The estimated un- certainty caused by random error is three times the standard deviation of

+ 0.062% and is based on the measurements of the densities [4] of liquid

methane taken on eight samples and on 22 independent measurements. The total

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

6 . ACKNOWLEDGEMENTS

Special acknowledgement is given to John LaBrecque of the NBS Statistical

Engineering Laboratory for the considerable help and advice given this project

during its various phases. Acknowledgement is also given to Janet Donaldson

of the same group for her recommendations on the method of acquiring data from

the automatic balance.

Jim Holste contributed very heavily in the construction and start up phase

of this project. He designed and built several important features of the DRS.

19
7 . REFERENCES

[I] 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] Renins, 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., and Frederick, N. V., A magnetic suspension

densimeter for measurements on fluids of cryogenic interest, to be submitted to Review of Scientific Instruments.

[5] Parrish, W. R. and Hiza, M. J., Liquid-vapor equilibria in the nitrogenmethane system between 95 and 120 K, Advances in Cryogenic Engineering

(Proc. 1973 CEC) , Vol. 19 (Plenum Press, NY, 1974).

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

[7] McSkimmin, H. J., J. Appl . Phys. 24_, 988 (1953).

[8] Corruccini, R. J. and Gniewek, J. J., Thermal expansion of technical

solids at low temperatures, Nat. Bur, of Stand. (U.S.) Monograph 27,

May 1961.

[9] Private communication.

[10] Chui, C. and Canfield, F. B. , Trans. Faraday Soc . 67_, 2933 (1971).

[II] Van Itterbeek, A., Verbeke , 0., and Staes, K, , Physica 29_, 742 (1963).

[12] Terry, M, J., Lynch, J. T., Bunclark, M. , Mansell, K. R. , and Stavely,

L. A. K. , J. Chem. Thermodyn. 1, 413 (1969).

[13] Gosman, A. L. , McCarty, R. D., and Hust, J. G., Thermodynamic properties

of argon from the triple point to 300 K at pressures to 1000 atmospheres.

NSRDS-NBS 27 (1969)

[14] Pan, W. P., Mady, M. H. and Miller, R. C, AIChE J. 2]^, 283 (1975).

[15] Goldman, K. and Scrase, N. G., Physica 4_5, 1 (1969).

[16] Saji, Y. and Kobayashi, S., Cryogenics 4_, 136 (1964).

[17] Mathias, E,, Onnes, H. K., and Crommelin, C. A., Ann. Phys. 3/7, 442 (1922).

[18] Street, W. B. and Staveley, L. A. K., J. Chem. Phys. 5£, 2302 (1969).

[19] Dobrovolskii , 0. A., and Golubev, I. F., Tr. Nauch . -Issled . Proekt. Inst.

Azion. Prom. Prodo Org. Sin. 8^, 14 (1971) .

20
8. APPENDICES

I

I

21
8.1. The Change in Volume of the Silicon Crystal from Hydrostatic

Compression and Temperature

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

the effect of its volume being decreased by hydrostatic compression. This is

described by

V = V^(l - kP)

where is the volume at the reference pressure, in this case about one atmosphere or one bar. P would be the pressure in excess of this and k the

compressibility;

. _ _ 1 ^ " V 8P

"6 — 1 This correction was found to be negligible since k = 1.01 x 10 bar and at

110 K and P 6 bar, ^ = 6 x 10 ^. In this case k was computed from silicon

data on velocity of sound by McSkimmin [7] using the usual relations for bulk

modulus and elastic constants as evaluated from sound velocities.

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

values from Corruccini and Gniewek [8]. We have

298 T „,_[. —

—= = 25.5 X 10

298

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

= 232.90 (1.000765) kg/m^

Pg = 233.08 kg/m^.

22
8.2. Silicon Crystal Weighings in Air

Date

Silicon Weight

in Air

gram

Temperature

Celsius

Pressure mm Hg

Silicon Weight

in Vacuum

gram

01-10-74 127 .3947 21 633 127 . 4335

01-15-74 127 . 3950 20 631 127 .4339

01-27-74 127 .3941 20 62 5 127.4335

02-28-74 127 . 3945 21 620 127.4 334

04-02-74 127 .3926 21 62 8 127.4320

04-05-74 127 . 3941 20 630 127. 4338

10-27-74 127 . 3930 23 625 127 . 4319

10-28-75 127 . 3927 21 620 127 .4316

Average 127.4330 + 0.0003

std. dev.

23
8.3. Densities of Single-Crystal Silicon

Densities of Silicon Temperature Preparation Std. Deviation, la

2 . 328932* 22-27°C Grown in Vacuum 1 ppm

2 . 329021* 22-27°C Grown in Argon 1 ppm

2.32904** 25°C Not known + 9 ppm

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

** An average of about 75 measurements. Renins 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 weighed in water and in air. Using

averages of four weighings in air and water the density computed at 30 °C was

3

p = 2.3291 g/cm , as compared to p = 2.3289 from the above after correction

for thermal expansion. This is a difference of about 0.009%.

24
8.4 Weight certificate

Henry TROEMNER, Inc.

MANUFACTURERS OF PRECISION BALANCES AND WEIGHTS and LABORATORY APPARATUS

6825 GREENWAY AVENUE, PHILADELPHIA, PA. 19142 PHONE 21 5 SA 4-0800 TRACEABLE CERTIFICATE

Voland Corporation

27 Centre Ave. New Rochelle, N. Y. 10802

Attn: Robert C. Luce

Order 1695

This is to certify that the weights furnished on your referenced order

have been calibrated to Class S of the National Bureau of Standards

tolerances under our N.B.S. Certificate No. as follows:

Weight Set 5 kg - 1 g

5 Kg. 2 kg. 2 kg. 1 kg

500 g, 200 g, 200 g, 100 g

50 g, 20 g, 20 g, 10 g

5 g, 2 g, 2 g, 1 g

^.B.S. Certificate No.

232.09/209275 Set A

232.09/209275 Set A

232.09/209275 Set A

232.09/209275 Set A

Dated: March 28, 1974 By:

Wilbert D. Abele

Vice President and General Manager

25
Richard D. Lamm

Goverr>{ir

Rov R. Romer

C ommis sinner

Donald L. Svedman

Dfputy Commi ssiune

COLORADO DEPARTMENT OF AGRICULTURE

406 STATE SERVICES BUILDING

1525 SHERMAN STREET

DENVER, COLORADO 80203

June 9, 1976

REPORT OF TEST

AGRICULTURAL COMMISSION

Clarence Slone, Center Chairman

William A. Stephens, Gypsum

V I ce-C hai rm'an

Ben Eastman, Hotchkiss

John L. Mallov, Denver

M. C. McCormick, Holly

Elton Miller, Fort Lupton Kay D. Morison, Fleming

William H. Webster, Greeley

Kenneth G. Wilmore, Denver

OWNER: National Bureau of Standards

Cryogenic Laboratory

Boulder, Colorado

Certification No. 3087

DESCRIPTION: Seven weights from NBS Kit No. 1^3922

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

20 .gram -0.0080 mg .022 mg 0.074 mg

20. . H*0.0l6 .022 0.074

10 -fO.009 .020 0.074

5 -0.0403 , .0134 0.054

0

a -to. 0216 .0134 0.054

2. . +0.0431 .0134 0.054

1 40.0229 .0093 0.054

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

F H BrZotidy l/Metrologist

Test completed June 9, 1976

Colorado Department of Agriculture

Metrology Laboratory

3125 Wyandot Street

Denver, Colorado 80211

Baro. Press.

Temp.

Rel. Hum.

627.0mm

23.4°C

45.5?^

THESE CERTIFICATIONS ARE TRACEABLE TO NATIONAL BUREAU OF STANDARDS.

ALL CERTIFICATION CERTIFICATES ISSUED BY COLORADO DEPARTMCNT OF AGRICULTL:RL-\VL!r AND MEASURES-FOR STANDARDS HLrL LIS EXPIRE AS INDICATED BtLOW:

(a) PRIMARY STANDARDS Five Years Alter Date o( Cir'.i:

(b) OFFICE (CR SECCND,',RY) STANOADOS - CNE YE'.R Mr-' 0 Of CERTIFICATI'"'!.

(c) Working (or Field) Standards One Year Altar Dale of Ce«lif

THE

THE

".! -' J

-cation

26
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 combinations

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 0.0008 g

based on 37 degrees of freedom. The linearity coefficient was 0.99960.

A summary of these measurements are shown below.

Independent Dependent Predicted Standard Dev.

Variable Variable Values of Predicted

A f\ f\ f\ 4.000 A AAA 4.000 A A A 1 4.001 • 20E-03

in: Q Q o Id - y y o

T r Q A o Id . y y o . 19E-U3

1 A n n n 10.999 T A A A "7 10.997 in AAA 11 .000 . 12E-03

2 . 0 U 0 O A A 1 2.001 O A A 1 2.001 . 24E-03

zT n n n 6.999 T AAA 7.000 ^7 AAA 7.000 . 16E-03

T AAA 1.000 1 A A 1.002 1 A A 1 1.001 . 26E-03

O AAA 8.999 9.000 9.000 . 14E-03

17.998 17.998 17.999 . 22E-03

8.999 9.000 9.000 . 14E-03

TO A A O 18 . 9 9 8 18.999 18.998 .24E-03

10.999 11 . 000 11 . 000 . 13E-03

11.999 11 .999 12.000 . 14E-03

14 . 99 8 14.999 14.999 . 17E-03

19.998 18.998 19.998 . 26E-03

4 . U (J U

A n A n 4.000 A AAA 4.000 . 20E-03

12 . 999 12 . 997 12 .999 . 15E-03

4.999 5,000 5. 001 . 19E-03

12 . 999 12.999 12. 999 .15E-03

1.000 1.002 1.001 . 26E-03

11. 999 12 . 000 12.000 .14E-03

18 .998 18.999 18.998 . 24E-03

13.998 14.000 13.999 .16E-03

19 .998 19.999 19.998 . 26E-03

17 . 998 17.999 17. 999 .22E-03

7.999 8.000 8 . 000 . 15E-03

15.998 15. 999 15. 999 . 19E-03

1.999 2 . 002 2 .001 .24E-03

5.999 6. 001 6 . 000 .17E-03

9.998 10 . 000 10 .000 . 13E-03

14. 998 15. 000 14. 999 . 17E-03

6.999 7.001 7.000 . 16E-03

3.000 3.001 3.000 . 22E-03

16. 998 17. 000 16 .999 . 20E-03

5.999 6. 002 6 .000 . 17E-03

3 .000 3. 001 3. 001 . 22E-03

9.999 10 . 000 10 . 000 , 13E-03

16.998 16. 999 16 .999 .20E-03

7.999 8. 001 8.000 .15E-03

13.998 13. 998 13. 999 . 16E-03

4.999 5.000 5.001 .19E-03

27 USCOMM - ERL
NBS-n4A IREV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 77-852

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLI-: AND SUBTITLE

CRYOGENIC FLUIDS DENSITY REFERENCE SYSTEM: PROVISIONAL

ACCURACY STATEMENT

5. Publication Date

ucLLlU-aLy TaT^iia'K*\T XylQ/7/ /

6. Performing Organization Code

275.08

7. AUTHOR(S)

B. A. Younglove and J. D. Siegwarth

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/Woric Unit No.

11. Contract/Grant No.

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

American Gas Association, Inc.

1515 Wilson Boulevard

Arlington, Virginia 22209

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less {actual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.) The measurement capability of the density reference system (DRS) of the National

Bureau of Standards, Cryogenics Division, is described. This system measures density,

pressure, and temperature of LNG mixtures for the purpose of testing densimeters

which are contained in the liquid sample. Sample composition is determined by weighing the gas samples separately before condensing them into the sample. The DRS measures density by weighing a single-crystal of silicon immersed in the LNG mixture.

This process is described and the equations used in the computation of density are discussed

.

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

measurement made on this system is + 0.062% (at 0.4 g/cc) . Using three times this

standard deviation as a limit for random error and adding + 0.026% as an upper bound

for known sources of possible systematic error, the uncertainty of a single determination by this system is + 0.21%. This statement of accuracy applies for the density

range 380 to 430 kg/m^ and 1200 to 1400 kg/m\ pressures to 7 bar, and temperatures

from 80K to 140 K. This statement is expected to be correct in the intermediate

density range and for all temperatures up to 300 K. Measurement uncertainties for temperature, pressure, and composition are discussed. Comparison of measurements for liquid argon densities with the results of

other laboratories is given.

17. KEY VCORDS (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 [Xj Unlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

For Official Distribution. Do Not Release to NTIS

UNCLASSIFIED 30

Order From Sup. of Doc, U.S. Government Printing Office 20. SECURITY CLASS 22. Price Washineton. D.C. 20402. SD Cat. No. C13 (THIS PAGE)

[X^* Order From National Technical Information

Springfield, Virginia 22151

Service (NTIS)

UNCLASSIFIED $4.00

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