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in NBS TECHNICAL NOTE 697

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 8

. 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

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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

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

2 Located at Boulder, Colorado 80302.
NATIONAL BUREAU CX C

OF STANDARDS /s LIBRARY / ° _ FEB 8 1978 .a 5"'

roV occ~<RJ-/ /\Jo-h97

AN EVALUATION OF

COMMERCIAL DENSIMETERS

FORUSEINLNG AIAI0T*w

J.D. Siegwarth and B.A. Younglove

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, CO 80302

and

J.F. LaBrecque

Applied Mathematics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, CO 80302

Prepared for

American Gas Association, Inc. 1515 Wilson Boulevard

Arlington, VA 22209

%

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

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

S-NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued October 1977
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 697

Nat. Bur. Stand (U.S.), Tech Note 697, 52 pages (October 1977)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1977

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

Stock No. 003-003-018627 Pnce$2.20 (Add 25 percent additional for other than U.S. mailing)
CONTENTS

Page

1. INTRODUCTION 1 2. THE DENSITY REFERENCE SYSTEM 1 3. DENSIMETERS 3 3.1. Vibrating Element Densimeter 3 3.2 Dielectric Cell Densimeter 4 3.3 Displacement or Archimedes Densimeter 4 4. DENSIMETER PERFORMANCE 4 4.1. Comparison of Haynes-Hiza and Density Reference System

Density Determinations 7 4.2. The Vibrating Cylinder Densimeter 11

4.3. Vibrating Plate Densimeter 19

4.4. Capacitance or Dielectric Type Densimeter 27

4.5. The Displacement Densimeter 35

5. CONCLUSIONS 4 2 6. ACKNOWLEDGMENTS 4 2 7. REFERENCES 4 3 8. APPENDIX I 44

in

AN EVALUATION OF COMMERCIAL DENSIMETERS FOR USE IN LNG

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

The cryogenic fluids density reference system has been used to

evaluate three basic types of densimeters: the vibrating element

type, the dielectric cell type and the displacement type. These

meters were used to measure densities in liquid methane and liquid

methane mixtures with ethane, propane, normal butane, and nitrogen.

Measurements were made over the density range from 400 to 480 kg/m 3

, temperatures from 108 K to 130 K, and pressures from 1 to 3 bar. A

hundred measurements were made at various densities, temperatures,

pressures and compositions.

Key words: Cryogenic densimeters; density reference system; liquid

methane; LNG.

INTRODUCTION

The density reference system (DRS) provides a well-characterized sample

of a cryogenic fluid such as liquefied natural gas (LNG) and related mixtures

in which densimeters can be placed for evaluation. The DRS measures liquid

density, temperature and pressure.

3 Densities varying from 400 to 480 kg/m have been determined from the

apparent mass of a silicon single crystal weighed in the liquid by an automatic balance. Temperature is calculated from vapor pressure thermometers

filled with methane whose pressure is measured with a quartz-spiral bourdon

gauge

.

Mixtures were made from laboratory grade (99.97 to 99.99 mol %) methane,

ethane, propane, n-butane and nitrogen.

Three basic types of densimeters were studied: the vibrating element

type, the dielectric cell type and the displacement type.

2. THE DENSITY REFERENCE SYSTEM

The density reference system is designed to compare other densimeters

to an accurate Archimedes type densimeter in an isothermal liquid. The

accuracy of this reference densimeter is discussed in a separate report [1].

The liquid sample, test densimeters, and other measuring devices are contained in a closed system, as shown in figure 1. An automatic balance is

in an upper gas space which is an integral part of the sample space. From

the balance arm is suspended a silicon single crystal, whose apparent mass
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vapor pressure thermometers measure the liquid temperature at the top and

bottom of the sample [1]. 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 were used to cool the sample, and electric heaters, also wound on the sample

holder, were used to heat it when changing temperatures between data points.

Each data point was taken with the sample and container very close to isothermal conditions. During the period of time data was being recorded, the heat

capacity of the sample was used to keep the temperature constant. The heat

leak to the sample was minimized by surrounding the sample cell with a nitrogen gas cooled shield. The shield temperature was 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 is capable

of mixing the fluid very rapidly at full speed. The speed of the pump has

to be reduced considerably during the actual measurements since rapid circulation of fluid sample affected the readings of the densimeters under

test. A low stirring rate, which did not affect the instruments, was used

during the measurement to maintain an isothermal sample.

The density variation in the sample holder was evaluated from the vapor

pressure thermometer measurements. The temperatures at the top and bottom

of the sample holder were computed from the vapor pressure equation of

Goodwin [2]. From the average of the temperatures, the density of liquid

methane was calculated according to the work of Haynes and Hiza [3]. The

Haynes-Hiza (HH) measurements agree with the density correlations of Goodwin

[2] to within the estimated uncertainty of both. Since the HH and the DRS

densimeters are both Archimedes types [4], the DRS has been compared to the

HH results directly. The density differences between the top and bottom of

the sample holder have been less than 0.04%.

3. DENSIMETERS

3.1 Vibrating Element Densimeter

The basic principle relating density to frequency is directly equivalent

to the classical mass and spring oscillator. The vibrating member of the

densimeter, a rectangular plate in one instance and a vibrating cylinder in

the other instance, has a natural frequency determined by the stiffness
constant and apparent mass of the vibrating element. The apparent mass of

the element depends on the density of the fluid surrounding it since in

vibration a portion of this liquid is also forced to move. The density, p, is related to the period of oscillation, t, by

p = A + Bt 2

. (1)

A and B are constants determined empirically at cryogenic temperatures.

3.2 Dielectric Cell Densimeter

The Clausius-Mossotti relation [5] is

p = (e - l)/(e + 2)a, (2)

where e is dielectric constant and a is the polarizability , generally taken

to be a constant, independent of density.

Over a limited range of composition, however, the density can be represented by a linear function of the temperature and dielectric constant [5]

rather than equation (2). This linear relation can be used along the saturation line of the fluid. The densimeter studied in this work uses a bilinear relation to relate dielectric constant and temperature to density.

3.3 Displacement or Archimedes Densimeter

The operation of this densimeter is based on the Archimedes principle;

that is, an object immersed in a still fluid experiences a lifting force

equal to the weight of the fluid it displaces.

The measurement equation for this device is

p = p (M - M )/M (3) o a

where p is the density of the submerged object and M its mass. M is its

apparent mass. The two unknowns p and M are determined for this instrument

by calibration at two or more well defined densities.

4. DENSIMETER PERFORMANCE

Each densimeter was compared to the DRS . As an independent check on

the DRS measurement, the density of saturated liquid methane was calculated

from the average temperature and then compared with the density measured

with the DRS. There were six fillings of the system, five using methane and one with an LNG-like mixture without nitrogen. Nitrogen was later added to

two of the methane fillings and the LNG mixture. These liquids are listed

4
in Table I. The symbols in this table appear in all the following figures

showing the pure methane and mixtures together.

The LNG mixture contained approximately 88-1/2% CH , 6-1/2% C„H , 3%

C H and 2% n-C.H .

Table I. Symbol

1. Methane + Methane +

2. Same filling

Methane + 1% nitrogen

3. Methane + Methane +

4.

Methane + 2% nitrogen A

Same filling

LNG

5. Same filling

LNG + 2% nitrogen A

6

.

Methane +

Two types of data are considered in this section:

1. differences, X. - DRS .

,

l l where X. is a density determination by one of the test densimeters and DRS. is the corresponding DRS value, and

2. percentage difference, 100% (X . -DRS . ) /DRS .

.

Plots are of the percentage difference data only.

Four plots of the percentage differences are provided for each of the

densimeter comparisons: methane data in chronological order and versus density (different symbols used for each filling) , and all data in chronological order and versus density (symbols given in Table 1) . The detailed

analysis of the data shown in the figures is described below.

If the DRS and the densimeter under test give the same density except

for random error, then the differences X. - DRS. for repeated density measl l c J urements will tend to cluster about zero. In this case the densimeter is

said to be relatively accurate with respect to the DRS. However, experience

has shown that the differences often show an average value that is not zero.

In addition, this average value may be density or temperature dependent.

This average value may also vary randomly with time or from filling to

filling.

In order to include all the above possibilities, the model used for com- paring densimeters to the DRS is
Xijk - DRS ijk

= m + s(D

i - D) + 6

3 + e

i jk ' (4)

where m is the average value of the difference over the range of densities*

D. , s is the slope over this range, D is the average of the D., 6. is a dif- 1 !

'

-j ferential shift occurring on the jth filling, and e. . is the random error

1 jk

occurring for the kth measurement of D. in the jth filling. The 6. can only

be evaluated from the methane data since there were no repeated fillings of

the other test liquids.

The scatter in the random components e. ., is expressed by their standard XJK

deviation. This will be called the within or within filling standard deviation. If the 6 . are also considered to be random, their standard deviation

is called the between or between fillings standard deviation. All these

parameters may also be functions of the liquid compositions. For a glossary

of the statistical terms, see Appendix 1.

When an estimated standard deviation is given, the degrees of freedom

(d.f.) are also given. Degrees of freedom is a measure of the amount of

information available for estimating a standard deviation. The d.f. is

usually the number of measurements less the number of other estimated parameters. For example, for methane there were 53 measurements. If m, s and

the four differential shifts 6. are estimated, there would be 47 degrees of

freedom remaining to estimate the within standard deviation.

The experimental data are fitted to the model given by equation (4)

using the method of least squares. The test of this model is if it provides

a statistically better fit than if some or all of the unknown parameters

were to be taken as zero. The tests for the presence of the parameters are made at the 5% level of significance, i.e., there is a 5% chance that the

test will say to include a parameter that is not needed to explain the data.

At a smaller level of significance there is less chance of including an unnecessary parameter, but there would also be less chance of finding a useful parameter.

When estimates of m, s, and 6. are given, they are usually given in

terms of confidence intervals, e.g.,

m + t- (std. dev. of m)

where m is the estimate for m and t is a percentage point of the t distribution [6] depending on degrees of freedom and the level of confidence desired.

The least squares procedure used to fit the data to equation (4) supplies

* The true value of D^ is unknown; the DRS value is used instead. The range

of the Dj_ is large compared to the random error of the DRS; so the error introduced by this should not be important.
both estimates of m and its standard deviation. A 95% confidence interval

used in estimating the value of a parameter means that 95% of the time when

such a confidence interval is constructed it contains the true value of the

parameter

No total uncertainty has been derived here for any of the densimeters

tested since some of the instruments were not provided with low-temperature

calibrations. A total measurement of uncertainty would include limits of error associated with calibration procedures, the limits of random error

(precision) and the limits on those systematic errors that result from

changes in the conditions under which the densimeter operates. Each of the

densimeters is compared to the DRS and the components of the error are presented; i.e., those associated with 6. and e. .. . In the description of each of the following comparisons, a table is

provided which gives a breakdown by composition of the statistical significance of the average value, m, the slope, s, and the largest 6.. A 95%

confidence interval is given for each significant parameter. The table gives

the within standard deviation (WSD) as well as the between standard deviation

(BSD) for the 5 .. It is not clear that the 5 . are random for any densimeter

-- in some cases it is clear they are not -- so the between standard deviations should be viewed in this context.

4.1 Comparison of Haynes-Hiza and Density Reference System Density Determinations . As discussed earlier, the Haynes-Hiza temperature-density relationship

for liquid methane [3], which agrees within experimental uncertainty with the

correlations of Goodwin [2], has been used to confirm the DRS density results,

The percent deviations of the HH density from the corresponding DRS density

determination for the five fillings are shown as a function of the chronological order of the data in figure 2. This replication of the methane data over a number of fillings provides a means of checking the reproducibility of

a densimeter from one filling to the next. In this instance, the means of

the five groups, m + 6 are not statistically different. Figure 3 shows the

J percent deviation as a function of density for the DRS. The figure shows

what appears to be a second. degree effect. While it would not be surprising

to find this kind of systematic difference between the two methods, the data

does not support this at the 5% level of significance. However, an offset is

detectable at the 5% level. See table 2. This offset is well within the

systematic error of the DRS [1].
Table 2. Statistical summary for HH-DRS

Methane

3 Significant at 5% level? 95% confidence interval (kg/m ) m yes .024 + .018 kg/m3

s no Largest 6

.

no

3 WSD = 0.065 kg/m

BSD = not significant

Here, as in all the following comparisons, a standard deviation, whether

within or between, combines the imprecision of both methods of determining

density.

Summary

The differences between the densities determined by these two methods do

show a small systematic offset, but no filling-to-filling changes, and the

estimate of their combined standard deviations is 0.065 kg/m . For the

3 methane normal boiling point density of 42 3.6 3 kg/m , this standard deviation

is equivalent to 0.016%.
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10
4.2 The Vibrating Cylinder Densimeter

The vibrating cylinder densimeter is shown schematically in figure 4.

The vibrating cylinder secondary electronic output meter can be adjusted to

indicate a minimum density as the zero indication and a maximum density as the full scale reading. It was found that initial settings recommended by

the supplier produced an offset of several percent in density.

Since the calibration supplied with this instrument was not suitable,

the instrument was recalibrated using the experimental data. The resonant

frequency of the instrument was measured directly using a frequency counter

with an 0.1 Hz resolution. Some of the resonant frequency and the cor- responding DRS density data were used to determine the constants of equation

(1) by means of a least squares fit. The result is,

p = -203.3672 + 5719.149/f 2 (5)

3 where f is the frequency in kHz and p is in kg/m . This calibration equation

was fit to all the data except that of the last methane run. The calibration

was done for the purpose of comparing the instrument to the DRS. The analysis of the data below indicates that a better fit might be obtained if a linear term in 1/f or temperature were included in equation (5)

.

The percent differences for the five methane runs are given in figure 5 in the order taken. There are some obvious differences in the operation of

the meter from one filling to the next--the upward shift during the second

day of the first run and the shift down on the last run--that are statistically significant when based on the estimated within filling standard

3 deviation of 0.20 kg/m (47 d.f.). The data for the first filling was made

over two days, and there is a shift in the data between the two days, thus

inflating the standard deviation for that filling. If one eliminates the

data for the first filling, the estimated within standard deviation is 0.092

kg/m3 (27 d.f .)

.

Occasionally a measurement by this densimeter indicated a considerably

smaller density than the corresponding DRS measurement. At the same time the

variation of the frequency reading, normally + 0.1 Hz, increased to about + 1 Hz. This increased "noise" in the frequency reading was probably due to the

presence of bubbles on the vibrating element and these data were excluded.

These noisy measurements occurred after the liquid sample had been rapidly

cooled, thus there could be some boiling near the vibrating element. No

controlled tests were done to see whether any liquid level effects exist. A

too low liquid level could degrade both the accuracy and precision of a density measurement.

Both the methane and LNG mixtures were used to fit equation (5) . The

estimates of m for the various mixtures, given in Table 3, indicate there

11
could be a shift for the higher nitrogen content; but comparable shifts did occur for the pure methane data (figure 5).

Equation (5) takes density, but not temperature, directly into account.

Because both methane and LNG mixtures were used, temperature and density are not directly related; the temperature ranges for the mixtures are about the same in each case, but the density ranges are not. As can be seen in figure

6 for methane, the percentage differences show evidence of what could be a temperature dependence, since the measurements are at saturation. Four of

the values of s for the five fluids are significantly different from zero at

the 5% level (see table 3), and there is a consistency in these estimates

with those for LNG being larger than those for methane.

The LNG data, figures 7 and 8, showed more variability than the methane

3 data. The combined standard deviation for the two LNG runs is 0.51 kg/m (20

d.f.), which is significantly different from the estimated standard deviation

of 0.20 kg/m (47 d.f.) for pure methane.

The shifts seen in figure 5 are significant, about 0.1% between the

first and second days of the first filling, and 0.05% between the last two

methane fillings. It cannot be said whether these shifts are random in

nature or are due to some overlooked systematic effect.

Summary

The calibration using eq . (1) removed most of the systematic offset for

this densimeter, but some density dependence is indicated. Whether the

shifts seen in the methane data are random or otherwise cannot be determined

at this time. The estimated within standard deviation increases significantly for LNG.

12
Fluid Access

Temperature and

Pressure

Transition Section

ft--"" Fluid Access

Vibrating Cylinder

VIBRATING CYLINDER

DENSIMETER

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18
4.3 Vibrating Plate Densimeter

The vibrating plate densimeter is shown schematically in fig. 9. The

calibration supplied with this instrument was for more dense fluids at room

temperature. Since the direct density reading of the instrument was 1.6%

high, the resonant frequency was measured directly using a frequency counter

with a 0.1 Hz resolution. A calibration equation for the vibrating plate

densimeter was then determined by a least squares fit of equation (1) to the

resonant frequency of the densimeter and the corresponding DRS density. The

fit was made to the pure methane and the LNG mixture data only. No mixtures

containing N- were included in the calibration for the reasons discussed

below. The calibration equation derived is:

p = - 550.1099 + 5430.736/f 2

, (6)

3 where f is in kHz and p is in kg/m . This equation was used to compare the

density measurements of this instrument with the DRS.

Figure 10 shows the percent differences for the five methane runs in

the chronological order taken. Figure 11 shows the same data as a function

of density. This instrument occasionally read a significantly lower density

than the DRS while the random variation of frequency readings increased

significantly. The increase in noise was attributed to bubble formations on

the vane as a result of rapid cooling of the test liquid and the data are not shown in the figures.

There is some shifting of the mean level within and between fillings.

If the 6 . are taken to be random, the estimate of their standard deviation

J 3 is 0.20 kg/m (4 d.f.). The data for the fifth filling showed the largest

shift. There is no obvious explanation for these shifts in terms of systematic effects.

Figure 12 shows the percent deviation for all liquids in chronological

order. The within run standard deviations among the liquids are not judged

to be significantly different. See table 4 for the within standard deviations for each liquid. The estimated within standard deviation for the

3 differences using both methane and mixture data is 0.16 kg/m (88 d.f.)

.

The mean values for all liquids containing nitrogen were found to be significantly different from zero in the positive direction (see table 4). The

LNG plus nitrogen offset is statistically smaller than those for the methane

plus nitrogen mixtures. This could have been influenced by whatever caused

the large downward shift in the last methane data. In regard to this, it

should be noted that no filling-to-filling effects were taken in to account

in forming the confidence intervals for m in table 4.

19
Figure 13 shows the percent deviation for all the sample fluids versus

density. Only the differences for the LNG with no nitrogen data shows a statistically significant trend with density and/or temperature. There is no obvious explanation for this, and since it does not occur for the LNG

data without nitrogen, it may be anomalous. The estimated within standard

deviation does not seem to change with composition.

Summary

The calibration of this densimeter is nitrogen dependent, but there

does not appear to be any strong evidence of a temperature or density dependence that has not been removed by the calibration. There are shifts in

the mean level from filling to filling, the largest of which occurs on the

fifth filling. The estimated within standard deviation does not show a statistically significant change with composition.

20
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26
4.4 Capacitance or Dielectric Type Densimeter

This capacitance system uses a relation linear in dielectric constant,

e, and temperature, T, to determine p,

p = A + B(e-l) + CT (7)

the values of A, B, and C having been selected from the designer's studies

of properties of LNG-type mixtures of methane, ethane, propane and normal

butane. The dielectric cell densimeter is shown schematically in figure 14.

After the "first methane sample density measurements, this densimeter

was readjusted. The data for this first run was then recalculated in ac- cordance with the adjustment. The plot of the percent deviations for all

the methane data versus order -- figure 15 -- shows significant shifting of

the mean level from one filling to the next. Figure 16 gives the percent

deviations of the methane data versus density. The apparent slope is

exaggerated in this case by using percent, but even for the density differences the slope is significant.

Figure 17 displays the percent difference versus order for all liquids

and figure 18 shows the percent difference versus density. The within

standard deviation for various liquids does not differ significantly. The

3 estimated within standard deviation based on all data is 0.078 kg/m (86

d.f.). It will be noted—see table 5--that the average difference changes

with composition. The 95% confidence intervals given in table 5 for the

3 average differences are based on the between standard deviation, 0.32 kg/m , and this assumes the 6. to be random. This assumption may not be supported

by future testing. The 95% confidence intervals for s in table 5 indicate

that slope also changes with composition.

Summary

This densimeter was factory calibrated; and reads high for the liquids

without nitrogen, and low for those containing nitrogen. Of lesser practical significance is a dependency on temperature or density. The shifts,

6., are indeed significant when compared to the estimated within standard

deviation

.

Calculations by Giarratano and Collier [7] have shown that the density

of an LNG mixture can be calculated from the dielectric constant and temperature using eq. (7) with some error. The size of this error varies with

composition. The errors for LNG mixtures containing no nitrogen but ranging

from pure methane to an LNG mixture similar to that studied here are as much

as 0.4%. The systematic offsets for the methane and LNG measurements in

this evaluation show a difference of 0.5%, in good agreement with their

work. If nitrogen is included in the mixtures, the error range in the

27
density determined from the dielectric constant and temperature becomes much

larger. If the nitrogen concentration range is from to 1.4%, the error could be as much as 1.8%. In this experiment, the methane plus nitrogen

mixtures are nominally 0, 1 and 2% nitrogen. From the offsets (figure 17)

,

it is estimated by interpolation that for a nitrogen concentration range of

to 1.4% the error could be as large as 1.9%, again in good agreement with

Giarratano and Collier [7]. To realize a density measurement with a dielectric cell with an accuracy approaching the precision of such a cell

requires that the composition, especially the amount of nitrogen, of the

fluid in question be known.

28
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34
4.5 The Displacement Densimeter

The displacement or Archimedes densimeter is shown schematically in

figure 19. This instrument consists of a float that is weighed by an electronic balance.

Figure 20 shows the percent deviation for the methane data versus order

while figure 21 shows the same data as a function of density. This instrument was supplied with a factory calibration that agreed with the DRS to

within 0.15% as shown in figure 22.

The shift observed for the mean level on the second filling is significant. The mean levels for fillings 1, 3, and 4 (see table I) are not distinguishable on a statistical basis. A 95% confidence interval for the mean

3 level based on these three fillings is -0.17 + 0.025 kg/m . A 95% confidence

3 interval for the average value for filling 2 is -0.53 + 0.040 kg/m -- a downshift of 0.36 kg/m . There is no obvious explanation for this shift.

The calibration was adjusted for the last filling to bring the densimeter

into agreement with the DRS. The mean of the differences on this last

3 filling is +.038 + .046 kg/m which is not distinguishable from zero at the

5% significance level. The percent difference for all liquids versus order

are shown in figure 22 and versus density in 23. There is an apparent shift

(see figure 22 and table 6) in the average of the differences when nitrogen

is present in the methane, but this is not observed for the LNG mixture. It

is not possible to determine from the data whether this small shift (0.025%

maximum) is due to the DRS or this densimeter. There are no significant

indications that this meter is temperature, density or composition dependent.

3 The within standard deviation for all liquids is 0.07 kg/m (91 d.f.).

Summary

The comparison in this case is between two Archimedes type densimeters,

and it was not expected that composition would be a factor. The means for

methane runs 1, 3, and 4 and the two LNG runs support this expectation.

However, the addition of nitrogen to the methane in both cases produced

detectable upward shifts in the means, though these may as well be due to the

3 DRS. The small within standard deviation of 0.07 kg/m (91 d.f.) make such

shifts easy to detect. There was one notable and unexplained shift in the

3 mean level of the differences — from -.18 to -.53 kg/m -- between the first

and second fillings of the sample holder. The calibration adjustment made

before the last filling resulted in an offset that was statistically indistinguishable from zero. Temperature density or composition dependence

does not seem to be a problem. The instrument calibration is such that the

density measurements agree with the DRS to within the stated accuracy of the

instrument.

35
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5. CONCLUSIONS

This series of tests has shown that from the standpoint of precision,

even with the run to run offsets included, all the instruments are suitable

for low temperature density measurements on a fluid of known composition.

There are, however, some problems with calibration as discussed in section

4. These tests have not established the stability of the various instruments at cryogenic temperatures over a long period of use. Some of the run-to-run offsets of the vibrating element densimeters may

have been the result of variations of the fluid sample level which could not

be determined accurately. If the level were too low, the densimeter readings are definitely affected and some offset may still exist at higher fill

levels since the acoustic mounting of the vibrating plate densimeter, at

least, affects the performance. The calibrations supplied with these densimeters were not suitable for use at cryogenic temperatures.

The measurements on the dielectric cell densimeter support the calculations of Giarratano and Collier [7]. Additional information, probably

the composition, must be an input parameter to a density measurement if the

measurement accuracy of this instrument is to approach the available precision when the fluid composition varies.

The main obstacle to the commercial use of some of these densimeters at

low temperature seems to be the lack of a suitable calibration. Also, a means of periodically checking a calibration in or near the field site is

desirable. The best method of calibration and field testing would seem to

be through the medium of a transfer standard rather than through the properties of a low-temperature fluids which are difficult to analyze in the

field and can easily be contaminated. The DRS could serve to calibrate and

maintain such transfer standards.

6 . ACKNOWLEDGMENTS

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 as well as Patricia Giarratano and Milton

Loeb for their contributions to this work.

This project was performed under a grant from the American Gas Association (A.G.A.), on behalf of its membership.

42
7. REFERENCES

Siegwarth, J. D., Younglove, B. A., and LaBrecgue , J. F. LNG density

reference system accuracy statement, to be oublished as an NBS

Technical Note.

[2] Goodwin, R. D., The thermodynamic properties of methane, from 90 to

500 k at pressures to 700 bar, Nat. Bur. Stand. (U.S.), Tech Note

653, 30 pages (1974) .

[3] Haynes, W. M. and Hiza, M. J., Measurements of orthobaric liguid

densities of methane, ethane, propane, isobutane and normal butanes,

J. Chem. Thermodynamics 9, 179 (1977)

.

[4] Ha-'ne 1;- W. M. t Hiza. M. J., and Frederick, N. V., A magnetic sus- pension densimeter for measurements of fluids of cryogenic interest,

Instrum. 47, 1237 (1976)

.

[5] See, for example, Condon, E. U. and Odishaw, H., editors, Handbook of

Physics, 4-112. McGraw-Hill Book Co. (1967).

[6] See, for example, Mandell, J., Statistical Analysis of Experiment

Data, John Wiley and Sons, Inc. (1964).

[7] Giarratano, P. J. and Collier, R. S., Evaluation of capacitance

densitometry by examination of the relationships between density,

dielectric .constant , pressure and temperature for LNG mixtures,

I and EC Process, Design and Development 16, 330 (July 1977) .

43
APPENDIX I Glossary of Statistical Terms

Confidence interval: An interval in which the true value of an unknown

parameter will lie a certain percentage of the time such an interval is

constructed. The percentage used indicates the degree of confidence.

Between standard deviation: A measure of the scatter of the random fluctuations that occurs in the mean from one filling to the next.

Degrees of Freedom: The amount of information available for estimating a standard deviation. It is usually the number of observations less the

number of estimated parameters.

Level of confidence: A level of probability at which a stated hypothesis

will be rejected on the basis of the data even though the hypotheses is

true

.

Within standard deviation: A measure of the random scatter observed in data

taken under those operating conditions occurring within a filling.

44
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN 6972. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

An Evaluation of Commercial Densimeters for Use in LNG

5. Publication Date October 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 cryogenic fluids density reference system has been used to evaluate three

basic types of densimeters: the vibrating element type, the dielectric cell type and

the displacement type. These meters were used to measure densities in liquid methane

and liquid methane mixtures with ethane, propane, normal butane, and nitrogen. Measurements were made over the density range from 400 to 480 kg/m 3

, temperatures from

108 K to 130 K, and pressures from 1 to 3 bar. A hundred measurements were made at

various densities, temperatures, pressures and compositions.

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)

Cryogenic densimeters; density reference system; liquid methane; LNG.

18. AVAILABILITY Unlimited

I ! For Official Distribution. Do Not Release to NTIS

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