NBSIR 82-1668

MEASUREMENT UNCERTAINTIES

OF LEVEL GAGES FOR LIQUEFIED

NATURAL GAS

J. D. Siegwarth

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

NBSIR 82-1668 ATioHii ei'auo

or STAN30&&O8

tJBJujn

[Jill 2 7 1982 MEASUREMENT UNCERTAINTIES /?& ^ cL&c - OF LEVEL GAGES FOR LIQUEFIED Q-Cioo

NATURAL GAS ' u:

/To,

2r

/<LVn.

J. D. Siegwarth

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

June 1982

Prepared for: The Maritime Administration

U.S. Department of Commerce

Washington, D.C.

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1. INTRODUCTION 1

2. GAGE TYPES 2 2.1 CAPACITANCE GAGE 2 2.2 CABLE GAGE 2 2.3 BUBBLER GAGE 3

3. CAPACITANCE TYPE LEVEL GAGES 3 3.1 GENERAL DESCRIPTION OF GAGES 3 3.2 FIRST CAPACITANCE GAGE 3 3.2.1 GAGE DESCRIPTION 3 3.2.2 MEASUREMENT UNCERTAINTIES 5 3.3, SECOND CAPACITANCE GAGE 5 3.3.1 GAGE DESCRIPTION 5 3.3.2 MEASUREMENT UNCERTAINTIES 6 3.4 DISCUSSION 6

4. CABLE GAGE TESTS 7 4.1 INTRODUCTION 7 4.1.1 GAGE ACCURACY TEST FACILITY 7 4.1.2 HYSTERESIS TEST FACILITY 9 4.2 FIRST CABLE GAGE, SERVO 11 4.2.1 GAGE DESCRIPTION 11 4.2.2 ACCURACY TESTS 11 4.2.3 HYSTERESIS TESTS 13

4.3 SECOND CABLE GAGE, SERVO 13

4.3.1 GAGE DESCRIPTION 13

4.3.2 ACCURACY TESTS 14

4.3.3 HYSTERESIS TESTS 14 4.4 THIRD CABLE GAGE, SERVO 14

4.4.1 GAGE DESCRIPTION 14

4.4.2 ACCURACY TESTS 17 4.4.3 HYSTERESIS TESTS 20

4.5 FOURTH CABLE GAGE, AUTOMATIC 22

4.5.1 GAGE DESCRIPTION 22

4.5.2 ACCURACY TESTS TO A SOLID SURFACE 23

4.5.3 ACCURACY TO A LIQUID SURFACE AND HYSTERESIS TESTS 23

5. BUBBLER TYPE LEVEL GAGES 25

5.1 GAGE DESCRIPTION 25

5.2 MEASUREMENT ERROR 28

5.3 CONCLUSIONS, BUBBLER GAGE 28

6. CONCLUSIONS 30

6.1 CAPACITANCE GAGES 30 6.2 CABLE GAGES 30

6.3 BUBBLER GAGES- 30

7. ACKNOWLEDGMENTS 30

8. REFERENCES 31

APPENDIX A— - 33

APPENDIX B 44
type. These types are described in more detail in Section 2 and in later sections. The capacitance type is generally used as the primary gage for custody transfer while the cable gage or the

bubbler usually serves as a back up gage. Gaging methods used for small tanks such as truck tanks

are not included in this study.

In this report the measurement uncertainties of some representative gages of the three types have

been measured or estimated from available information. Level gaging for custody transfer is assumed to take place when the tank level is static so the liquid surface is relatively quiet.

Gage accuracy when the surface is moving is not estimated. Some of the gaging devices are too slow

to even follow the liquid surface if the tank is rapidly filled. The uncertainty and hysteresis of

four different types of cable gages have been measured at ambient conditions. These tests and the

results are described in Section 4.

Because the measurement of level by capacitance gages and bubbler gages depend on bulk parameters

rather than the difference between liquid and v^por, as do the cable gages, adequate testing

requires the use of a liquid. The liquid, if the gage is used in LNG, should be LNG. No facility

presently exists that is capable of such measurements. Limited resources precluded such tests in

this work. The measurement uncertainties for capacitance gages, Section 3, and bubbler gages,

Section 5, have been estimated from existing information. The temperature within a tank and the

external environment affect cable gage accuracies. The uncertainties introduced into cable gage

measurements by the environment and ways of eliminating them are covered in Appendix A.

2. GAGE TYPES

2.1 CAPACITANCE GAGE

Capacitance level gages are conceptually simple devices. One type has been described in the literature [18]. They are cylindrical capacitors consisting of two uniform coaxial tubes whose total

capacitance is proportional to length if end effects are neglected. A vertical coaxial capacitor

in vacuum has a capacitance of C x

. If this capacitor is filled with a dielectric liquid to a height h, then

C = 2nh(£

J? -l)ln b/a + C x = hC liq + C x (2.1)

where e. is the dielectric constant of the liquid, b and a are the outer tube ID and inner tube OD

respectively, and C-j. is the capacitance over and above the vacuum value added by the liquid dielectric. Actual ly,

1 the empty portion of the gage contains a gas so e - 1 is replaced by £ - £ were £ is the gas dielectric constant and Cj is now the gas filled value of C. For C-, . to regain

proportional to h, z^ and £^ must remain independent of time and fill level.

1C|

Capacitance gages have limited application because the liquids in which they are used must leave no residue on the surfaces of the capacitor. Also, the liquids must have very low electrical conductivity. Liquefied natural gas appears to meet both these requirements.

2.2 CABLE GAGE

Cable type level gages consist of a surface sensor of some description suspended on a vertical

wire, tape or cable [14-17, 19]. As the liquid surface and the surface sensor move, the wire, tape

or cable is wound on, or unwound from, a storage drum in a gage head to maintain the sensor at the

liquid surface. The change in length of wire, etc., is measured either by the drum rotation or by

a calibrated sprocket located in the gage head. The drum or sprocket drives a counter which gives

the level of the liquid. This type of gage is widely used and can be used for most any liquid.

A number of manufacturers build cable operated gages in a range of designs. Some gages, called

automatic gages, are mechanical while others are servo driven. In the latter the surface sensor transmits signals enabling the drive motor to maintain the sensor at the liquid surface.

2
2.3 BUBBLER GAGE

Bubbler gages measure hydrostatic head. The pressure of a noncondensing gas required to displace

all the liquid out the open bottom end of a drop tube that extends to the tank bottom is approximately the hydrostatic pressure. Usually, gas is bubbled slowly out the bottom of the tube to insure the liquid level has been forced to the bottom. From the hydrostatic head and the liquid

density, the liquid level is calculated.

3. CAPACITANCE TYPE LEVEL GAGES

3.1 GENERAL DESCRIPTION OF GAGES

A schematic diagram of a capacitance level gage is shown in figure 1. The gage consists of flanged

sections of tube 1 with sections of smaller tube 2 mounted concentrically inside and supported by

insulating posts 3. The inner tube sections are electrically isolated from each other by either a gap or a dielectric plug 4. The outer tube flanges 6 are bolted together so the outer tubes form a single conductor. This outer tube is electrically isolated by the insulator 5 from the tank 8. One lead from the outer tube and leads from each of the center tube sections are brought out of the

tank through a seal 7. Often, the center sections of a capacitance gage are connected together

electrically within the tank so that leads from only a top, bottom and center section need be

brought out along with a lead from the outer tube.

A properly installed gage is supported vertically by the floor of the tank and is supported in the

transverse directions but not constrained in the vertical direction at all other points. The

segmented design insures that the gage can be handled and installed. It also permits selecting

tubes of uniform dimension to minimize variation in the capacitance per unit length. The main

purpose of segmenting the gages is to electrically isolate the center segments. Isolating sections

allows the gage segments to be electrically switched so only the segment containing the liquid

surface and a nearby completely filled segment used for reference are electrically active. Activating only the segment containing the liquid surface and ratioing that capacitance value to the

nearby full section capacitance greatly reduces sensitivity of the measurement to changes in the

liquid dielectric constant. The effect of uncertainties in the dielectric constant of the gas in

the unfilled sections are reduced or eliminated. When a section is filled or emptied, the gage

readout automatically switches to the next higher or next lower segment respectively.

The absence of moving parts is an attractive feature of this gage especially for shipboard applications and for tanks subjected to rapid filling and emptying rates. The measurement accuracies

estimated are for the tank under static conditions and may not apply while the level is changing.

The two commerically available capacitance level gages are described briefly below.

3.2 FIRST CAPACITANCE GAGE

3.2.1 GAGE DESCRIPTION

The gage described in this section [18] consists of two thin walled aluminum tubes. The outer tube

is about 6 cm ID and the inner about 4 cm OD. The inner tube is supported by the outer tube via

two orthogonal insulated bolts along diameters. The various centering and supporting insulators

are shielded to eliminate leakage currents to the center tube. Shims are placed at the insulator

points to compensate for non-linearities introduced by the insulators, so that dC/dh = constant

where C is the capacitance and h is the height. The flanges are fitted and riveted to the outer

tube in a jig. The flange face separations are tested with a gage rod to % mm. The sections can

be 3.6 m or 5 m in length with one section an odd length as required to bring the assembled gage to the desired height in the tank. Entrance holes for the LNG are provided at the flange collars but

nowhere between flanges to avoid weakening the tube.

3
7

Capacitance Level Gage

Figure 1. Schematic diagram of a capacitance level gage.

The outer electrode 1 has flanged connections 6. The inner electrodes 2 are positioned supported by the insulators 3 and separated by gaps or insulating

plugs 4. The insulator 5 supports the gage from the bottom of the tank 8. The electrical leads 7 are brought out of the tank through gas light seals.

4
The gage and associated electronic circuitry is designed so that the full and empty conditions can

be simulated at ambient conditions. This provides a method of calibrating the gage when the tank

and gage are at ambient temperature. This calibration procedure cannot be used in an empty cold

tank because variations in the gas temperature result in sufficiently large variations in the

capacitance of the gage sections. When the tanks are empty and cold, the zero values of each

segment can be tested by manually switching in each segment and observing the level reading. If

the level reading is not the known height to the bottom of the segment, the segment zero level

value is adjusted to read the correct value. When the tank is filled with LNG, and the same segment is switched in, the gain or span of the electronics can be adjusted to give the correct

full reading. This is done for each segment.

3.2.2 MEASUREMENT UNCERTAINTIES

The lengths of the segments at the LNG boiling temperature of about -160°C, are known to

± h ± 0. 03M mm

the second term in this uncertainty arises from the uncertainty of the thermal expansion coefficient of aluminum and M is the change in length from ambient to the LNG boiling point. The gage

sections above the liquid surface can be expected to be at some temperature other than the liquid

temperature but these sections do not enter the level measurement. The temperature uncertainty

there contributes no error. The uncertainty a of a level measurement when the level reaches a joint between two electrically separated segments n and n + 1 is

n o = [0.25 V n + 0.03IM ] mm (3.1)

1

n

Only the uncertainty of the section length and the uncertainty of the expansion coefficient [21]

contribute to the measurement error when the liquid level is located at a joint. This equation

assumes that no error is introduced by the readout circuitry.

As the level of the liquid moves above a joint between electrically separated segments, the linearity and resolution of the electrical components must be included in the gage accuracy. Some

unpublished tests of gage sections using freon indicate a level measurement uncertainty no larger

than ± 3 mm [20]. This error should be maximum when the level is around the mid point of a segment. The non-linearity introduced by the gap between the ends of the center tube segments is small and included in the ± 3 mm according to the manufacturer.

The manufacturer estimates the total uncertainty due to calibration, capacitor dimensions and

linearity, and the electronics as ± 3.5 mm for a single section of the gage. The total uncertainty

he places at ± 7.5 mm. The system measures level with a resolution of 0.1 mm and displays the

measurement to 1 mm.

3.3 SECOND CAPACITANCE GAGE

3.3.1 GAGE DESCRIPTION

The gage described below consists of a 6.65 cm diameter ID 5 mm wall aluminum tube of with a 1.3 cm diameter aluminum tube down the center. The 1.3 cm tube is centered by three plastic insulating

rods inserted through holes placed 120° apart around the tube in a plane perpendicular to the tube

axis, and clamped against the inner tube by a band around the outside of the outer tube. These

support assemblies are placed periodically along the tubes. No shielding of the insulators or compensation for them was found necessary.

The tubes are segmented usually in 5 m lengths by flanges welded to the outer tube. The inner tube

axial spacing is maintained by insulating spacers between adjacent ends. Holes are provided at

5
intervals in the outer tube walls to permit entrance of the tank contents. The flanged outer tube

is built to a length and measured. The variation in length is estimated to be ± 1 mm.

The gage calibration is done when the tank is completely empty and completely full. With the tank

empty, the segments are switched in one at a time and the zero reading of each segment is adjusted

to the proper level reading. When the tank is filled, each segment is switched in and the span is adjusted to give the proper full reading. A point sensor on the top segment provides an intermediate point to calibrate the top segment.

3.3.2 MEASUREMENT UNCERTAINTIES

The uncertainty cr of the level at a joint is for this gage is

n a = [V n + 0.03 I Mn

] mm (3.2)

where n is the number of segments submerged and Mn is the thermal contraction of the cooled seg- ments. The level measurement uncertainty increases as the liquid level moves up into a segment.

Non-linearity of the gage results from variation in the tube dimensions (~0.013 mm on the inner

tube 0D and 0.0025 mm on the outer tube ID). The height uncertainty from these variation is ± 4%

mm but only a maximum of ± 3 mm has been observed according to the manufacturer. The manufacturer

estimates that temperature variation in the tank and variation of the electronics contribute errors

of ± 1.2 mm and ± 5 mm respectively. The sum of these errors is 9.2 mm and the rms value is 6 mm. The systematic error from equation (3.2) for 5 m sections with a 1 mm length uncertainty i s ± 5 mm

at the top of a 25 m high tank which raises the rms uncertainty to about ± 8 mm at the top of the

tank.

3.4 DISCUSSION

The capacitance level gages of the two manfacturers differ in detail. Fundamentally, they are similar and the experiences and needs of field use have resulted in modifications that have en- hanced their similarities.

The uncertainty estimates cited in the manufacturers' literature are ± 7.5 mm and ± 10 mm for the

first and second type gages respectively. If the error estimates by the manufacturers for linearity, gas temperature in the unfilled portion, electronics and thermal expansion coefficients of

the aluminum tube are correct, then the error estimates by both manufacturers are conservative.

Test data taken by one' manufacturer , using freon at ambient temperature to simulate LNG tends to confirm the conservative nature of the estimate since the gage agreed with a ruled standard to ± 3 mm [20].

Freon, however, will not behave the same as LNG. The latter can foam, the heavier hydrocarbons

might preferentially adhere to the gage surfaces and cause larger level error readings than noted

for freon. Variation in both gas and liquid density in the tank can introduce measurement error. Segmenting the gage eliminates any error that otherwise would have been introduced by the com- pletely filled or completely empty segments. The gage accuracy cannot be tested or monitored

readily. The full and empty calibration measurements are probably separated by 24 hours at least

for transport tanks and perhaps by weeks or months in storage tanks. The top section-full calibration can only be tested by raising the liquid level above the gage either while filling or after

filling by pumping liquid from tank to tank unless an intermediate level sensor is provided.

Circulation of the liquid and gases during the filling and emptying of the tanks and ship motion

while at sea can be expected to minimize liquid variations. However, special precautions are necessary to prevent density stratification at the very bottom of spherical tanks during filling.

Stratification has been observed in spherical tanks especially when top filled. As the tank is cooled to the LNG cargo temperature, methane is flashed off while heavier components collect.

Since a very small volume is incorporated in the bottom of a spherical tank, these heavy components

can form a layer of sufficient depth to interfere with the automatic switching of the gage to higher segments as the liquid level rises.

6
If the gage can be calibrated at ambient temperature, then in ship tanks it could presumably be

calibrated once a year during the usual yearly inspection. Shore based storage tank gages, since

the tanks may never be warmed to ambient, do not present sufficient opportunities for ambient

recal ibration.

A possibility of overestimating capacitance gage accuracy exists. To establish accuracy of capacitance gages, the gages should be tested over a period of time in LNG service. This could be done

in a special calibration facility or in a storage tank by comparing them to another gage of proven

accuracy. Such a gage does not now exist, but a cable compensated gage, if tested for accuracy

(see Appendix A), could be used.

4. CABLE GAGE TESTS

4.1 INTRODUCTION

Cable gages as presently installed can be subject to large level measurement errors. However, the

compensation methods outlined in Appendix A could significantly improve gage accuracy. With

compensation, cable gages could meet and probably exceed the estimated accuracy of capacitance

level gages. The low cost of a cable gage and the relative ease with which it can be removed and

serviced make the cable gage an attractive alternative for the capacitance gage.

The error estimates for cable gage measurements in Appendix A assume that the gage itself

contributes a negligible amount to the level measurement error when compared to those introduced by

temperature and tank movements. To ascertain that the intrinsic errors of the gage are indeed

small, the accuracy of four different types of cable gages representing most types commercially

available, were tested in an ambient temperature test facility. The facility, the tests and the

results are discussed in the remainder of this section.

4.1.1 GAGE ACCURACY TEST FACILITY

The accuracy of the gages, essentially the accuracy of the cable position measuring device, was tested in a facility installed in the air shaft of the University of Colorado Physics Building.

Access to the shaft permitted testing gage accuracy at six points in a 31 m height. A schematic of

this installation is shown in figure 2. The horizontal cross section of the air shaft is about 1 m by 3h m. At alternate floor levels, a 3/4 m wide by 2 3/4 m high ventilation opening covered by a grill work penetrates the narrow side of the shaft. These openings occur on the even numbered

floors on the side used for the tests. A lk m high frame was clamped in place across each opening

supported by the floor. A right triangular plate with its plane vertical was attached to the top

end of the frame as shown in figure 2. At the free end of this plate, a piece of aluminum angle was bolted with one flange horizontal and above the triangular plate. This horizontal or reference

surface was milled flat. The arm could be rotated about two orthogonal horizontal axes so the

milled surface could be leveled.

The reference point at the shaft bottom consisted of two horizontal plates separated by a section

of pipe which had been machined square on the ends and clamped between the plates. The top plate

served as a reference surface and the lower plate, a base. The cantilevered end of the reference

plate was leveled by adjusting leveling bolts at the corners of the triangular base plate.

The reference point on the 10th floor frame was mounted approximately ^ m above the floor to provide clearance between the gage heads and the reference surface to accommodate the surface sensors. The gage heads were mounted lk m off the floor on two horizontal about 15 cm (6 in.) aluminum

channels supported on the 10th floor end by the frame supporting the reference point and on the

opposite end by a frame hanging from the 11th floor.

These channels also supported an iron-36% nickel calibration tape used to measure the separation of

the reference surfaces. This tape was suspended from a U shaped frame that could be rolled forward

to place the tape in the notches milled in each of the reference surfaces when measuring their

separations. The notches were aligned so the tape hung straight through them. During gage tests,

the tape was rolled back out of the way of the gage as shown in figure 2.

7
Ambient Calibration Facility

Figure 2. Ambient calibration facility for cable gages.

8
With the calibration tape positioned in the notches and the 5.2 kg tape tensioning weight in place,

the tape was scribed at a level approximately 16 mm above each reference point by using an 5/8 in. gage block laid on each reference surface as a bottom guide for the scriber. The relative positions of the resulting six scribe marks were measured in the tape calibration facility at Gaithersburg. The calibration certificate for this tape appears in Appendix B.

This tape was used periodically during the tests to remeasure the relative positions of the six

reference surfaces. The distance of each scribe line above the reference surface was measured as often as twice a day during tests. A steel scale, calibrated in hundredths of inches was used to make these offset measurements to an estimated precision of about 0.1 mm. The overall accuracy of

the spacings between levels is estimated at ± 0.3 mm. This estimate comes from some photogrammetric calibration accuracy tests in which this tape and similar tapes were used. [22]

The air temperature in the shaft was monitored by liquid in glass thermometers at each level. The

temperature varied by as much as 3h°C from tfoe top to the bottom of the shaft in early May when the

outdoor temperature was generally lower than inside temperatures. The major part of the difference

occurred between the 2nd floor and 0th floor (the shaft bottom) where the airshaft is not sur- rounded by offices. The air temperature at each floor changed less than 1°C over the period of a day or over the course of several days. During the summer months, the gradient up the airshaft was generally less than 2°C and the bottom level was often as warm as the top. Again temperature

changes over the course of a day or days were less than 1°C. Mainly because the building is air

conditioned from May to August the average shaft air temperature only changed from about 22 to about 26°C and the total height change in the test area was less than lh mm between the zero and

10th floor. Because the shaft height and air temperature changed by such small amounts, reference

point positions relative to the calibration tape were measured no more than twice a day during the

actual tests.

4.1.2. HYSTERESIS TEST FACILITY

Tests using the fixed reference points in the air shaft only emulate a dropping liquid surface and

thus did not provide a convenient means of examining gage hysteresis. Consequently, the servo

gages were tested for hysteresis on a mill table. The servo gage hysteresis was assumed independent of the gage head elevation as indeed it should be. The error of the fourth cable gage, an automatic gage, is not expected to be independent of position hence the hysteresis of this gage was examined in the air shaft test facility.

To test the servo gages for hysteresis, they were mounted on a tower about 1.5 m high clamped to the table of a large horizontal mill. The gageheads were offset from the tower on the ends of two approximately 15 cm (6 in.) channels as shown in figure 3. A horizontal aluminum plate was rigidly

attached to the mill head to provide a movable reference surface in contrast to the air shaft test

facility where the reference points were fixed. An electronic machine scale measured the vertical

motion of the mill head to 0.1 mm resolution. The mill head hysteresis and scale accuracy was tested with a dial indicator calibrated in units of 0.001 in. The indicator was mounted on a ver- tical rod attached to the gage mounting plate. The dial indicator agreed with the machine scale to better than 0.02 mm and showed no evidence of hysteresis in the mill head. The dial indicator was compared to some gage blocks with which it agreed to ± .01 mm.

The hysteresis of the gages using buoyancy change to monitor liquid surface position was measured

both against a solid surface and a liquid surface. The liquid surface was provided by water in a 30.5 cm diameter shallow pan. If the measured hysteresis differs between water and a solid sur- face, the hysteresis at an LNG surface can be inferred. A gage using thermal surface sensors required a liquid nitrogen surface to properly test it. The shallow pan was replaced by a 20 cm diameter 90 cm deep nitrogen dewar.

The tests were done by raising and lowering the mill head, generally in millimeter steps and

recording the gage head and mill head height readings.

9
Gage

Hysteresis Test Facility

Figure 3. Hysteresis test facility for cable gages.

10
4.2 FIRST CABLE GAGE, SERVO

4.2.1 GAGE DESCRIPTION

The servo gage described in this section uses a displacer suspended on a wire to detect the liquid

surface. The wire winds in a spiral slot on a precisely machined drum [19]. The drum is connected

through a magnetic coupling to a torque sensing device. When the liquid level falls away from the

displacer, the torque increases, and a switch contact closes in the torque sensor. A motor, via a worm and gear, drives the displacer down until it contacts the liquid. There the torque decreases

which opens the switch and stops the drive motor. Conversely, if the level rises, the torque falls

too low and the opposite switch closes in the torque sensor causing the drive motor to lift the

displacer back to the liquid surface. The torque sensor causes the drive motor to position the

displacer so the torque is neither high nor low enough to close either switch. A counter is

attached to the motor shaft and geared so the count is equal to the height in meters for the unit

tested. The shaft also drives switches that control a stepping motor connected to a similar

counter at a remote site. The counters have a h mm resolution and were read to 0.1 mm.

For the tests performed the displacer was sometimes replaced by a brass weight equal to the displacer weight of 223 gm, The bottom of the weight was machined flat so it would rest in a reproducible fashion on the reference surfaces. No compliance was introduced between the weight and

reference point to simulate a displacer in liquid since compliance already exists in the magnetic

coupling within the gage.

4.2.2 ACCURACY TESTS

The accuracy tests took place over a span of 6 days with measurements made on the first two and

last two days. The gage readings at the reference points on the first measurements down the shaft

disagree with all succeeding values by about 3 mm. The later readings were smaller. The difference probably resulted from the wire crossing the ridge between channels on the drum somewhere

between the 2nd and 0th floor. This 3 mm decrease in reading was observed at one reference point

during all the succeeding measurements and that one was eliminated by dropping the level sensor

(the brass weight on the end of the wire) to the next reference point down and raising it again.

Probably, the wire crossed over a ridge again when it was pushed to one side to allow the weight to clear a reference arm. The data point was not used in the analysis.

During the tests the displacer weight was raised and allowed to settle again from 5 to 8 times on each reference surface before moving on the next. The average of each set of readings is shown in

table la. The total scatter of these repeated readings was ±0.1 mm. The gage readings were not adjusted to zero at any reference point. The table is sectioned to show the day the data were

taken and the arrow shows whether the sensor was being raised or lowered.

During the period of time these tests were done, some of the reference level positions were meas- ured by the calibration tape 7 times. Four of those times, all the reference level positions were

measured. The measured offsets, after adjusting to the average value since the vertical position

of the tape can vary, had a spread generally less than 0.1 mm with the largest being 0.15 mm. Since this spread is within the estimated resolution of a single reading of position relative to a tape scribe mark (± 0.2 mm), no corrections for changes of reference point separations due to building temperature changes were necessary.

Since the spread of the averaged readings for each measurement at a reference level does not exceed

0.3 mm, the averaged values for each measurement at a level were averaged and compared to the

calibration tape measurements of level position. In table lb the measurements by the calibration

tape and the level gage are converted to the distances from the 10th floor reference surface to each of the others. The spacings given by the level gage are larger but only by 0.8 mm at the

most. The errors suggest a small non-linearity but only two of them exceed the scatter of the

data. The results shown in table 1 are from the direct reading dial. The data from the remote

readout unit averaged in the same way gave precisely the same values for the reference level

separations.

11
12

Remote

readout

gives

precisely

the

same

distances
The manufacturer's specifications call for the gage error AL to be

AL < (0.5 + 0.035L) mm "fine precision"

AL < (0.5 + 0.13L) mm "commercial precision"

where L = the level in meters, and for infinite density liquid which the reference surfaces simulate. The gage tested was "commercial precision." At a level of 31 m the allowable AL values are

± 1.6 mm and ± 4.6 mm for 'fine" and "commercial precision," respectively. At 16.66 mm, where the

measured difference was maximum, which was 0.8 mm, the error permitted is 1.1 mm for the "fine

precision" gage. Thus, this unit easily exceeds the requirements for "fine precision" at ambient

conditions. The scatter of the data, only 0.3 mm total spread at each level, suggests that a non-linear correction could be applied to make the gage accuracy even greater.

The average air temperature in the shaft decreased by about 1°C over the course of the tests. The

temperatures in the air shaft decreased monotonically 3VC from the top to the bottom of the shaft.

The approximate shrinkage of 31 m of stainless steel wire for a 1°C temperature drop is 0.5 mm. A ^ mm change could be resolved. No change of that magnitude is evident in the results.

4.2.3 HYSTERESIS TESTS

The gage was tested for hysteresis on the horizontal mill first by using the brass weight against

the flat table. The table was moved up and down between +1, 0, and -1 mm for five complete cycles.

The five readings at each level generally showed a spread of 0.2 to 0.3 mm total. The averaged

value of level reading for decreasing levels were 0.1 mm higher than the average values for increasing levels at the same mill head position and for both the local and remote readout. This

indicated hysteresis is well within the scatter of the individual measurements.

When the reference surface was water, the direct readout suggested 0.1 to 0.2 mm hysteresis while

the remote readout suggested 0.2 to 0.3 mm. The displacer sensed a water surface that had a cross- sectional area about 8 times larger than the float so the water height correction between the

extremes of the displacer position relative to the surface is 0.04 mm. Hysteresis to a liqueified

gas surface could be expected to double the hysteresis added by water which could be the difference

between the water and solid surface hysteresis, 0.2 mm - 0.1 mm = 0.1 mm, doubled plus 0.1 mm or 0.3 mm for the direct readout. The above estimates of hysteresis are tenuous because the magnitudes estimated are smaller than the scatter of the individual measurements at each level. Therefore, to within the measurement precision, hysteresis is not detectable. Some additional level

measurement error results because the wire weight adds to the displacer weight as the level drops.

The wire weighs 0.15 gm per meter which is 4.5 gm when extended 31 m. The displacer is 14 cm diameter so that in LNG at 500 kg/m3

, the displacer can be expected to ride about 0.6 mm lower at

30 m depth than at 0 m depth. This error is proportional to level and if more precise measurements

are desired, height corrections for the wire weight can easily be made.

4.3 SECOND CABLE GAGE, SERVO

4.3.1 GAGE DESCRIPTION

The servo gage described in this section suspends the surface sensor on a stainless steel tape.

The tape is actually two side by side strips of stainless steel electrically insulated from the

environment and each other by a plastic coating. The level sensor is a 10 cm diameter foam float

free to move over a range of about 1 cm with respect to the sensing head. A coil in the sensing

head, driven by an AC voltage supplied from the gage head through the stainless steel tapes, senses

the position of the some magnetic material attached to the float. A servo motor is controlled by

the signal from the sensing head and adjusts the position of the head until a null position is

achieved. The servo motor drives the tape storage drum. The tape passes over a sprocket wheel

whose teeth engage in perforations in the wider of the two stainless steel strips then down to the

sensing head. The sprocket wheel drives a mechanical counter and can also drive a transmitter to a remote readout. The least count on the counter drum corresponds to 1 mm. The 1 mm lines are about

1.5 mm apart permitting the counter position to be estimated to 0.1 mm. Because the storage drum

diameter increases as the tape is wound, the driving speed was greater than 0.6 m/min. near full

13
and about 0.4 m/nrin. near empty. The control circuit drives at a rate proportional to offset near

the null point making overshoot almost undetectable as the sensing head approaches the rest position.

4.3.2 ACCURACY TESTS

The gage accuracy was tested relative to the reference levels during three round trips up and down

the air shaft. The gage head approaches the reference levels always from above so the float could

rest on the reference surface. The bottom reference point was raised by a gage block approximately

10 cm (4 inches) because the tape was not long enough by a few cm to reach the bottom reference

surface.

The averaged value for the level gage reading at each reference level for all the measurements at each level is shown in table 2a. The total spread of the data at each level is 0.5 mm or less.

This precision approaches the resolution of the gage scale. The location of the dial reference

causes some reduction of reading precision because of parallax.

Table 2b and figure 4 show the difference between the reference surface spacings determined by

calibration tape and from the gage readings.

The bars on the averaged data points in figure 4 show the total spread of the data averaged at that

point. The gage reads a value for the reference point readings 6 mm too small corresponding to a liquid level 6 mm high at the 31 m level. The average differences for the intermediate levels fit

a linear correction to ± 0.2 mm, which is well within the limits of the combined precision of the

gage readability and the calibration tape measurement. A correction factor can readily be applied

to the gage readings for high accuracy measurement. For this gage 1.00020 x (gage reading)

corrects the readings to the calibration tape -Scale. The manufacturer has found half this offset

in one tape calibration and suspects additional offset might be there. At this writing, he is endeavoring to eliminate this offset.

The effect of cryogenic temperatures on the plastic coated tape was given cursory examination by

cooling a section of the tape in liquid nitrogen. No reduction in the tape flexibility was evident

in the section at liquid nitrogen temperature nor was there any evident effects from differential

contraction.

4.3.3 HYSTERESIS TESTS

The hysteresis tests on this gage were done first with the float in the sensor head resting on the

shelf attached to the mill head. Three complete cycles (moving the table zero to + 1 mm to zero to

- 1 mm to zero is one cycle) and a cycle to ± 0.2 mm resulted in no measurable difference between

the gage and the mill head reading.

Next, the float was tested with a water surface in a 30.4 cm diameter pan. Over the course of

three cycles through 1, 0 and - 1 mm, the maximum hysteresis was again less than 0.1 mm, i.e., no hysteresis was detected to the readability of the gage. During these water tests, the float

settled 2 to 3 mm into the liquid. If the liquid were 500 kg/m3 natural gas, the float would be

expected to settle 4 to 6 mm into the liquid. If the LNG density changed by 10% the gage would

change by 0.6 mm at the same liquid level. If higher precision is desired a correction can be

introduced by measuring the liquid density and calculating the relative shift resulting from

density change.

4.4 THIRD CABLE GAGE, SERVO

4.4.1 GAGE DESCRIPTION

The cable gage described in this section uses a hollow cable to connect the surface sensor to the

gage head [17]. A number of electrical leads pass through this hollow cable. The leads connect a densimeter, a thermometer and the surface detectors in the surface sensor to their respective

electronics in the gage head. The two surface detectors are thermal devices and cause the surface sensor to be driven to a position such that the lower detector is immersed, and the upper detector

is above the liquid surface. The surface detectors are separated vertically by about 3 mm.

14
Table 2. Second cable gage results

Table 2a--Averaged reading and total spread

Average gage Total

Floor level reading (m) spread (mm)

10th 79.3940 + 0.1

8th 74.3250 + 0.1

0.2

6th 68.5210 + 0.2

- 0.0

4th 62.7376 + 0.3

0.2

2nd 56.9602 + 0.3

0.2

0th 48.4678 + 0.2

0.3

Note: Averages of: 14 to 19 readings over 2 days. Each level approached

three times each going up and going down.

Table 2b--Compari son to calibration tape

Distance below 10th

floor reference

Gage

*g M

average

Tape

s ref<m)

SL - SL . g ref

(mm)

10th 0 0 0

8th 5.9690 5.0701 1.1

6th 10.8730 10.8748 -1.8

4th 16.6564 16.6594 -3.0

2nd 22.4338 22.4382 -4.4

0th 30.9262 30.9322 -6.0

15
DISTANCE BELOW TOP REFERENCE (m)

Figure 4. Results of the accuracy test of the second cable gage.

16
The cable consists of a flat wire wound in a tight coil around which one layer of 30 to 40 fine

wires is twisted in a spiral of about one turn in 5h cm. Around the outside, a single much heavier

wire is spiraled at a pitch of about one turn per 4 mm. A notched drive wheel meshes with this

spiral wire and drives the sensor up and down. A stepping motor powers the drive wheel and the sensor position is monitored by counting the pulses to the stepping motor. The instrument is

provided with a calibration by setting an appropriate number into some switches. This number

determines the advance of the counter per pulse to the stepping motor. The excess cable is stored

on a spring-motor-driven drum in the drive head. The readout resolution of 1 mm cannot be interpolated since this is the least count of an electronic counter.

This gage has a unique feature. Rather than using a point on the tank roof for a reference point

for setting the gage zero, this gage can be rezeroed by allowing the surface sensor to come to rest

on the tank bottom. The ensuing reduction of weight trips a switch in the gage head that resets

the level readout to a zero value. Then the surface sensor is returned to the liquid surface.

This method of determining the gage zero removes errors introduced by temperature distributions in

the tank walls and ullage provided the tank and environment are at steady state conditions (see

Appendix A for details).

4.4.2 ACCURACY TESTS

This device senses level by means of temperature probes and always hangs with full weight on the

cable other than for a small buoyancy effect change. Thus, the level sensor could not be lowered

against a reference surface to measure its position because the cable would slack. Instead the sensor was brought to a point where the counter read a fixed level, around 13 to 15 cm above each

reference surface, and the separation from the reference was measured with a dial indicator. The

dial gage reading remained 15.57 mm (0.613 ± .001") when placed between the two plates separated by

127.0 mm by a 5-inch gage block throughout the test of this gage. The dial gage read so that the

spacing between the sensor bottom and the reference point was

S = (5.000-r + 0. 613 ) ( 0 . 0254) m

where r is the dial gage reading in inches. The spacing S was subtracted from the gage reading x to give the reference point position in the gage coordinates. The reference position p is then

p = x - (5 - r + 0.613)(0.0254) m

The spacing of the other reference points from the bottom reference point is

p-p

Q = x - x

Q + (r-rQ )(0.0254) = Ap

where p , x

Q

, and r

Q are the zero floor reference level values. The results have been examined by

plotting A

Pgage -Ap

actual as a function of p-p

Q

.

Initially this gage was tested without the fixed guide wires since the gage design did not require

them if no currents were present that could deflect the level sensor and cable from vertical.

However, during these initial tests, the level sensor rotated around the axis of the cable as much

as 5 turns in the course of traversing the height of the shaft. The measurements often did not

repeat by a few millimeters when the sensor was returned to a reference point and the gage reading

was non-linear by about 1 cm over the height of the shaft.

A second set of tests was conducted with guide wires installed to constrain the sensor from rotating. In practice, most gages are installed with these guide wires.

The addition of the guide cables removed the non-repeatability observed in the first tests and

significantly reduced the non-linearity. The results are shown in table 3 and figure 5.

As can be seen in figure 5, the scatter of the level readings are almost all within the resolution

of the gage, estimated below to be ± 1.0 mm. The scatter is shown by the brackets at each refer- ence levei. The estimated uncertainty of the dial indicator measurement, ±0.2 mm, has not

17
Table 3. Third cable gage results

Table 3a--Di fferences from reference level positions

Reference level

Floor

Deviation of the gage reading from

£ - a , g ref

reference val ue

Oth 4- 0 t +1.3 4- 0 t -0.1 4-0 t 0

2nd -6.3 -6.7 6.1 -6.5 -6.6 -6.7

4th -7.0 -7.2 -7.1 -8.0 -6.9 -7.4

6th -7.2 -7.7 -7.5 -7.6 -7.8 -7.7

8th -4.4 -6.0 -5.1 -5.7 -4.6 -5.2

10th -2.9 -3.5 -3.6 1

1 Changed r

Q

here because gage sensor stalled against top reference point.

Table 3bCompari sons of averaged

calibration tape

gage separations

val ues

to

£ , ref

Cal ibration

tape (m)

£

g Gage average

(m)

£ -£ , g ref

(mm)

0 -0.6 -0.6

8.5869 8.5803 -6.6

14.3653 14.3580 -7.3

20.1500 20.1424 -7.6

25.9544 25.9492 -5.2

31.0242 31.0209 -3.3

18
DISTANCE FROM BOTTOM REFERENCE (m)

Figure 5. Results of the accuracy tests of the third cable gage.

19
been included in the resolution. Only two repeat values of the zero reading at the shaft bottom were obtained rather than three because the sensor momentarily caught on the 10th floor reference

arm as it approached the top in the last measurement. This shifts the zero because the stepping

motor stalls but the counter continues counting steps. The going down zero was used for the

measurements back down the shaft.

As the dotted line in figure 5 shows, the gage calibration needs to be adjusted to count 3 mm higher over the 31 m between top and bottom. With that adjustment and a shift of the zero reading

to read 3mm high, the gage accuracy would lie within ± 3 mm of the true value over the range. If

higher accuracy is needed, a curve may be fit through the data in figure 5 and a correction applied

to the gage readings. This would yield levels accurate to about ± 1 mm.

The non-linearity shown in figure 5 probably originates with the cable. Very slight differences in

the spacing of spirals of the wrapping can accumulate to measurable errors. This variation could

be introduced during the manufacture of the cable. Stresses in the cable introduced during the

manufacture probably cause the center of the cable to twist relative to the ends. Because of the

spiral wrap, this adds turns of the wrap between the center and one end while reducing by the same amount the number of wraps between the center and opposite end. The deviation from linearity shown

in figure 6 would result if a lh turn twist were present in the center of the cable since the pitch

of the wrap is about 4 mm per turn.

Before pulling the sensor up the last time, the cable was constrained from rotating and the center

twisted counter clockwise 15 turns then released. This caused a slight change in the difference

readings at the 8th and 10th floors. Any difference was less than 2 mm. This implies that the

cable is quite stable with respect to twist at ambient temperature.

Because of the non-linearity of the instrument, the gage should be calibrated using several rather

than two reference levels for best accuracy.

The gage is driven by a stepping motor and the calibration of 0.26229 mm/ step is added to a register recording 0.00001 mm in the last place. The reading is displayed to the nearest millimeter so the readout uncertainty is ± 1 mm. The uncertainty associated with the difference between

two readings is also ± 1 mm.

The mechanism that zeros the counter when the sensor contacts the tank bottom is a weight-actuated

switch that trips when some of the sensor load is taken up by the tank floor. During the tests

without guide wires, the gage was allowed to zero several times on the bottom reference then raised

to a height reading of 130' mm above the bottom reference and the height measured with the dial

indicator. The results are shown in table 4. The total spread of the data is less than 1 mm. This is within the resolution of the gage and suggests that the zeroing process does not add a significant error to the position measurement.

4.4.3 HYSTERESIS TESTS

This gage thermally senses the liquid surface. To do the hysteresis tests, a 90 cm deep by 20 cm diameter dewar containing liquid nitrogen (LN 2 ) was placed on the shelf on the milling machine

head. A 16h cm diameter copper can was placed inside the dewar. A ^ cm diameter hole was drilled

through the wall of this can so that when the level sensors were lowered to the height of the hole,

the bottom of the sensing head was still about 8 cm above the bottom of the copper can.

The copper can was filled with LN2 to the level of the hole. The annular gap was also filled but

to a lesser height. The level in the inner can could be maintained to the level of the hole by

adding small amounts of LN2 and allowing the excess to run through the hole into the annulus. All

of the boiling caused by heat leak takes place in the annular space. No boiling was noted in the

inner can.

Hysteresis was first examined by varying the mill head position between +5 mm to -5 mm in 1 mm

steps. The gage drive was set to automatic, the mode that causes the sensor to follow the liquid

surface. The results of one such measurement is shown in figure 6. The hysteresis is about ± 3 mm. The gage would start to change between the mm steps. This is indicated by the curved dotted

20
HEIGHT

FROM

REFERENCE

ACCORDING

TO

GAGE

(mm)

Figure 6. Results of a hysteresis test on the third cable gage.

21
Table 4--Rezero accuracy of the third cable gage

Rezero date Dial gage*

7-8-81 130. 5 mm

7-14-81 130. 5 mm

7-15-81 131. 1 mm

7-24-81 130. 5 mm

130. 5 mm 130.3 mm

^Reading with sensing head raised to a reading of 13.0 cm above zero value.

Note: The average height measured by the dial indicator is 130.6 mm. The total spread of the data is 0.8 mm.

sections of the curve. If instead the table is stopped when the gage started to change, then the

table position and new gage reading recorded, the hysteresis was similar in magnitude. The manu- facturer's estimate of the hysteresis is 3 mm.

The gage was also tested in the manual mode by first driving the gage sensor up about 1 cm then

switching to automatic and allowing the gage to set itself at the liquid level. Next, the gage

head was driven down and allowed to return to surface automatically again. This was done at other

positive and negative table positions. The gage returns to the same position to within about 1 mm regardless of whether the gage sensor was driven up or down. This was also true at points offset

from the table zero position. Some change of the LN 2 level and perhaps rotation of the sensor

head, since no guide wires were used, caused shifts during the course of these measurements but the

results suggest that the level uncertainty resulting from hysteresis could be reduced to ± 1 mm by

following this procedure.

4.5 FOURTH CABLE GAGE, AUTOMATIC

4.5.1 GAGE DESCRIPTION

Historically, the earliest gages of the cable type were the automatic gages. Automatic gages are completely mechanical devices unless fitted with a remote display unit [15]. They are easy to make

intrinsically safe, often a requirement for shipboard use. The gage tested here is built especially for shipboard use on cryogenic liquids and is a roof mounted gage. A foam float is con- nected to the gage head via a perforated stainless steel tape. In the gage head, the tape passes

over a sprocket wheel which drives a counter and is wound on a spring motor driven storage drum.

The spring motor winds the tape on the drum as a rising liquid level raises the float but is

sufficiently weak that the weight of the float unwinds the tape as the level falls.

The gage tested is the automatic gage widely used in large LNG tanks. In marine service, the float

is stored at the topmost position when the ship is in motion to prevent damage to the gage. A crank on the gage head engages the storage drum permitting the float to be raised. The float is

held at the gage head by a latch mechanism.

The direct readout dial is in meters with graduations of 1 mm. The mm marks have about a 1 mm spacing and the reading was estimated to 0.1 mm. This unit measures ullage height rather than

liquid height. The zero of the gage was not changed from the zero setting when received.

22
4.5.2 ACCURACY TESTS TO A SOLID SURFACE

The gage tests in the air shaft facility were done first by allowing the float to come to rest on each reference surface. An aluminum plate was attached to the bottom of the foam float to give it

a more durable and reproducible surface. One set of gage readings at the reference levels were

taken going down and back up the shaft. These results are shown in table 5. The gage and calibration tape distances agreed to ± 0.8 mm.

Table 5--Compari son of calibration tape and fourth cable gage

against a solid reference surface

Floor

Cal ibration

Tape

Spaci ngs (m) £ - £ f (mm)

g ref

Gage '(down) Gage (up) down up

10th 0 0 0

8th 5.0701 5.0700 5.0697 - 0.1 - 0.4

6th 10.8746 10.875 10.8745 + 0.4 - 0.1

4th 16.6595 16.6590 16.6587 - 0.5 - 0.8

2nd 22.4384 22.4380 22.4382 - 0.4 + 0.2

0th 31.0338 31.0335 31.0332 - 0.3 - 0.6

4.5.3 ACCURACY TO A LIQUID SURFACE AND HYSTERESIS TESTS

Servo-operated cable gages either reduce or eliminate offset errors that can be introduced into

automatic gage measurement by drag in the bearings or nonlinearities in the spring motors. Measuring hysteresis of a gage at closely spaced levels is adequate to characterize the measurement

accuracy of a servo gage. However, hysteresis in an automatic gage should be tested over the

entire height range of the gage. Some manufacturers use a single liquid level to test automatic

gages over the measurement range by coiling and storing the of tape at the float. Others use devices for measuring the effect of the spring motor tension over the length of the tape.

The performance of this level gage when measuring a liquid surface was tested in the air shaft

facility by placing a vessel of water on each reference surface large enough for the float. This

vessel containing the float is shown in figure 7. The water level was maintained at a fixed height

above the reference surface by a 9.5 mm O.D. overflow pipe. The pipe passes vertically through the

notch in the reference plate with the end open and about 7 cm above the vessel bottom. The pipe is

soldered through a brass block which is clamped to the reference surfaces so the open end of the

pipe is always the same distance above the reference surface. A 13 mm diameter hole up the center

of the float permits the float to be placed over this tube. The bolt, nut and locknut used to attach the float to the tape was removed and replaced by an 8 mm diameter tube to provide a vent so the water height in the hole would be the same as in the rest of the vessel. A spring, washer and

split key kept the tube vertical on the float; a second split key attaches it to the link.

The measurement process consisted of attaching the constant level pipe and water vessel to the

reference level at which the gage was to be tested and pouring in sufficient water so that when the

float was placed in the vessel, water overflowed. The water contained a small amount of detergent

to reduce the surface tension. After the water drained down to a low flow rate and the gage

reading had stopped changing, the gage was read. Then the float was raised about 1 cm and allowed

23
Perforated Tape

Vessel

Figure 7. Schematic of the liquid reference surface device.
to drop. When the gage reading was stable again, the reading was recorded and 50 to 100 cc of

water was added to the vessel and allowed to drain away. When the draining had again nearly

ceased, the gage reading was recorded. This raise and refill cycle was repeated at least once. After refilling, the gage was read when the flow dropped to the same rate rather than when the flow

stopped completely. The gage reading had ceased changing well before a reading was recorded.

The data were recorded at each reference level for four trips, two down and two up the shaft. The

differences measured between reference levels are shown in table 6a. Agreement is assumed between

the gage and reference at the highest level. The latched position which is used in service as a calibration reference point, is included. The reference surface separations are averaged for the

measurements and compared to the tape determined reference level separations in table 6b and

figure 8. The bars on each data point in the figure show the full spread of the scatter in the

data. The 3.2 mm bias can be expected to rise to 6.4 mm for a liquid of 500 kg/m3 density.

The small scatter of the data relative to the bias suggest that a correction could be applied,

therefore a measurement accuracy of ± 1 mm is possible under laboratory conditions, well within the

manufacturer's estimated uncertainty of ± 1 cm.

The ± 0.5 mm scatter of the data has not been separated into the error due to the water level

variation and the error due to the gage. The difference between the average float position when

water was added and the position after the float was raised and dropped was usually less than 0.5

mm, and only occasionally slightly over. Some of the scatter could result from variations in the

water level, the extent of which could not be easily determined. The hysteresis, then, in this

gage is about 0.5 mm and possibly less.

These measurements suggest that a correction can be applied to the gage for the offset due to the

spring motor tension bringing the gage into the same accuracy range as servo gages. However, the

accuracy of this gage is probably more sensitive to wear and contamination than servo gages so the

accuracy could decrease with time in service.

5. BUBBLER TYPE LEVEL GAGES

5.1 GAGE DESCRIPTION

Bubbler level gages and differential pressure level gages have been described in the literature by

M. P. Wilson, Jr. (13) Since these gages are usually assembled from commerically available components rather than manufactured as a package, no manufacturer's literature was found. The principle

of measurement is simple. The hydrostatic head of the liquid at the tank bottom is measured and

converted to the liquid height in the tank by dividing by the liquid density. The density must be

measured or calculated. The head pressure of a 25 m depth tank filled with liquid methane at a density of 400 kg/m3 is:

P = (g Q x 1000g/cm2

) (5.1)

If the acceleration of gravity, is in cm/sec 2 then the pressure is in Pascals. If a tank is to be gaged to 1 mm, the pressure gage must resolve pressure to 1/25,000. Accuracies of 1 part in

10,000 of full scale are available with some of the commercially available pressure measuring

instruments, however, this is a resolution of only 2.5 mm in a 25 m deep tank.

Both bubbler gage methods and static differential pressure measurement methods for LNG service are described by Wilson. The differential pressure method wherein a differential gage is connected

across the top and bottom of the tank is commonly used where penetrations into the bottom of the

tank are permitted. Since tank penetrations are often not allowed at the bottom of LNG tanks

especially ship tanks and pressure gages are operated only with difficulty at low temperature,

static differential gages often cannot be used in LNG service. The uncertainties of AP gages

should be similar in magnitude to bubbler gages excluding the dynamic pressure drops in the latter.

25
Table 6. Fourth cable gage results

Table 6a--Gage readings

Floor

Gage determined reference level spacing

4 t 4 t

1 atched -0.4841 -.4872 -.4853 -.4840

10th 0 0 0 0

8th 5.0704 5.0711 5.0709 5.0711

6th 10.8764 10.8760 10.8767 10.8758

4th 16.6610 16.6614 16.6616 16.6620

2nd 22.4404 21.4410 22.4399 22.4408

0th 31.0364 31.0367 31.0359 31.0371

*Di stances

with gage

between reference surfaces

and reference agreeing at measured to a liquid referencethe 10th level.

surface

Table 6b- -Comparison of calibration tape and fourth cable gage

Floor

Gage average

(m)

8, res Calibration tape

(mm)

£g - £ref

(mm)

1 atched -.4844 --- ---

10th 0 0 0

8th 5.0709 5.0701 0.8

6th 10.8762 10.8746 1.6

4th 16.6615 16.6595 2.0

2nd 22.4405 22.4384 2.1

0th 31.0365 31.0333 3.2

26
(mm)

DISTANCE BELOW TOP

REFERENCE LEVEL (m)

Figure 8. Results of the accuracy tests of the fourth cable gage.

27
Two variations of the bubbler gage from the description by Wilson are shown in figure 9. The extra

tube and Ap gage in the right side of figure 9 provides sufficient information so the liquid

density in the region h can be calculated. The bubbler gage design on the right side illustrates a method of eliminating any pressure drop occurring in the bubbler line. When gas is bubbling

through the lines shown in figure 9, the pressure measured by the Ap gage is the head pressure of

the liquid above the bottom end of the bubbler tube.

An alternative method of measuring the liquid head is illustrated by Wilson but not shown here.

Liquid gas interface detectors are located at the bottom of the tube and when this interface is

properly centered by adjusting the static pressure in the tube to the tank bottom the pressure is

recorded.

5.2 MEASUREMENT ERROR

The uncertainties discussed here are for the 25 m deep tank discussed in section 5.1.

If the gas in the bubbler tubes were weightless, then the Ap observed would be the hydrostatic

head. Since the gas has mass, a head pressure also exists for all the gas between the liquid and

the gage. The magnitude can be illustrated by the head correction for the bubbler line when the

tank is full. The absolute pressure is then 2 bar in the bubbler line and the head correction is somewhere between (g x 6g/cm2 )Pa, for the nitrogen gas at ambient temperature and (g x le^g/cm^Pa

if the nitrogen gas Ts at the methane boiling temperature. Furthermore, since methane is a little over half as dense as nitrogen and probably fills the reference side of the Ap measurement, an additional correction of about (g x 11.7g/cm2 )Pa for each meter the gage is placed above the tank

is required. This decreases as tBe tank level drops to about (g x 0.5g/cm2 )Pa as the tank ap- proaches empty but now, the height from the liquid to the gage i§ much larger so the total correction required is still large. An uncertainty in the pressure correction of (g x lg/cm2 )Pa is a 2.5 cm error in the liquid level measurement for a liquid with a 400 kg/m3 density.

The density measurement should be made near the bottom of a tank to provide a density value at low

filling levels. If h in figure 9 represents 10% of the tank height, then the difference of the two gage readings from eq 5.1 will be (g x 100g/cm2 )Pa for liquid methane of 400kg/m3 density. The

pressure gages can introduce a 1% error in the density measurement if they are 0.1% gages. Also,

the uncertainty in the bubbler line nitrogen gas density contributes to the density uncertainty.

The density measurement in a full tank may not represent the density at other levels in the tank

especially in a shore storage tank where stratification can take place. The bubbling nitrogen also

could alter the local density around the bubblers. A density measurement uncertainty of 1% does

not seem unlikely. An error of 1% in density introduces an uncertainty of 1% in the level even before the gas column uncertainties are included.

If the gas is bubbling into the tank, probably the bubbler line contains N 2 but a pressure drop is

present in the line. If the static method shown in figure 9, left side, is used or the interface

detector method, the composition of the gas in the lines can be expected to be some mixture of

methane and nitrogen. The uncertainty of the gas column density could easily be as large as any

pressure drop that might be experienced in a line through which gas is flowing.

Bubbler gages have been relegated to backup use for capacitance gages on ship tanks. Gage accuracy

has probably been a factor in this but reliability has been a large consideration too. Very dry

clean gas, usually nitrogen gas, must be used or the bubbler nozzles rapidly plug with ice or other

solids. Plugging has been a problem. Any leak in the lines from the pressure gage to the tank

result in a false level reading and errors introduced by small leaks can easily go undetected.

5.3 CONCLUSIONS, BUBBLER GAGE

A bubbler gage can easily be in error by tenths of a meter in a 25 m tank mainly because of

uncertainty in the liquid density measurement and several centimeters additional because of

uncertainty in gas head corrections. The poorer accuracy, along with failure due to leaks and

plugging, limits the application of these gages to back up use for custody transfer measurement.

If the gaging application does not require high accuracy, AP and bubbler gages have advantages.

They are least affected by surface turbulence thus are useful for level monitoring during rapid

f i 11 ing of a tank.

28
Bubble Level Gages

Level @h

N 2

In — =

2

N2In

2

<Sh

Kg)=

£

Level and

Density

LNG Transport Tank

Figure 9. Schematic of some bubbler gages for LNG service.

29
6. CONCLUSIONS

6.1 CAPACITANCE GAGES

Level measurement uncertainty is estimated to be 7.5 and 10 mm by the manufacturers. Based on tests in freon by one manufacturer, these estimates are conservative since the freon tests showed

an uncertainty no larger than ± 3 mm. However, a number of uncertainties, whose effect has apparently not been tested directly, arise when the gage is used in LNG. Foaming of the LNG and coating

of the tube surface can cause errors if either occurs. Temperature and composition differences of

gases and liquids in the active sections introduce errors. Drift of the electronics between the

time of calibration and the time of measurement has the potential to cause errors. Laboratory

tests in an LNG environment or at least tests in an LNG tank against an accurate standard are needed to obtain better estimates of capacitance gage measurement uncertainty for LNG service.

6.2 CABLE GAGES

Tests at ambient conditions in this laboratory of four representative gages of the cable type show

that all can measure level in the laboratory to precisions of around ± 1 mm or better. The tests

of three of the four instruments showed small systematic errors but those can be removed by calibration. The accuracy of the gages tested should be quite sufficient for most applications as long as the operating temperatures are near ambient and isothermal and the gage head mounting does

not change height. The servo gage described in section 4.4 has been designed to eliminate at least

partially the temperature and head movement effects.

Appendix A treats the level measurement error due to the tank environment and gives rough estimates

of the magnitudes of these errors. They are 10 to 100 times as great as the intrinsic uncertainty

of the gage. The errors generated by the environment can be significantly reduced by the use of

the compensation methods discussed in Appendix A.

Compensating a cable gage could make it more accurate than a capacitance gage. A compensated gage

would cost much less and be more easily removable for repairs. The capacitance gage still has the

advantage of no moving parts.

The servo gages are designed with electrical delays in the feed back circuits so that a disturbed

liquid surface does not cause the gage to hunt. The servo gages do not move until the average

level over time, changes. Wear is subsequently less and because of the feedback, wear should not have a large effect on the accuracy.

The automatic gage tested is completely mechanical and has no damping system. It is a marine

version of the commonly used float gage. The automatic gage tested showed a laboratory accuracy if

calibrated of better than ± 1 mm. How well this level of accuracy would hold as the gage wears is not known.

6.3 BUBBLER GAGES

Commercially available pressure gages can probably measure pressures accurately to an equivalent to about 2 mm of liquid height. Gage temperature and composition uncertainties in the pressure

measuring lines will degrade the accuracy of the height measurement. The dominant uncertainty in

the level measurement, however, is the determination of the density of the liquid which is neces- sary to change pressure to a height. A 1% error in the density determination introduces a 1% error in the gaging of a tank. Leaks can cause erroneous pressure readings and impurities in the

bubbling gas can plug the lines. The limitations on bubbler gage accuracy for custody transfer

measurement cannot be easily eliminated.

7. ACKNOWLEDGMENTS

The author wishes to thank the manufacturers and users of gages who provided information for

this report and the gage manufacturers who provided the cable gages tested. The author also wishes

to thank the Physics Department of the University of Colorado, and especially John C. Groft and

Professor Albert Bartlett of that department, for making the airshaft in Gamow Tower available for

the cable gage tests.

30
8. REFERENCES

[1] Armstrong, G. T. , Hydrocarbons for Fuel -- 75 Years of Material s Research at NBS , Nat. Bur. Stand. (U.S.) Spec. Publ. 434 (May 1976).

[2] Haynes, W. M. , Hiza, M. J. and McCarty, R. D. , Densities of LNG for custody transfer, LNG 5,

International Conf. on Liquefied Natural Gas, Proc. 5th (Dusseldorf, Germany, Aug 29-Sep 1,

1977)

, Vol 2, Session III, Paper 11 (Institute of Gas Technology, Chicago, 111., 1977).

[3] McCarty, R. D. , Four Mathematical Models for the Prediction of LNG Densities , Nat. Bur. Stand. (U.S.) Tech. Note 1030 (Dec 1980).

[4] Brennan, J. A., Better LNG flow measurement sought, Oil Gas J. 76(5), 168+173-4+177 (Jan

1978)

.

[5] Parrish, W. R. , Arvidson, J. M. and LaBrecque, J. F. , Development and Eva! uation of an LNG

Sampling System , Nat. Bur. Stand. (U.S.) NBS I R 78-887 (Jul 1978).

[6] Jackson, R. H. F. , Collier, R. S. , Haber, S. and Tryon, P. V. , Custody Transfer Systems for

LNG Ships: Tank Survey Techniques and Sounding Tables, Nat. Bur. Stand. (U.S.) NBSIR 79-

1751 (1979).

[7] Haight, R. J. , Hocken, R. J. , Borchardt, B. R. , Carroll, C. L. , Hartsock, R. G. , Reeve, C.P.,

Scire, F. E. and Veale, R. C. , Estimated Accuracy of Calibration of Some Membrane-Type LNG

Transport Tanks , Nat. Bur. Stand. (U.S.) NBSIR 80-2141 (1981).

[8] Hocken, R. J. and Haight, W. C. , Multiple redundancy in the measurement of large structures,

CIRP Ann. 27, 357-60 (1978).

[9] Siegwarth, J. D. , Younglove, B. A. and LaBrecque, J. F. , An Eval uation of Commercial

Densimeters for Use i n LNG , Nat. Bur. Stand. (U.S.) Tech. Note 697 (Oct 1977).

[10] Siegwarth, J. D. and LaBrecque, J. F. , A Portable Cal ibration Densimeter for Use i

n

Cryogenic Liquids , Nat. Bur. Stand. (U.S.) Tech. Note 1035 (Mar 1981).

[11] Siegwarth, J. D. and Labrecque, J. F. , Cryogenic Fluid Density Reference System : Provisional

Accuracy Statement (1980) , Nat. Bur. Stand. (U.S.) Tech. Note 1041 (Jun 1981).

[12] Roder, H. M. , ASRDI Oxygen Technology Survey Volume V: Density and Liquid Level Measurement

Instrumentation for Cryogenic Fluids Oxygen, Hydrogen, and Nitrogen, NASA SP-3083 (1974).

[13] Wilson, Jr., M. P. , "LNG Tank Level Measurement," AGA Operating Section Proceedings, Proceedings of the Transmission Conference, Las Vegas, Nevada, T-223 (1976).

[14] Jelffs, P. A. M. , "Calibration of Containers and Gauges," Journal of the Institute of Petroleum, 58, 118 (1972).

[15] Paterson, I.W.F., "Standardization for Installation of Automatic Gages," Journal of the

Institute of Petroluem, 58, 209, (1972).

[16] Watson, P. B. , Journal of the Institute of Petroleum 58, 126 (1972).

[17] Halverson, G. , "Automatic Continuous LNG Level -Gaugi ng and Temperature Measuring Systems,"

Instrumentation in Cryogenic Industry, 1, paper 602 Houston, Texas, (1976).

[18] Williams, R. A., "High Accuracy Level Gaging," Proceedings 55th International School of Hydrocarbon Measurement, Norman, Oklahoma (1980) pg 332. Similar papers appear in 1977 to 1982

schools. Also, see Moore, C. F. and Blanchard, R. L. , "Custody Transfer Instrumentation

Systems for LNG Marine Transport Projects", Fourth International kConference on Liquified

Natural Gas, Algiers, Algeria (1974).

31
[19] Eilers, C. , "Modern Automatic Tankgauging Systems," Proceedings 55th International School of

Hydrocarbon Measurement, Norman, Oklahoma (1980) pg 345.

[20] Unpublished report of gage tests in a freon by manufacturer.

[21] LNG Materials and Fluids - A User's Manual of Property Data in Data in Graphic Format , by

D. B. Mann, Editor. Manual sponsored by American Gas Association, Maritime Administration,

Office of Standard Reference Data and American Bureau of Shipping. Published by National

Bureau of Standards, Thermophysical Properties Division 773, Boulder, Colo., 325 pages (1977).

[22] Siegwarth, J. D. and LaBrecque, J. F. , "Estimated Uncertainty of Calibrations of Free Standing

Prismatic Liquefied Natural Gas Cargo Tanks." NBSIR to be published.

32
APPENDIX A

Level Measurement Errors

Caused by LNG Tank

Envi ronments

33
LEVEL-MEASUREMENT ERRORS CAUSED

BY LNG-TANK ENVIRONMENTS

J. D. Siegwarth

I. Introduction

Custody transfer of liquefied natural gas (LNG) is currently accomplished by static measurements of

volume. The liquid levels in calibrated tanks, usually transport tanks, are measured before and

after the custody transfer operation to determine the volume of LNG changing ownership. When a level measurement is made in an iso-thermal and geometrically unchanging tank, the total error of

the measurement is the combined systematic and random error of the level gage. Most tanks and

especially LNG tanks are neither isothermal nor geometrically unchanging. Thus, the tanks introduce additional systematic errors into the level measurement. The size of these additional systematic errors, which will be called tank systematic errors henceforth, depend on the type of level

gage, the method of installation and the variation with time of various tank parameters such as temperature and internal pressure. The systematic and random error of some types of gages can be

determined in the laboratory. The tank systematic error, which in many cases dominates the measure- ment error, does not lend itself readily to laboratory examination.

Though a number of different physical principles have been incorporated into cryogenic level

measuring devices [1,2], only two general types are now commonly installed for accurate LNG level

measurement. Systematic errors for one of these types called here the cable type [3,4] are discussed here.

A cable gage consists of a surface sensing unit such as a float suspended on a cable, tape or wire.

A control unit consisting of some sort of mechanical device or servo mechanism maintains the sensor

at the liquid surface and measures the length of tape, cable, or wire wound or unwound from a storage drum when the liquid surface is raised or lowered. This control unit is usually mounted

externally on the top or near the base of the tank. The level may be displayed on a mechanical or electronic counter at the control unit or electrically at a remote site. This type of gage, which

will for brevity be called a cable gage in the remainder of this paper, can be adapted to measure

level of most liquids.

The second type, the capacitance level gage [5] consists of a coaxial cylindrical capacitor with a length equal to the tank height, mounted so the axis is perpendicular to the liquid surface,

because the liquid has a higher dielectric constant than the gas, the capacitance is proportional

to the height of the liquid between the coaxial tubes. This type of gage is suitable mainly for

cryogenic service since the electrical conductance of the liquid must be small and the capacitor

plates cannot become permanently coated with the liquid. Systematic errors associated with this

type will not be discussed here.

Though the following discussion is applied to LNG tank gaging, the analysis of the cable gages

applies equally well to gaging any other liquid. Other authors have briefly discussed tank systematic errors associated with some of the level gages [3,6,7],

II. Errors Associated With Some Typical Cable Gage Installations

Tank-Top Mounting

Figure 1 illustrates a common method of installing a level gage on a typical LNG tank. The gage

head (1) may be mounted anywhere from the center to the edge of the outer tank roof. The liquid

surface sensor (2) may or may not be located in a stilling well (3) and is suspended by the cable (4).

The design is a typical large above-ground LNG storage tank design consisting of a cold inner

tank with liquid-tight sides and bottom (5) and a gas-tight outer container (6) at ambient

34
1

Figure 1. Schematic of an LNG tank and a roof-mounted level gage

35
temperature. The space between the walls and the floors of the two tanks contains insulation (7).

The ceiling of the inner tank is suspended from the domed roof of the outer tank and serves mainly

to support insulation.

Assume, as starting conditions for the analysis of the tank systematic gaging errors, that the tank

is empty, isothermal at ambient temperature, and at atmospheric pressure. The sensor rests on the

tank bottom. Linder these conditions, the gage reading is R which could be, but is not necessarily, zero. As the inner tank is cooled, the cable shrinks and the reading R is now

R = R

a + l c (1)

where 1 is the thermal change of the cable length. The cable shortens so more cable unwinds to reach tHe bottom of the tank hence R is less thajn R . The length change of the cable is given by

l c = j\(T)dx ’ (2)

o

where H is the height of the tank and the thermal expansion p (T) is defined here as:

L (T) - L (ambient)

P

c (T) = L^(ambient) (3)

Here, L is a length of cable and T is the temperature which is a function of both the elevation x and theiime t. That is.

T = f

c (x,t) (4)

and p at time t is a function of x. The correction 1 in eq (2) can then be calculated provided

f (x), the temperature distribution in the ullage spaHe has been measured.

If the gage mounting point or support moves up by either thermal expansion of the tank shell or increasing pressure difference between the inside and outside roof surfaces, the gage reading

decreases. Including the roof movement in eq (1),

R + 1 - 1 a c s (5)

where 1 is the thermally generated change of height of the tank outer shell, defined by equations

identical to (2), (3), and (4) except the subscript c is replaced by s to designate the shell, and

1 is the change of roof elevation resulting from the pressure change. The pressure, hence 1 , is

aTso a function of time. P

If the tank is cooled and filled with LNG to the height h while holding the sensor fixed to the

tank bottom, R is given by eq (5), but the 1 term can be split into the portion below the LNG surface and that above:

R = Ra

+ Vh + h W- Vo - \

( 6 )

|_| where ], , for example, shows the limits of the integral defining 1 , (eq 2). Since the LNG is at its boiling point, the liquid temperature gradient is assumed smal*?. Thus in the liquid p (T(x))

is constant. Then 1 in this region integrates to the product of h and p

(T-,) as shown iH eq (6)

where T, is the liquid boiling temperature. The surface sensor is now released and allowed to seek

the surface. After the temperature distribution of the cable from h to H again assumes the gas

temperature along its length, a length of cable h (1-p (T,)) has passed into the gage head. This

adds to the left side of eq (6) to give R. Since p is negative (see eq 3), a length of cable

longer than h has been wound. The gage reading is How,

R = R +11'

a c

J h

- 1 s

J because the P

o V c terms cancel.

(7)

36
Equation (7) is a general expression that can be applied to any gage installation by introducing

the p and p for the materials of the gage cable and support structure respectively and integrating bitween the appropriate limits. The gage reading, R, can change with time while h remains

constant because the time dependence in T and P introduces a time dependence in the three 1 terms.

Usually the difference between two levels h 2

- h x is the quantity desired rather than an absolute

value for h. Thus, subtracting eq (7) for h x from the same equation for h 2 and solving for h 2

- hj

gives

h 2

- hj — (1 1 H

- 1 1 H u ) c2 J h 2 cl J h]/

+ <'s2 - Vo + V

- 'pi ( 8 )

When the level changes the 1 term difference will not be zero nor will the 1 term difference be zero because the tank pressure can be expected to change when the level changis. The l g term

difference is non zero if the external temperature is changing.

The 1 and 1 corrections can in principle be calculated if the temperature distributions as a function of Height of both the gas space and the shell of the tank are known. The former may be

measured since the temperature profiles of the contents are usually measured but the outer shell

temperature distribution is probably not measured. In both cases corrections, if made, are likely

to be based on estimates rather than temperature measurements.

Gage Head Mounted at Ground Level

Gage I diagrammed in the tank in figure 2 is a gage installation similar to that recommended in

British Standard 3792/1964. The tank is of the same design as that in figure 1. This installation

method is independent of the tank roof if the flex section (3) has sufficient flexibility to eliminate any thrust on the gage guide arm (1). However, the arm end (1) does move up and down

with temperature because of thermal expansion of the tape guide which is anchored at the bottom of

the shell while the remainder is allowed to slide in the mounting brackets.

In the expression for the gage reading as a function of height, eq (7), both 1 and 1 are now calculated by integrating along the path of the cable, that is, from 0 to 2.1H

s for th£ installation

diagrammed in figure 2 gage I. The expression for R is,

R = R a + 1 Jh'

1H

- Vo""- ] p + h - (9)

The integrals from 0 to H are essentially the same as for the gage installation shown in figure 1 except now the expansion of the guide tube rather than the tank enters the expression for 1 . The

portion of the integral determining 1 and 1 between H and 2.1H is just the difference between the

length of the guide and the cable. The 0.1 H in the guide length allows for the horizontal guide

section at the tank top.

The temperature distribution in the guide and enclosed cable can be assumed the same. Thus only

differences of B and B give a non zero value to the difference of 1 and 1 between H and 2.1H.

C 5 C S Any motions in the vertical direction of the end of the arm, (1) due to wind or differential

expansion between the guide and brace (3) will be included in the lp term.

The relationship between true level change h 2 - hi, and gage reading R 2

- R x for this gage

installation is obtained by subtracting eq (9) for R 2 from eq (9) for Rj. Solving this difference

for h 2

- h x gives

37
( 10 )

Variations of this mounting exclude the flexible section (3) figure 2 gage I at the tank top. The

roof-movement error again fully enters measurement as when the gage is roof mounted.

Bottom-Referencing Level Gage

This type of cable gage drives down, senses the tank bottom for a reference point, then measures

the surface. This cycle can take an hour to complete for a full tank. The suspending cable is

hollow with electrical leads inside.

The gage reading with the sensor at the bottom, R^, is the same as eg (6):

where the b subscripts indicate the value with the surface sensor resting on the tank bottom. The

gage reading with the sensor at the liquid level is given by eq (7). Combining eqs (11) and (7)

and solving for the level h gives

The 1,1 and 1 terms would cancel if there were no change in the pressure in the tank, the

temperature distribution in the ullage of tank or temperature change of the ambient shell in the

time lapse between sensing the bottom then the liquid level. The contribution of the 1 terms are probably small but not zero. Thus, when the difference of two levels is measured, the bottom must

be sensed at each level and the level must be static through the time between the bottom and

surface measurements for best accuracy.

Level gages can be installed by two methods that eliminate most of the sources of errors discussed

in the previous section. The first method, the stilling well method, is based on the fact that eq

(7) contains the difference between the 1 and 1 terms. Thus, if the temperature distributions

are the same and P

c

( x ) = |3 (x) the terms Can cancel.

The second method, the cable-compensation method is merely a means of measuring the magnitude of

the gage-support motion that also includes a measurement of-cable length change.

Stilling-Well Method

The stilling-well method is shown by gage II diagrammed in figure 2. The level gage is mounted on the top of the stilling well (5). The stilling well is supported by the floor and passes through a flexible seal (6) in the tank roof. The gage reading for this installation is, from eq (7),

The 1 term, where 1 is now the expansion of the stilling well rather than the tank shell, has

been split into a term for the liquid region and a term for the gas region. No pressure term

appears because a suitable flexible seal (6) eliminates any pressure effect on the gage support.

If the floor settles slightly with filling the gage reference follows it and compensates for the

settling provided the mounting point movement reflects the average tank-bottom settling.

If the coefficient of expansion of the cable and pipe are the same and T (x,t) is the same as

T (x,t) a^ it almost certainly is since the cable sees only the stilling-well temperature, the term

(T

c

~ 1 )] h is zero in eq (13). The actual level difference, h 2

- h x , when the level changes from

h x to n 2 , can be determined by taking the difference between eq (13) expressed for R 2 and R x and

solving for h 2- h x

(ID

( 12 )

III. Gage Installation Methods Providing Compensation

(13)

38
I n i

Figure 2. Schematic of a LNG tank showing different level-gage

installations. I is a ground-level reading gage, II

is a stilling-well compensated gage, and III is a cable-compensated gage. Complete descriptions are contained in the text.

39
7

h 2

- hi = (R2 - R x )/(1 - Psd^). (14)

The thermal expansion p (T-j) is known for most materials and can be assumed approximately constant

because T-j changes littfe with height.

Though this method of installation permits high accuracy, a stainless-steel tube and a tape or wire

is probably the only combination practical to use as an expansion-matched cable and support. The

expansion of a cable rather than a tape or wire, probably will not match the expansion of the tube even though made of the same material [3].

A stainless-steel stilling well would not only be expensive installed at the time the tank is built

but also difficult, if not impossible, to retrofit in an already constructed storage tank.

Cable-Compensated Method

The second method for a compensating gage installation that can achieve the same accuracy while

permitting a wider choice of cable material is gage III illustrated in figure 2. A second or reference cable (7) of the same material as the gage cable is attached to the bottom, preferably by

the weight (8). This reference cable could be a guide cable for the level sensor. This cable is

attached to another 1 evel -readout mechanism which could be another gage head or a more simple

device contained within the level-gage head to record small motions. The reference cable reading r is given by a relation identical to eq (6):

where again r is the reading with the whole tank at ambient conditions and could be set to zero. This second live! indicator records the changes of the reference cable length relative to the gage

mounting. These changes are probably no more than ± 20 cm in a 40 m high tank.

Since this reference cable is chosen to match the coefficient of the gage cable, eq (15) subtracted

from eq (7), the expression for the reading of a roof mounted gage, gives

The height difference between two levels h 2 and h x derived from eq (16) is related to the gage and

reference readings by:

The quantity r 2

- r x was provided mechanically for a stilling-well mounting when the stilling-well

and cable have matched thermal coefficents. This reference cable method permits r2- r x to be read

separately and subtracted or subtracted within the readout logic. Cable compensation should be

cheaper to install than the stilling-well compensation and can easily be retrofitted to existing

tanks.

The reference cable method can be used for correction of the level gage using the bottom as a reference. The stilling-well method would not serve since the hollow cable does not have the same

thermal expansion as the bulk material [3]. This compensating method could be used also when the

gage head is mounted at grade level provided that the same wire or tape extends all the way from

the level sensor to the control unit.

A reference cable can correct any of the gage installations described here for the errors introduced by thermal and mounting effects. If the bottom of the tank settles uniformly relative to the

outer shell as the tank fills, the reference cable corrects for this just as does the stilling

well. The errors remaining are primarily the uncertainties in thermal -expansion data and the gage

accuracy.

(15)

R ' r = R a

' r a" h MT

l } + h (16)

h 2 - hj = [R 2 - R x -(r2 -r x )]/(l - P

C (T -, ) )

(17)

40
IV. Qualitative Error Estimate for a Typical LNG Storage Tank

Maximum values for the various tank systematic gaging errors for a tank 40 m high by 60 m diameter

are estimated here for the gage installations discussed above. The error estimates are based on the assumption that the gage readings are taken to be the true levels. Some corrections, like the

ullage temperature effect on the level have been discussed by other authors and some corrections

may be made to level measurements at some installations. Corrections are generally not made for

ambient temperature variation of the gage support height or pressure-caused variations of that

height.

For the error estimates here, the average temperature of the ullage is assumed to be -100°C. In an actual tank, this temperature is not constant and the temperature distribution varies with time and

the filling or emptying of the tank.

The tank outer-shell temperature can vary considerably since the tank contents provide no thermal

inertia to the shell as the contents do for single wall tanks containing ambient temperature

liquids. The temperature of the shell is estimated to vary over the range of 60°C from a hot sunny

day to a cold night. The absorption and emissivity of the tank influence this range as well as the

weather.

No measured value was found in the literature for the magnitude of the roof movement in the vertical direction due to the pressure of the contents. Estimates range from one to several centimeters

[3]. The magnitude of the roof movement depends on the structural design and the magnitude of the

internal pressure and the range permitted.

The maximum values for the estimated errors presented in Table 1 are based on the assumption that

the tank goes from filled to empty while at the same time, factors introducing the tank systematic

errors change from one extreme to the other. The different errors are added to give the total errors discussed below. These total errors are for purposes of comparing the various installation

methods and do not apply to any specific installations.

The first line in Table I gives an estimate of the tank introduced systematic errors of a conventional tank top installation. The maximum possible error for a steel tank and stainless steel tape

or wire is about 11 cm. A cable could give a larger maximum value [3].

The estimated errors when the gate head is mounted at ground are given in the second line of

Table I. A larger number of parts permits a wider variety of materials. The level systematic error varies from slightly smaller to larger than the 4 cm estimated for a roof mount, line 1. The

use of invar in the ullage reduces the error there but increases the error resulting from expansion

differences between the guidetube and cable wire or tape.

The total tank systematic error introduced by the tank structure to the bottom sensing gage line 3,

Table I, is difficult to estimate. Referencing the bottom removes all the error due to tank

parameter change if the parameters do not change between sensing the surface and sensing the

bottom. In actual cases some change can occur and then the cycle time of the gage is important. A few centimeters total error seems possible.

Estimated errors for stilling-well compensation is given on line 4, Table I. The assumption that

T(x) of the wire cable or tape and stilling well are equal is reasonable but the assumption that

P

c (x) ?nd Mx ) are the same is more dubious, especially for a cable [3]. The manufacture of a tube differ! enough from that of tape or wire that making them of the same material might not assure equal expansivity. Thus a total tank introduced systematic error of a stilling well com- pensating installation could be 2 or 3 cm. A careful choice of materials could reduce the systematic error estimate to a low enough value that gage errors could then dominate.

The error estimate for the cable compensated level gage is given in line 5 of Table 1. This tank

systematic error is estimated to be the smallest because invar can be used for the gage and refer- ence cables thereby reducing the p(T,) contribution to its smallest value. This type of compensation offers the highest flexibility since even a cable, rather than just a wire and tape can be

compensated and any material can be used. Two cables, wires, or tapes can more easily be tested in

41
Table 1. Maximum estimated errors introduced into level measurement if

(R 2

- R x ) is assumed to be the level change for a 40 meter depth

LNG tank with carbon steel outer shell. NA means "not applicable".

Gage mount ^c (T), Ave T is -10Cl°C 1 (T) for AT = 60°C

Pressure

method stainless steel ref. pt. Tape Guide (1) Other

cable motion Diff

1 Roof 8 cm 2h cm NA ~1 cm -

2 Grade level 8 cm 2.5 to 6 cm -2 to +7 cm NA <5 cm

BS 3792/1964 (3) (4) (2)

3 Bottom 0 to ~lcm 0 to 7h cm NA 0 to ~1 cm 1 cm

sensi ng (5) (6)

4 Still well +8 -8 NA 0 <3 mm

top (7)

5 Roof +8 -8 NA 0 <1 mm compensation (7,8)

(1) Magnitude depends on flex of roof and whether the gage is near the edge.

(2) Vertical motion of arm end from bending effects of temperature and wind.

(3) 2.5 cm for steel to 6 cm for aluminum.

(4) -2 cm for carbon steel guide tube and SS cable. 7 cm for invar cable and

aluminum guide tube. Sign gives correction relative to (3).

(5) This estimate is reasonable only if the bottom is referenced before and

after a level change.

(6) 8 (T-,) estimated larger since cable may vary in expansivity.

(7) Uncertainty in p (T,) of 3%. (8) Uncertainty in p^(T-j) estimated for invar cable.

*An invar cable can reduce this error to about 1 cm for the gages of lines

1, 2, and 5 but might not be feasible for the gages of lines 3 and 4.

42
the laboratory to assure that their thermal expansions match sufficiently. The gage cable and

compensating cable can be located within a few centimeters of each other so the temperature distribution along them can be expected to be the same.

V. Summary

In this paper equations have been derived for calculating systematic errors introduced by the LNG

tank environment. If appropriate measurements, especially temperature distribution measurements,

are made the corrections could be calculated. The time variation of the parameters needed to correct the tank systematic error and the large number of measurements required make calculated

corrections difficult.

Two relatively simple installation methods have been described in this paper that greatly reduce or eliminate tank systematic level gaging errors.

[1] Roder, H. M. , ASRDI Oxygen Technology Survey Volume V: Density and Liquid Level Measurement

Instrumentation for Cryogenic Fluids Oxygen, Hydrogen, and Nitrogen, NASA SP-3083 (1974).

[2] M. P. Wilson, Jr., AGA Operating Section Proceedings, Proceedings of the Transmission Conference, Las Vegas, Nevada, T-223, American Gas Assoc., Arlington, Va. , (1976).

[3] G. Halverson, Instrumentation in Cryogenic Industry I, Houston, Texas, paper 602, Instrument

Society of America, Pittsburg, Pa. (1976).

[4] C. Eilers, Proceedings, 55th International School of Hydrocarbon Measurement, Norman, Oklahoma, page 345. Available from Laurence S. Reid, P.0. Box 1188, Norman Okla. (1980).

[5] R. A. Williams, Proceedings 55th International School of Hydrocarbon Measurement, Norman,

Oklahoma, page 332. Available from Laurence S. Reid, P.0. Box 1188, Norman, Okla. (1980).

[6] P. B. Watson, J. Inst. Pet. 58, 126 (1972).

[7] P. Jelffs, J. Inst. Pet. 58, 118 (1972).

43
APPENDIX B

Determination of Reference

Mark Separations on the

Calibration Tape

44
Determination of Reference Mark Separations

on the Calibration Tape

The tape was hung in the shaft so the last entry in the report of calibration (following page) was

at the top. The table must be inverted to give the distances of each scribe line below the top one which gives:

0.0 m 5.07048 m 10.87539 m 16.66045 m 22.43954 m 31.03509 m

for the spacings.

For this tape the elastic change is

AL/L = 2.061310" 5 • M ( 1 )

where M is the mass in kilograms.

The weight on the bottom of the tape was 5.245382 kg. The average mass M acting on a section of

the cable is

M = 5.245382 + (31 - L/2)(. 026762) kg

where L is the length of the section being corrected for tension. The second term is the correction for the weight of the tape. Since the tape was calibrated with a 10 kg weight supplying the

tension, from eq (1) the corrected length in meters is:

L c = L(1 + 2.0613 x 10“ 5 x [M - 10 kg]) .

The corrected length is less than L since M is smaller than 10 kg. The temperature correction is

less than 0.1 mm for 31 m and not included.

The scribe mark separations, L c from the topmost are taken to be

5.0701 m 10.8745 m 16.6590 m 22.4376 m 31.0324 m

for these tests. These values are converted to the reference level separations by appropriately

adding or subtracting the differences of the offsets of the scribe marks from the reference surfaces. The offsets were measured to about 0.1 mm with a steel machinist's scale.

45
FORM NBS-4U

(REV. 12—W)

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON, D.C. 20234

REPORT OF CALIBRATION M1606

NBS No. 14916-A

For: One Invar Tape

Submitted by: James D. Siegwarth

Division 773.10

NBS Boulder

Boulder, CO 80303

The tape was calibrated using a helium-neon laser interferometer as the

length standard while under tension and uniformly supported on a horizontal

flat surface. The distances between the terminal points of the indicated

intervals at 20 degrees Celsius (68 degrees Fahrenheit) under 10 kilograms

tension are given below. The terminal points of the indicated intervals

are the centers of the graduations at the edge of the tape ribbon nearest

the observer when the zero graduation is to the left.

All measurements were made in a controlled environment near 20 degrees

Celsius and an assumed coefficient of thermal expansion of 0.0000004 per

degree was used to correct the lengths to 20 degrees.

The uncertainty of the reported lengths is 0.000005 meter per meter and

is taken to be the sum of the random and systematic components of error. The random component is taken to be three times the observed standard

deviation. The systematic component consists solely of the uncertainty

of the laser interferometer and is estimated to be 0.000002 meter per

Tension

(kilograms)

Length

(meters)

10

10

10

10

10

8.59555

14.37464

20.15970

25.96461

31.03509

meter

Measurements were made by

Robert j/ Hocken, Chief

'Automat/d Production Technology Division

Center for Manufacturing Engineering

Date: June 4, 1981

46
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 82-1668

2. Performing Organ. Report No. 3. Publication Date June 1982

4. TITLE AND SUBTITLE

Measurement Uncertainties

of Level Gages for

Liquefied Natural Gas

5. AUTHOR(S)

J. D. Siegwarth

6. PERFORMING ORGANIZATION (If joint or other than N BS, see in struction s) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

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

Maritime Administration

Department of Commerce, Washington, D.C.

10. SUPPLEMENTARY NOTES

L221 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. 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 measurement uncertainties of three types of gages commonly used in large liquefied

natural gas storage and ship transport tanks have been studied and the results of this

study are reported here. The types are bubbler, capacitance, and cable gages. Measurement uncertainties for various types can be determined but the test conditions must be

carefully specified because many of the largest errors result from parameters external to

the gaging device. The gage installation, the tank design, and the liquid properties all

influence gaging accuracy. A modification of cable gage installations that should

significantly improve gaging accuracy is presented. Intrinsic accuracies of some representative cable gages are reported from tests done at ambient temperature under nearly

isothermal conditions. The gages tested, if calibrated, can all measure level to about

one mm under the test conditions. Capacitance gages should be tested in liquefied

natural gas to establish their measurement uncertainty. Bubbler gages require knowledge

of liquid density, the temperature distributions in and contents of the connecting tubes,

pressure drops, and head corrections; otherwise, the errors can be several centimeters.

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and separate key words by semicolon s) bubbler gage; cable gage; capacitance gage; level gage; liquefied natural gas

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

|j^] Uni imited

| 1 For Official Distribution. Do Not Release to NTIS 52

1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. 15. Price

[XXl Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $9.00

USCOMM-DC 6043-P80

U.S. GOVERNMENT PRINTING OFFICE: 1982-579-168/293 REGION No. 8