A PORTABLE CALIBRATION DENSIMETER FOR USE IN CRYOGENIC LIQUIDS J. D Siegwarth and J. F. LaBrecque Thermophysical Properties Division A portable densimeter designed specifically for calibrating liquefied natural gas densimeters but suitable for density measurement of a wide range of liquids, is described. The densimeter has been compared to the Density Reference System densimeter at the National Bureau of Standards and found to agree to well within the combined systematic error. The density results of this instrument and that of the DRS densimeter are statistically indistinguishable. Key words: Densimeter; density reference system; liquid methane; LNG. The cryogenic liquids Density Reference System [1] (DRS) at the National Bureau of Standards in Boulder, Colorado, originated as a device for testing calibration and performance of commercially built densimeters for liquefied natural gas (LNG) service. A number of commercial densimeters were tested with this system and the results reported [2]. All the densimeters tested functioned adequately. These tests, however, disclosed a need for better calibration methods for the commercial densimeters. We implemented a transfer standard program at NBS as a method of providing a suitable calibration for commercially built LNG densimeters. In this program, a manufacturer or user of densimeters selects a commercial densimeter against which he will calibrate his densimeters by comparison in a homogeneous fluid. We periodically calibrate his selected densimeter in the DRS and this becomes the transfer standard. We rebuilt the density reference system into a flexible configuration so densimeters of various designs could be more easily introduced and more rapidly calibrated [3]. The new DRS was designed also with the intention of demonstrating a type of system that could safely handle combustible gases in an industrial calibration laboratory since for best results, a densimeter should be calibrated in a fluid similar to that in which it will be used. After the DRS was rebuilt, the availability of an electronic balance capable of weighing 200 g to 0.001 g resulted in our rebuilding the DRS densimeter to incorporate this balance. We found this new balance both compact and sufficiently robust to suggest the possibility of constructing a portable silicon densimeter. This portable densimeter could then be installed in any commercial calibration facility to calibrate the reference densimeter of the facility. This method has the definite advantage that it permits us to test a whole facility rather than just the calibration densimeter used in the facility. The transporting of this portable densimeter should not add any additional uncertainty to the instrument since the reference weight makes it self-calibrating. We have built such a portable densimeter and tested it in the DRS. We describe this densimeter and these comparison measurements in this report. From these results, we have generated an accuracy statement for this densimeter. 2. THE PORTABLE REFERENCE DENSIMETER The Portable Reference Densimeter (PRD) shown in fig. 1 is very similar to the DRS densimeter described in ref. 3. The PRD is an Archimedes type densimeter consisting of a silicon single crystal float of accurately known weight that is weighed while immersed in the liquid whose density is desired. We weigh the 162 g silicon single crystal with a commercially built electronic balance capable of weighing 220 g to 1 mg. The sensing unit has been removed from the instrument case and installed in a 178 mm diameter closed aluminum case designed to withstand an internal pressure in excess of 1 MPa. A simplified drawing of this instrument is shown in fig. 1. "A" is the silicon single crystal shown lifted from the suspension cage "B" and clamped between supports "C" and "D". The bottom supports "D" are raised when the 15 mm ID thin walled stainless steel tube "E" is lifted by a pneumatic cylinder actuating the bell crank mechanism "F". The upper supports are fixed to the 25.4 mm OD by 0.6 m long thin wall stainless steel tube "G". This length was dictated by the distance from the top plate to the sample liquid in the DRS where it was tested and may be changed. The cage "B" is suspended from the electronic balance sensing unit "H" by the 1.6 mm diameter tube "I". The balance "H" is mounted on a cantilevered plate "J" so that should gas tight balance case "K", capable of holding 10 bar interval pressure, flex when pressurized the leveling of the balance is unaffected. This permits a lighter construction for the balance case than used for the DRS densimeter. The tungsten reference weight "L", used to monitor the balance calibration, is shown placed on its suspension cage "M". This cage replaces a section of the suspension tube "I". Some swivel joints in this suspension permits flexing but not rotation. A pneumatic-cylinder driven bell crank, similar to "F" but not shown in the drawing raises "N" which lifts the reference weight "L" off the suspension and clamps it against the fixed top support "0". The "0" ring seal at "p" connects this densimeter into an LNG sample container. This joint is a gland seal rather than a flange seal so the instrument can be tilted according to the bull's eye level "Q" to align the suspension "F" to tube "E". A gas tight seal "R" is provided for the electrical leads "S". The case "K" is clamped together with sufficient bolts through the flanges to withstand a 10 bar internal pressure. The apparent mass of the reference weight is approximately the same as that of the silicon float when the latter is suspended in liquid methane. We compared this apparent mass value, corrected to a true mass value by using the temperature and pressure of the sample gas to determine the buoyant effect, to the true mass values of the tungsten as determined by precision weighing. This procedure provides a continual monitoring of the balance calibration. Tungsten was chosen for the reference weight because its high density reduces the magnitude of the buoyancy correction hence any effect of uncertainty in the gas density in the region of the reference is minimized. 3. DENSITY MEASUREMENT AND SYSTEMATIC UNCERTAINTIES The density of the liquid in which the float is immersed is given by the relation [3]: where Ms (=162.2502+0.0005 g, 99% confidence interval) is the true mass of the silicon single crystal, Ma is the apparent mass value with the silicon on the suspension and immersed in the liquid, Mao is the weight of the suspension in the liquid (this reading is zero ± 0.001 g as a general rule because the balance is zeroed in this configuration) and ps is the density of the single crystal silicon at the liquid temperature and pressure. The silicon single crystal density at 110 K from ref. 2 is assumed to be 2.3308 + 0.00007 g/cm3. This includes both the estimated experimental uncertainty in the density and the thermal expansivity. The true mass values of the silicon crystals and the reference weights for the DRS and the PRD are given in table 1 along with an estimate of total uncertainty for each value. Total uncertainty is defined as t/- the sum of the systematic error limit plus the 99% confidence limit for the average of the n weighings. Each true mass value is an average of n weighings made on separate days. The systematic error in each case is the systematic uncertainty specified for the set of class S weights used. The estimated errors for the various measured quantities are shown in table 2 which is similar to the same table in ref. 3. We have not included the error for temperature gradient and drift of a liquid sample [3] because we are now examining the systematic error of the densimeter only, not the densimeter plus sample container. As before [3], the total systematic error shown in table 2 is assumed to be the square root of the sum of the squares of the individual contributions. If the densimeter is used in liquids at temperatures well removed from 110 K an expression for ps(T) is related to the 0°C density by where L is a crystal dimension. Gibbons [4] gives values of B(T) for T = 40 to 300 K at intervals of 10 K. He reports the probable error for expansivity to be less than 0.5% at each point. Gibbons does not define probable error, but in one definition [6] it is 0.6475 times the standard deviation. This suggests that his estimated standard deviation for expansivity is less than 0.8% for each value. He also does not mention if inherent systematic error in his experimental apparatus was considered. Differences between his values and those of other experimenters are noted in the paper. As a possible aid to interpolation in Gibbon's table for the expansivity of silicon the following fourth degree polynemial was fit to his values of B(T) for T = 70 to 300 K: |