Method for determining a measurement error caused by a filling error

Abstract

A method for determining a measurement error caused by a filling error, in particular the presence of gas bubbles, during measurement of the density of a liquid by means of a densimeter having a flexural resonator containing the liquid to be measured. During a measuring operation, a period duration of an oscillation of the flexural resonator induced by an induction unit is measured by a measuring device and the density of the liquid is determined by an evaluation unit.

Claims

1. A method for determining a measurement error (ρ.sub.error) caused by a filling error during measurement of a density(ρ) of a liquid by means of a densimeter having a flexural resonator containing the liquid to be measured, wherein, during a measuring operation, a period duration of an oscillation of the flexural resonator induced by an induction unit is measured by a measuring device and the density (ρ) of the liquid is determined by an evaluation unit, the method comprising: determining a first pressure-dependent density difference (Δρ(P)) by subtracting the determined density (ρ) of the liquid pressurized with a first pressure (P.sub.0) by a pressurizing means during a first measuring operation and of the liquid pressurized with a second pressure (P) by means of the pressurizing means during a second measuring operation; and determining the measurement error (ρ.sub.error) via the equation $\mathrm{\Delta \rho }\left(P\right)=\left(P-P_0\right).Math.\left(\frac{{\rho }_{\mathrm{error}}}{P}+\frac{1}{E}\right),$ wherein for solving the equation, either a compressibility (E) depending on the measured liquid is selected or at least one further density difference (Δρ(P)) is determined by subtracting the determined density (ρ) of the liquid pressurized with the first pressure (P.sub.0) by the pressurizing means during the first measuring operation and of the liquid pressurized with at least a further pressure (P) by the pressurizing means during at least one second measuring operation.

2. The method for determining a measurement error (ρ.sub.error) according to claim 1, further comprising detecting the filling error when a predetermined threshold value of the measurement error (ρ.sub.error) is surpassed by the determined measurement error (ρ.sub.error).

3. The method for determining a measurement error (ρ.sub.error) according to claim 1, wherein the pressure used for determining the measurement error (ρ.sub.error) is between 100 kPa and 200 kPa, or between 101 kPa and 150 kPa.

4. The method of claim 1, wherein the filling error includes a presence of gas bubbles.

5. The method for determining a measurement error according to claim 1, wherein the determination of the measurement error (ρ.sub.error) is conducted during adjustment of a measuring temperature of the liquid in the flexural resonator to a target temperature of the liquid in the flexural resonator set for the conduction of the measurement.

6. The method for determining a measurement error (ρ.sub.error) according to claim 5, wherein the target temperature of the liquid in the flexural resonator is between 10° C. and 90° C., or between 14° C. and 20° C., or between 15° C. and 16° C.

7. The method for determining a measurement error (ρ.sub.error) according to claim 1, wherein a measurement of a reference pressure density at a reference pressure is conducted before each density measurement, and a measure for variation of the reference pressure density determined at the reference pressure is determined, wherein measurement is cancelled when a threshold value of the variation of measurement is surpassed, and the determined densities are discarded.

8. The method of claim 7, wherein the reference pressure is ambient pressure.

Description

(1) The present invention will now be described in more detail by means of exemplary embodiments with reference to the figures.

(2) FIG. 1 shows a schematic representation of the essential components of a densimeter according to claim 1 for determining a measurement error caused by a filling error, in particular the presence of gas bubbles.

(3) FIG. 2 shows a graph displaying the time course of density measurements of four samples of a first intransparent liquid, which were subjected to eight different pressures.

(4) FIG. 3a shows a graph of the density differences determined from measurement of the first liquid as a function of the applied pressure.

(5) FIG. 3b shows the measurement error ρ.sub.error determined from the density differences for all measurement series according to FIG. 3a in a table.

(6) FIG. 4a shows a graph of the density differences determined from measurement of a second, transparent liquid as a function of the applied pressure.

(7) FIG. 4b shows a measurement error ρ.sub.error determined from the density differences for all measurement series according to FIG. 4a in a table.

(8) FIG. 1 shows the components of a densimeter 1. The densimeter 1 comprises a flexural resonator 2, which may be filled with the liquid to be measured and is connected to an induction unit 3, which is suitable to induce natural oscillations of the flexural resonator 2. The flexural resonator 2 is furthermore connected to a pressurization means 6, by means of which the liquid in the flexural resonator 2 can be pressurized. The measuring device 4 is connected to an evaluation unit 5, which is suited to convert the measured frequencies into corresponding density values of the liquid.

(9) FIG. 2 shows, in a graph 7, a measuring example of an intransparent liquid in the form of a measurement series of the density ρ for four samples of a lubricating oil that have filling errors of different magnitudes in the form of gas bubbles in various sizes and numbers and to which different pressures are applied.

(10) A measurement series 8 does not have any observable gas bubbles and is de facto to be considered as free from filling errors. A measurement series 9 has a minor filling error in the form of several small bas bubbles, a measurement series 10 has a larger filling error than measurement series 9, and a measurement series 11 has a larger filling error in the form of several large gas bubbles.

(11) In the measurement conducted in a preferred embodiment of the method, each sample is subjected to eight different pressures P before density measurement, wherein the largest pressure P is applied first, the subsequent pressures P are successively reduced, and the smallest pressure P is applied last. In addition, a reference pressure density measurement 12 is conducted at a reference pressure, which was set during measurement at atmospheric pressure shown in FIG. 2, before each density measurement with an applied pressure. As is to be expected for a compressible liquid, the measurement at the largest pressure has the highest density value, and the measurement at atmospheric pressure has the smallest density. In addition, FIG. 2 shows that variation of the reference pressure density measurements 12 for all measurement series 8 to 11 is very low, which is apparent from the good reproducibility of the reference pressure density measurements 12.

(12) FIG. 3a shows, in a graph 13, the course of the pressure-dependent density differences Δρ(P) for the four samples of the lubricating oil from FIG. 2, which were determined from the reference pressure density measurement and the pressurized density measurements of the lubricating oil, as a function of the applied pressure. The curves determined by curve fittings of the individual measuring points according to the above equation show that a curve 14, which was generated from the measurement values of the quasi bubble-free measurement series 8, has the lowest slope and thus the lowest pressure-dependent change of density Δρ(P). A curve 17, on the other hand, which was generated from the measurement values of the measurement series 11 with the highest filling error, has the highest slope and the largest pressure-dependent change of density Δρ(P). In general, the degree of slope of a curve increases with the magnitude of the filling error, as is also shown by curves 15 and 16, which were determined from the measurement values of the measurement series 9 and 10.

(13) FIG. 3b shows, in a table 18, the measurement error ρ.sub.error determined from the density differences of the respective measurement series 8, 9, 10, and 11, wherein the measurement series 8 has the smallest measurement error ρ.sub.error of 0.000021 g/cm.sup.3. At a customary threshold value of the measurement error ρ.sub.error of 0.0001 g/cm.sup.3, this would mean that, as is correct, no filling error is detected for the sample, but the determined quantitative measurement error can be used for a further evaluation of measurement data of this sample and is thus important for interpretation of the data.

(14) In the measurement series 9, 10 and 11, on the other hand, a filling error caused by the presence of gas bubbles in the sample is correctly detected in quantitative filling error determination, so that no further time-consuming measurement of this sample is conducted hereafter and valuable measurement time can be saved. FIG. 3b also shows that, according to the quantitative nature of the method, the measurement error ρ.sub.error increases with an increasing filling error of the measured sample.

(15) For an independent examination of the increase of the measurement error as a function of the magnitude of the filling error and thus the quantitative nature of the method, the density difference between one of the reference pressure density measurements 12 of the filling-error-free measurement series 8 and a respective one of the reference pressure measurements 12 of the filling-error-containing measurement series 9, 10, 11 may be used. The density difference between the reference pressure density measurement 12 of the filling-error-free measurement series 8 and the measurement series 9 showing a small filling error is 1.6×10.sup.−4 g/cm.sup.3, the density difference between the reference pressure density measurement 12 of the measurement series 8 and the reference pressure density measurement 12 of measurement series 10 having a larger filling error than measurement series 9 is 6.4×10.sup.−4 g/cm.sup.3. The density difference between the reference pressure density measurement 12 of the measurement series 8 and the measurement series 11 showing the largest filling error is 11.2×10.sup.−4 g/cm.sup.3.

(16) It is thus clearly visible from these determined density differences that the density difference between the reference pressure measurements 12 of the quasi filling-error-free measurement series and the reference pressure measurements 12 of the filling-error-containing measurement series 9, 10, 11 increases with an increasing filling error as a function of the magnitude of the filling error, which additionally underlines the quantitative nature of the method.

(17) FIG. 4a shows, in a graph 19, an measurement example of a transparent liquid in the form of the course of the pressure-dependent density differences Δρ(P) for three samples of a base oil, which were determined from reference pressure density measurements and pressurized density measurements of a base oil, as a function of the applied pressure. This also shows, based on the curves determined via curve fittings of the respective measurement points, that a curve 20, which was generated from the measurement values of a quasi filling-error-free sample, has the lowest slope and thus the lowest pressure-dependent change of density Δρ(P). A curve 22, which was generated from the measurement value of the sample with the largest filling error, again has the highest slope as well as the largest pressure-dependent change of density Δρ(P), and a curve 21 lies between curves 20 and 22.

(18) FIG. 4b shows, in a table 23, the measurement error ρ.sub.error determined from the density differences of the respective measurement series or curves, wherein the measurement series of curve 20 has the smallest measurement error ρ.sub.error, which is why, contrary to the measurement series of the curves 21 and 22, good filling of the flexural resonator 2 with base oil and thus no filling error are detected. It is to be noted that the measurement series of curve 21 and optionally 22 may of course be recognized as sufficient, which depends on the predetermined acceptable threshold value of the measurement error ρ.sub.error.

(19) The density determination method described herein is not limited to the indicated formula and may also be applied by using a similar mathematical model, e.g. by supplementing the model used herein for describing the ideal gas with a correction term for an approximation to the behavior of a real gas or with a correction term for the compressibility of the flexural resonator a high pressures or with any other similar modification.