IAEA-SM-367/8/02/P High Quality Tank Calibration Study JSGO H.Higuchi, S.Takeda NMCC--S. Uchikoshi, Y. Watanabe, K. Kaieda IAEA--D. Sellinschegg, R.Binner 1. INTRODUCTION: The Japanese Nuclear Material Control Center (NMCC) is testing techniques to be used for tank calibration and solution volume measurements using dip-tube bubbler probe systems under large-scale conditions. For large-size reprocessing plants, such as the Rokkasho Reprocessing Plant (RRP), highquality calibration and solution volume measurement techniques are of great importance for accountancy purposes. NMCC has constructed a test facility, the Large Scale Tank Calibration (LASTAC) facility, for the purpose of extensively testing calibration procedures used to determine solution volume of a large accountancy tank. The LASTAC tank is structurally equivalent to the input accountancy tank at RRP, containing the same volume (25 m 3 ) and internal piping, machinery, and instrumentation. The LASTAC tank calibration exercise consists of 5 experiments with 12 calibration runs performed under several different conditions. The calibration liquid used, the solution temperature, solution mixing in the tank, zero-reset between pressure readings, ventilation, and increment interval times were all varied according to the following experimental set-up: Experime nt Runs Solution Temp. Pressure zero reset Mixing Ventilatio n Increment Interval 1 1,2,3 H 2 O 20 C yes yes no 12 min. 2 4,5 H 2 O 20 C no no no 4 min. 3 6,7 H 2 O 40 C no no no 4 min. 4 8,9,10 H 2 O 20 C no no yes 4 min. 5 11,12 NaNO 3 20 C no no no 4 min. For each run, the solution was filled into a supply tank and left standing for at least 24 hours in order for the solution temperature to reach thermal equilibrium with the ambient room temperature. The input accountancy tank was then filled via a prover tank using roughly two hundred 100-liter increments, whereby the weight of the added solution was determined via electrobalance measurements of the prover vessel. Pressure readings were obtained from 6 dip-tubes in the accountancy tank: 1 reference dip-tube at the top of the tank, 1 level pressure dip-tube giving a differential pressure reading to the reference diptube, and 4 solution density dip-tubes, which give three pair-wise differential pressure readings. The airflow rate through all diptubes was kept at a constant rate of 7 liters/hour for all runs. 2. DATA STANDARDIZATION: The measurement data obtained from the above runs was standardized to take into account buoyancy corrections and thermal expansion effects of the tank and dip-tubes. For the thermal expansion corrections, an average of the tank temperature measurements was used for every run. The following temperature ranges were observed during the 12 runs:
run Avg. tank temperature (TX-503, C ) Avg. prover temperature (TX-301, C) Diff. (prover-tank) ( C) Variation in prover Temp. (ºC) 1 24 26 2 1 2 23 24 1 1 3 23.5 24.5 1 1 4 22.5 24 1.5 1 5 23 24.5 1.5 1 6 41 43 2 2.5 7 41 42.5 1.5 3 8 25 26 1 1 9 24.5 25.5 1 1 10 24.5 26 1.5 1 11 21 23 2 2.8 12 22 24 2 2.7 runs 1-10(H 2 O): For the thermal expansion correction, a reference temperature of 25 degrees Celsius was chosen, which corresponds closely to the actual average tank temperature for the runs performed under the design conditions of 20 degrees. For each increment, a standardized solution height was calculated by: H = (1 / (1+=,T)) (,P / (g local H)) where =... thermal expansion coefficient (0.00001728 per degree C),T... difference of avg. tank temperature to reference temperature of 25º C,P... LX-501: Pressure(level dip tube) - Pressure(reference dip tube): = (pressure measurement in mmh2o) g std (density of H 2 O at 4º C) g std... standard acceleration of gravity (9.80665 m/s^2) g local... local acceleration of gravity (9.79985 m/s^2) H... density of H 2 O at avg. tank temperature For each increment, a buoyancy-corrected mass was calculated by: where M c = M meas ( 1 + (H air /H prov ) - ((H air /H ref ) (1+H air /H prov ))) M meas... measured increment mass (prover before - prover after transfer(wi-301)) H air... density of air (0.0011g/ccm) H prov... density of H 2 O at measured prover temperature H ref... density of standard reference weights (8 g/ccm) The cumulative mass was then calculated for each increment and converted to a standardized volume by where =,T, and H are defined as above. V = (1 / (1+3=,T)) cumulative mass / H
runs 11 & 12 (NaNO 3 ): For runs 11 and 12, an estimate of the solution density had to be determined. The level density measurement DX-501 was used for this purpose. First, the separation,s between the density probes (C3 & C4) used to determine the differential pressure was calculated from runs 1-10 by:,s = (1 / (1+=,T)) (DX-501(mmH 2 O@4ºC)) H 0 4ºC g std / (g local H H2O,tank temp. ),s was calculated for runs 1-10 for all increments starting at a height of approx. 970 mm, then averaged over all increments and all runs to yield an estimate of the separation between the two density probes of,s = 499.358 mm. The density of NaNO 3 used for runs 11 and 12 was then estimated by: H 11,12 = (1 / (1+=,T)) (DX-501(mmH 2 O@4ºC)) )) H 0 4ºC g std / (g local,s) and averaged over all increments starting with increment 54, yielding a value for the density of H 11,12 = 1.3064 g/cm 3 The standardized heights and volumes where then calculated for runs 11 and 12 using the same formulas as described above for runs 1-10, using H = H prov. = H 11,12 3. CALIBRATION: A calibration function was fitted to runs 1-10 using the following cutpoints and curve type: cubic from 0-448 mm cubic from 448-614 mm quadratic from 614-682 mm cubic from 682-830 mm linear from 830-874 mm linear from 874-1041 mm linear from 1041-1640 mm linear from 1640-1752 mm linear from 1752-2195 mm linear from 2195-2446 mm quadratic from 2446-2529 mm linear from 2529 mm to max. height Due to a problem with run 7, which is still under investigation, the residuals for this run are significantly different from all other runs. It was therefore decided to eliminate run 7 from further evaluations until the problem has been resolved. The same function type was therefore fitted to runs 1-6 and 8-10, and the resulting residuals (measured volume - volume calculated from calibration function) are plotted in Figure 1. It is seen that the residuals now fall into several groups. Runs 1-3 show very similar residuals to each other, as do runs 4-5 and runs 8-10 (albeit runs 8-10 exhibit a larger spread than the other groups). Clearly, for runs 1-3, the zero reset of the pressure measurements, the longer interval length and the effect of mixing seems to have some influence on the results, as does the effect of ventilation for runs 8-10.
8 6 4 Residuals (liters) 2 0 0 500 1000 1500 2000 2500 3000-2 run1 run2 run3 run4 run5 run6 run8 run9 run10-4 -6-8 Height (mm) FIG. 1. Residuals for LASTAC runs 1-6 & 8-10 (measured volume - calculated volume) calibration curve based on 9 shown runs Calibration based on runs 4 & 5: 8 6 4 2 Residuals (liters) 0-2 run4 run5-4 -6-8 0 500 1000 1500 2000 2500 3000 Height (mm) FIG.2. Residuals for LASTAC runs 4 and 5 (measured volume - calculated volume) calibration curve based on runs 4 and 5 Runs 4 and 5 exhibit the smallest run-to-run variation of any of the groups. The differences in the residuals (actual volume - predicted volume using the calibration equation) for these two runs range from -0.3 liters to +0.7 liters at any given height over the entire range of volume in the tank, up to the full volume of 20 m 3. This small difference between these two runs can be explained by the small temperature variation seen in the solution temperature during the runs, the fact that no mixing or
ventilation occurred during these runs, and by the small random measurement uncertainties of the pressure measurement devices. It was therefore decided to use runs 4 and 5 as "reference" runs on which to base the calibrations function to which all the other runs are compared. Figure 2 shows the residuals calculated from runs 4 and 5 based on a calibration function fitted to the data of these two runs. Using the same above cutpoints and function types, the beta-vector for this calibration is: >= 0.0761(> -0.6030(> 0.0021(>! 7.4554E-6(> " 5.5766(> # 0.0122(> $ -1.1046E-5(> % 8.1063(> & 0.0062(> ' 9.1371(> 0.0010(> 1.9299E-6(> 9.1368(>! 9.1287(> " 9.2093(> # 9.1534(> $ 9.1975(> % 9.4252(> & 9.0270(> ' 0.0020(> 9.4314(> where > (D'D) -1 (D'Y) D... design matrix Y... Volumes For a given height H, volume is then calculated by V = D H >, where D H is the row of the design matrix corresponding to H ( see Annex 1 for description of the design matrix and numerical example for calculating volume). 4. FIT OF DATA TO CALIBRATION FUNCTION: - runs 1-3: Figure 3 shows the residuals of runs 1-3 to the above calculated calibration function. These runs exhibit a difference to runs 4 and 5 of up to 8 liters at full volume; i.e., the actual measured height in the tank is less than that measured in runs 4 and 5 for the same measured accumulated volume. This difference can be explained by considering that zero-resets were performed between the pressure readings taken for these runs, which causes an underestimation of the actual pressure. (See Figure 4, which shows the effect on the pressure readings of performing a zero reset). The run-to-run variability is likewise somewhat larger than for runs 4 and 5, which may be a result of mixing performed for runs 1-3.
8 6 4 Residuals (liters) 2 0-2 run1 run2 run3-4 -6-8 0 500 1000 1500 2000 2500 3000 Height (mm) FIG. 3. Residuals for LASTAC runs 1,2,3 (measured volume - calculated volume) calibration curve based on runs 4 and 5 a) Reading is shifted by adjustment òñ Magnitude of shifted pressure is increased according to increase of level pressure Start of zero reset Valve A Pressure sensor 2 Open 5 Close Valve C Differential Pressure (mmh2o) Ò Valve B Start of zero reset Opening valve C Ó Ô Õ Shift Adjusting to zero Shift Actual reading Stoping pour of liquid Starting pour of liquid Measurement Ó Ô Õ Shift Adjusing to zero 1 Close 6 Open High Low 3 Close 4 Open Ö Ø Finish of zero reset Pressure reading still is decreased after adjustment Time FIG. 4. Effect of Zero-Reset
- run 6: Figure 5 shows the residuals of run 6. Run 6 was run with higher solution temperatures than the other runs, however the residuals do not show any significant differences to those for runs 4 and 5, which form the basis for the calibration curve. This is a good indication that as long as the temperature is kept constant during a run, the thermal expansion correction applied to the data adequately compensates for any constant temperature difference between runs. 8 6 4 Residuals (liters) 2 0-2 run6-4 -6-8 0 500 1000 1500 2000 2500 3000 Height (mm) FIG. 5. Residuals for LASTAC run 6 (measured volume - calculated volume) calibration curve based on runs 4 and 5 - runs 8-10: Figure 6 shows the residuals of runs 8-10. With increasing height, the residuals for these runs exhibit a slight trend toward smaller (negative) residuals, showing a difference of -1 to -4 liters at full tank volume when compared to runs 4 and 5; i.e., the actual measured height in the tank is more than expected for the same accumulated volume as measured for runs 4 and 5. This difference apparently results from the fact that the ventilation system was on during these runs, causing a difference in volume of liquid in the internal piping. The run-to-run variation for this group of runs is also larger than for runs 4-5, which may likewise be an effect caused by the ventilation being on. - runs 11 & 12: Figure 7 shows the residuals of runs 11 and 12 (sodium nitrate) to the calibration function established from runs 4 and 5, which were performed with H 2 O. Runs 11 and 12 exhibit a difference to runs 4 and 5 of up to 4 liters, and in general show good agreement to the calibration function. A major source of uncertainty for these runs lies in the fact that in this case, a single value for the density ( for the calibration liquid NaNO 3 ) was determined using the density dip-tube measurements, whereas for all the other runs well-established tabulated values for density of demineralized water were used. An additional source of uncertainty is introduced by the fact that the probe separation distance of the density dip tubes decreases with increasing solution level (see discussion of this effect below). Even with these sources of uncertainty, there in general appears to be good agreement of runs 11 and 12 to the calibration function.
8 6 4 Residuals (liters) 2 0-2 run8 run9 run10-4 -6-8 0 500 1000 1500 2000 2500 3000 Height (mm) FIG. 6. Residuals for LASTAC runs 8,9,10 (measured volume - calculated volume) calibration curve based on runs 4 and 5 8 6 4 2 Residuals (liters) 0 0 500 1000 1500 2000 2500 3000-2 run11 run12-4 -6-8 Height (mm) FIG. 7. Residuals (measured volume - calculated volume) for LASTAC runs 11,12 (Sodium Nitrate) calibration curve based on runs 4 and 5 5. DIFFERENCE IN DIFFERENTIAL PRESSURE MEASUREMENTS ACROSS THE DENSITY DIP TUBES: Figures 8 and 9 show the differential pressure measurements DX-501(C3-C4) and DX-502(C3-C5) for the 20ºC-runs, obtained from the density dip tubes over the increment range for which the relevant probes where immersed in liquid. The pressure readings all show a downward trend with increasing tank volume, which results in a decrease in the calculated probe separation distance with increasing liquid level; i.e., although density and probe separation distance remain constant in actuality, the
pressure difference across the density dip tubes decreases. The effect is seen for all the runs, and for all three differential density probe measurements: Average Pressure Drop Across Runs between Measurements Taken at First Point of Submergence and at Full Tank Level (%) runs DX-501 (C3- C4) DX-502 (C3- C5) DX-503 (C4- C6) 1-3 0.06 0.09 0.04 4,5 0.06 0.08 0.03 6,7 0.06 0.08 0.04 8-10 0.03 0.08 0.04 11,12 0.03 0.09 0.06 498.40 498.20 mmh2o 498.00 497.80 497.60 497.40 497.20 497.00 51 56 61 66 71 76 81 86 91 96 996.00 995.80 101 106 111 116 121 126 Increment 131 136 141 146 151 156 161 166 171 176 181 186 191 196 201 206 211 FIG.8. DX501 (Differential Pressure between C3 and C4) run1 run2 run3 run4 run5 run8 run9 run10 995.60 mmh20 995.40 995.20 995.00 994.80 994.60 994.40 994.20 994.00 101 105 109 113 117 121 125 129 133 137 141 145 149 153 157 Increment 161 165 169 173 177 181 185 189 193 197 201 205 209 FIG. 9. DX502 (Differential Pressure between C3 and C5) run1 run2 run3 run4 run5 run8 run9 run10
An additional experiment was performed to test the effects of airflow rate on differential pressure measurements. An additional manometer was installed to measure the differential pressure between the level dip tube C2 and the density dip tube C3. Four runs were performed under identical conditions, except that the air flow rates through the density dip tubes C3 and C4 were changed for each run (C4 is located in the same shroud as C3). The airflow through C2 was kept constant for all runs. The results are shown in Figure 10: Differential Pressure C2-C3 (mmh2o) C3: 7lit./hr, C4:7lit./hr C3: 20lit./hr, C4:7lit./hr C3:0.3lit./hr, C4:7lit./hr C3:0.3lit./hr, C4:0lit./hr C2:7lit./hr Level [mm] FIG. 10. Differential Pressure between Level Dip Tube C2 and Density Dip Tube C3 for Different Airflow Rates through Density Dip Tubes Figure 10 shows an effect that is opposite to the one seen between the density dip tubes. With increasing air flow rate through the density dip tube, the differential pressure between it and the level pressure dip tube increases as the tank is filled. Since the level dip tube is not located in a shroud, the presence of a shroud clearly has an effect on the differential pressure measured between the two submerged dip tubes. And since the air flow rate through the density dip tube effects the magnitude of the differential pressure, it is apparent that a higher air flow rate introduces enough air into the water column above the dip tube to appreciably reduce the density of the water column exerting pressure on the tip of the tube. This process for increasing differential pressure however does not explain the reduction in differential pressure seen in Figures 8 and 9, for dip tubes both of which are located in shrouds. Possible causes for this effect include accumulation of air bubbles along the shrouds and/or the dip tubes themselves, effects on bubble size with increasing solution height, a failure to achieve complete fluid homogenization within the shrouds, air lift effects in the shrouds, or other not-yet identified effects. Further careful analysis of the data and possibly additional experiments will be needed to pinpoint the exact causes of the observed phenomena. 6. TEMPERATURE EFFECTS: - Temperature variation during calibration: When the temperature of the calibration liquid varies during the calibration period, the density of the calibration liquid will vary accordingly. In addition, temperature variations during the calibration cause heterogeneity in liquid temperature. This makes accurate density determinations difficult if not impossible, unless the liquid is sufficiently mixed after each increment and the temperature is
measured after mixing. However, mixing is usually avoided during calibration runs to keep evaporation as small as possible. Weighing of calibration liquid increments and pressure measurements by electromanometers are high quality measurements. Since the density measurement is the only other measurement of importance in tank calibrations, the quality of the calibration is determined by the density measurement. Thus the entire calibration process is degraded by failure in keeping the temperature constant during the calibration. All runs performed during the LASTAC calibration exercises showed little variation in liquid temperatures during the individual runs. Thus the above described effects were effectively kept to a minimum and allowed a very good fit of the data to the calculated calibration function. - Temperature variation between calibration runs: Variation of temperature between calibration runs is not as serious a problem as temperature variations within a run. The calibration curve of a tank should be more or less independent of the calibration temperature if the thermal expansion of dip tubes and of the tank is properly taken into account in establishing the standardized height and volume data used for the calibration. 7. CONCLUSIONS: The LASTAC calibration exercise has demonstrated in an impressive way the power of tank volume measurements by measuring pressure with bubbling probes, showing that run-to-run variability of approximately 0.1 liters can be achieved under tightly controlled conditions (see runs 4 and 5). This experiment has proven that the quality of volume measurements is determined by the quality of the density measurement. This conclusion has long been expected, since the remaining measurements like weighing of liquid increments and pressure measurements by electromanometer are high quality measurements. If demineralized water is used as calibration liquid, then the density is known with very high accuracy as a function of temperature (the standard deviation of error is approx. 0.002 kg/m 3 ). By using demineralized water as calibration liquid we can make use of this fact by keeping the temperature of the calibration liquid as constant as possible throughout the calibration run. In other words, the quality of the calibration is inversely proportional to the variation of the liquid temperature during calibration. For a high quality calibration, not only should the prover temperature be kept constant, but also the temperature of the calibration liquid should be allowed to equilibrate with the cell temperature before it is used in the calibration. It appears that the latter requirement can only be met when the tank is calibrated during the commissioning period of the plant, because it seems to be more complicated if not impossible to meet this requirement after the tank becomes operational. For this reason it is recommended that the high quality calibrations be performed during the commissioning of the plant, and that the resulting calibration function and associated calibration errors be used for the lifetime of the tank. Periodic checks of the calibration may be necessary to confirm that nothing has changed during normal operation. But re-calibration including re-determination of the calibration function together with the associated calibration errors should be avoided. A point on which a better understanding needs to be reached concerns the variation in differential pressure seen across the dip tubes with increasing solution height, which is highly dependent on the air flow rate and on the proximity of other dip tubes introducing additional air into the water. Low air flow rates and the separate placement of dip tubes away from possible interference of air emitted by other dip tubes can reduce the difference in differential pressure considerably. Since high-quality intank density measurements are of increasing importance for material accountancy purposes and are dependent on these differential pressure readings, all effects that influence these measurements need to be understood.
ACKNOWLEDGEMENT: The authors would like to thank the organizers of the LASTAC calibration exercise for their excellent work. The LASTAC calibration data provides the most comprehensive calibration data set available for safeguards. The different calibration runs were carefully designed and each calibration was performed with high quality measurement instruments and with the aim to keep the temperature of the calibration liquid as constant as possible. The result is an excellent set of data demonstrating the power of volume measurements by using bubbling probes. Design Matrix: ANNEX 1 A row in the design matrix for a given height H is given by: H(mm) D H 0-448 1 H H 2 H 3 0 0 0... 0 0 0 448-614 1 448 448 2 448 3 (H-448) (H-448) 2 (H-448) 3... 0 0 0 614-682 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 682-830 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 830-874 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 874-1041 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 1041-1640 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 1640-1752 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 1752-2195 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 2195-2446 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... 0 0 0 2446-2529 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... (H-2446) (H-2446) 2 0 2529-max 1 448 448 2 448 3 (614-448) (614-448) 2 (614-448) 3... (2529-2446) (2529-2446) 2 (H-2529) e.g., for H=2000 mm: D 2000 = (1 448 448 2 448 3 166 166 2 166 3 68 68 2 148 148 2 148 3 44 167 599 112 248 0 0 0 0) Volume Calculation: For a given height H, volume is calculated by the vector multiplication V H = D H >, where >' = (0.0761, -0.6030, 0.0021,..., 0.0020, 9.4314) = (> > > e.g., for H=2000mm: V 2000 = D 2000 > = (1 0.0761+ 448 (-0.6030) + 448 2 0.0021 + 448 3 (7.4554E-6) +... + 112 9.1534 + + 248 9.1975) = 14735.66 liters