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c E N T R E
S T U D I E C E N T R U M V O O R K E R N E N E R G I E
D' E T •
u D E
REPROCESSING INPUT TANK CALIBRATION EXERCISE (RITCEX)
D E Volume 1 : FINAL REPORT
L' E N E R G I E
R. CARCHON, P. OE REGGE, F. FRANSSEN
N U C L E A I R E
June 1986
E. Plaskylaan 144, 1040 BRUSSEL BLG 588 144, avenue E. Plasky, 1040 BRUXELLES (BELGiE) (BELGIQUE)
REPROCESSING INPUT TANK CALIBRATION EXERCISE (RITCEX)
Volume 1 : FINAL REPORT
R. CARCHON, P. DE REGGE, F. FRANSSEN
June 1986
BLG 588
fl. CARCHON. P. DE REGGE, F. FRANSSEN BLG 588 (June 1986)
REPROCESSING INPUT TANK CALIBRATION EXERCISE (RITCEX)
Summary. - Tho Reprocessing input Tank Calibration Exercise (RITCEX) was intended to evaluate current instrumentation and study possible improvements for the input volume measurement in a reprocessing plant. For that purpose, a recalibration of the input tank of Eurochemic has been performed. The data have been analyzed by all the participants and the results are reproduced in the document. The experience obtained allowed to propose some basic principles, recommendations and guidelines for the design and calibration of an accountancy input tank, from the safeguards point of view.
R. CARCHON. P. OE REGGE. F. FRANSSEN BLG 588 (June 1986)
REPROCESSING INPUT TANK CALIBRATION EXERCICE /RITCEX)
Samenvatting. - De oefening ter calibratie van Se input tank van een opwerkingsfabriek (RITCEX) had tr! doel bestaand instrumentarium te evalueren alsook mogelijke verbeteringen bij de bepaling van het input volume in een opwerkingsfabriek te bestuderen. Met dat doel werd een hercalibratie van de inpu'. tank van Eurochemic uitgevoerd. De gegevens werden geanalyseerd door alle deelnemers, en de resultaten zijn weergegeven in het document. De opgedane ervaring liet :oe enkele basis principes, aanbevelingen en richtlijnen te formuleren aangaande ontwerp en calibratie van een input tank, vanuit het standpunt der garanties.
R. CARCHON, P. DE REGGE, F. FRANSSEN BLG 588 (June 1986)
REPROCESSING INPUT TANK CALIBRATION EXERCICE (RITCEX)
Resumé. - L'exercice de calibration de la cuve d'entrée d'une usine de retraitement (RITCEX) avait pour but d'évaluer l'instrumentation disponible et d'étudier des améliorations possibles dans la mesure du volume d'entrée dans une usine de retraitement. A cet'e fin. une -«calibration de la cuve d'entrée d'Euroehemic a été effectuée. Les données ont été analysées par tous les participants et les résultats sont reproduits dans le document. L'expérience acquise a permis de proposer certains principes de base, des recommendations et des idées guide pour le ojveloppement et la calibration d'une cuve d'entrée du point de vue des garanties.
ACKNOWLEDGEMENTS
This report may not be considered as the r e su l t of inves t iga t ions of one person or one i n s t i t u t e , but as the common repor t ing of the i n t e r n a t i o n a l co-operation of many persons and i n s t a l l a t i o n s from a l l over the world, as mentioned below. The RITCEX organizers would l i k e to express t h e i r g r a t i t u t e to the Eurochemic s t a f f for making t h i s exercise poss ib le , and also to the p a r t i c i p a n t s for t h e i r very cons t ruc t ive con t r ibu t ions .
PARTICIPANTS
Bertcel, Brussels , Belgium : J . Janssens J. Nobels
BNFL, Risley, U.K. : R. Howsley
Brookhaven Nat. Lab., New York, U.S.A. L. Green L. Solem
CEA, CEN Cadarache, France : M. Neuilly
CEC, CBNM, Geel, Belgium : P. De Bièvre
CEC, DCS, Luxembourg : H. Arenz P. Louis G. Meyers J. Toussaint E. Van Der Stijl
CEC, JRC-Ispra, Ital> : C. Foggi G. Guzzi H. Muntau R. Trincrerini
DWK, Hannover, F.R. Germany : R. Weh
ECN, Petten, The Netherlands : B. Beemsterboer W. Zijp
ENEA, Casaccia, Italy : M. Aparo G. Bardone F. Bellisario M. Dionisi
ENEA, EUREX, Saluggia, Italy : V. Call S. Ilardi W. Marsotto B. Mattia V. Pagliai
ENEA, ITREC, Pollcoro, Italy : G. Arcuri M. Blanchi S. Miglietta V. Morano
EUROCHEMIC, Dessel, Belgium : M. Ascani A. De Bie L. Geens C. Gevers H. Van Bijlen I . Van De Ven 7 . Van Es E. Det i l leux F. Dobbels W. Hild J . Mertens J . Van Geel
EXXON Idaho, Idaho F a l l s , U.S.A. F. Cartan W. Harris
F*3FC, Dessel, Belgium : P. Boer m ans
IAEA, Vienna, Austria : K. Gharwal G. Hough H. Shimojima S. Suda D. Thurman
KFK, Karlsruhe, F.R. Germany : D. Sell inschegg
PNC, Tokai, Japan : Y. Murakami T. Uchida 0. Yamamura
SCK/CEN, Mol, Belgium : C. Beets P. Bemelmans R. Boden R. Car^hon J . De Backer P. De Regge F. Franssen G. Stiennon F. Ven
THORP Repr. Techn., S e l l a f i e l d , U.K. :
H. Hall
P a r t i c i p a n t s ( con t inued)
TOLEDO, B e e r s e l , E v ^ r * . : L. Baartmaiv» E. De Konii •
TOLEDE-E-iropt. Köl \ ?.R. Germany : L,. Sicf t ter
UKAEA, Harwe l l , K. : G. WelXs
UKAEA, SMàCT, Karwt LI , U.K. A . Y:*:.?>
WAK, Karl sic..-'?, F.R Germany : R. Bv:vg T h . Ç f l m e r i ••:.••.
H. H--:i; J . u -v s rh B. S*-o]ani-
WIDRA, Eupe.'k, 3e.l£; .a : F . L.-Uisii--
TABLE OF CONTENTS
VOLUME 1. FINAL REPORT
Abstract 1
Introduct ion 2
Chapter I . Phase A - Evaluation of His to r ica l Data 4
A. I . The data 4 A.2. Evaluation of converted h i s t o r i c a l data 10
A.2 .1 . The approach of Tokai Works (Japan) 10 A.2.2. The approach of the SCK/CEN (Belgium) 13 A.2.3. The KFK evaluations 15 A.2.1». The ECN evaluations 19 A.2.5. The CEA evaluat iens 21 A.2.6. The Brookhaven NL evaluation 22 A.2.7. The DWK evaluations 22
Chapter I I . Phase B - Cal ibra t ions and r e - c a l i b r a t i o n s of an accountabi l i ty input tank and i t s evaluations 24
B . . . Engineering Review of the Tank 2'4 B.2. Preparatory work 27 B.3 . The ca l ib ra t ions by weigh-in method 28 B.4. Summary of RITCEX evaluations 29 B.5. Results of the use of t r ace r t e chn ique 37
Chapter I I I . Pha3e C - Design Pr inciples and operat ional procedures tor an an ideal accountancy input tank 46
C . I . Introduction 46 C.2. The design of the tank 46 C.3. Procedures to c a l i b r a t e the input tank 53 C.4. Operating procedures of the tank 59 C.5. Recommendations for design of accountabi l i ty tanks
(Brookhaven National Laboratory) 60 C.6. Recommendations for design of accountabi l i ty tank
(BNFL-UKAEA) 63
Chapter IV. Conclusions 65
References 67 Figures (reproduced from copies provided by the authors) 68
VOLUME 2. DETAILED STATISTICAL EVALUATIONS OF THE MEASURED DATA
RITCEX 12-A Evaluation of RITCEX a data/ENEA ** Casaccia M. Aparo, M. Dionisi, C. Vicini
RITCEX 1 2 ^ Evaluation of calibration data of RITCEX/KfK Karlsruhe D. Sellinschegg
RITCEX 12-C IAEA evaluation of RITCEX Calibration Data/IAEA - Vienna H. Shimojima, S. Suda, K. Gharwal
RITCEX 12-D Evaluation of RITCEX converted data by t>NC alytical Method/PNC Japan T. Uchida, Y. Murakami
RITCEX 12"E ITREC evaluation of RITCEX Calibration Data/ENEA - ITREC C.RE -TRISAIA " G. Arcuri
1
ABSTRACT
The RITCEX (Reprocessing Input Tai.k Calibration Exercise) was intended to evaluate current instrumentation and study possible improvements for the input volume measurement in a reprocessing plant. The input tank of Euro-chemic has been recalibrated by means of several instruments and procedures that could be compared under process conditions.
Two types of scales with digi tal readers were used for weighing the increments added to the tank. The following instruments were installed to measure the liquid height in the tank : the original Eurochemic U-tube mano-1
meters, ENEA's time domain reflectometer, the SCK/CEN acoustic system, and the IAEA RUSKA electromanometer.
The accuracy achieved in the experiment via liquid manometers i s s l ight ly better than 0.5 %. The advanced instrumental methods, electromanometer and acoustic system, provided resul ts with a considerably better precision and revealed the presence of systematic error sources which were par t ia l ly quan-* t i f ied . However they s t i l l res t r ic ted the achievable accuracy of the measure-4
ments. The accuracy of the TDR measurements was limited essentially by the graphic recording system. S ta t i s t ica l evaluations of the measured data are provided in volume II of th is report .
The feasibi l i ty of the tracer technique for the calibration and the f i s s i l e material assay was investigated as well, using lutetium, lead and neodynium. The tracer concentrations were measured in different laboratories . An average deviation for the solution weight calculated from the tracer technique with respect to the reference weight of M kg at the 1600 kg level and 5 kg at the 2600 kg level has been obtained. The mean uranium inventory calculated from the measurements using the method of concentration ra t ios agreed within 0.5 $ with the reference value. The range of the individual measurements expressed as an interlaboratory standard deviation is of the order of 1 Ï .
Based on the experience obtained basic principles, recommendations and guide-* lines for the design and calibration of an accountancy input tank in a reprocessing plant are provided in a separate chapter. Only the safeguards aspects are consider-d.
2
INTRODUCTION
The ESARDA Working Group on Reprocessing Input Verification stated in i t s May 1983 meeting at Versai l les that "significant improvements in precision and accuracy of uranium and plutonium destructive measurements have been observed during the l a s t few years". In the Reprocessing Plant, where the Nuclear Material Accountancy i s based on the "volume times concentration" method, the need ex i s t s therefore to re-as*^ sess the precision and accuracy of the volume determinations. A f i r s t move has been made in th i s direction with the Reprocessing Input Tank Calibration Exercise, RITCEX. The Belgian Nuclear Research Centre, SCK/CEN at Mol, Belgium, conducted t h i s exercise during the month of January 1981, at the f a c i l i t y of EUROCHEMIC's Reprocessing Plant at Mol, Belgium, with the assistance of the s taff members of the plant. The exercise i s one of the tasks of the Belgian Support Programme to IAEA-Vienna. The exercise was intended to provide ultimately a contribution to the improvement of the input volume determination in a reprocessing plant. The tank calibration i s of prime importance for the achievements of t h i s goal. Several individual steps influence the uncertainty of the tank ca l ibrat ion . Each of these steps must be evaluated thoroughly in order to l imi t or at l eas t to estimate i t s contribution to the tota l uncertainty of the c a l i bration. The primary goal, however, was to detect and subsequently to eliminate any systematic error. During the exercise , several instruments and procedures were compared under real process conditions. Two scale fabricators, TOLEDO and WIDRA, insta l led their weighing instruments with d ig i ta l readers. They were used for weighing the increments to be added for calibrating the tank. The most sui table approach for calibration of these s ca l e s , and for estimation of their accuracy and precision was sought. Several measurement instruments were instal led to evaluate the l iquid depth in the tank. A comparison i s made of the response of the original EUROCHEMIC U-tube manometers, to ENEA's TDR, to SCK/CEN's acoustic system and f inaly to the RUSKA electromanometer system of the IAEA, already proven in TASTEX ['\H]. In addition, two out of four c lass ica l incremental calibration runs wi l l be compared with the tracer techniques, applied in th is experiment, using different tracers . The tank used for th i s exercise was decontaminated so that i t was access ib le for insertion of direct feed l i n e s . Therefce the four runs carried out can be considered as direct cal ibrat ions . Some t e s t s , however, were done to simula te remote cal ibrat ions . All available data and the experience of par t i c i pants are employed to describe the best suited procedures for calibration or recalibration of a vessel and to determine the best methods to evaluate the col lected data. The l a s t aim of f,ne exercise i s to combine a l l ideas and experience, r e s u l t ing in the design of the ideal input tank, including i t s form, instrumentation and operation procedures, from the point of view of safeguards.
Act iv i t ies
The minutes of the general information meeting, including the f inal ized time schedule, were mailed to the interested persons on 27th October 1983. The month of November 1983 was almost entirely devoted to the calibration of the TOLEDO anC. WIDRA sca le s . Besides calibrations with the standard weights provided by the scale fabricators, standard weights ownea by Franco-Belge de Fabrication de Combustibles (FBFC), were also used. These weights were
3
calibrated by the Belgian Ministry of Economic Affairs. An agent of this Ministry assisted at one of these scale calibrations and stated that the re** quirements implemented by RITCEX greatly exceeded those of commercial applications of the scales. Additional standard weights were provided by JRC-Ispra. These weights "ere calibrated by the Eichamt of Bremen (FRG), and are used in an interlaboratory experiment all over Europe, in order to get an estimate of the precision and accuracy of the scales used in LEU fabrication plants.
Due to the holiday periods in the month of December 1983, only some adminis-
trative work on the organization of the exercise could be accomplished. However, some important tests were done, such as tests on the humidification of the feed lines and more scale calibrations. A first test on the RUSKA elec* tromanometer was performed by the IAEA. On the 20th and 21st December 1983» a meeting was held at SCK/CEN, Mol, on the evaluation of historical data of six calibration runs of the tank concerned . Some important decisions were taken during the meeting :
•* the number and the size of the increments for future calibrations were fixed;
» the distribution of the raw data was discussed and the methods for correct* tion of these data were decided.
Finally, during the month of January 1984, four calibration runs were perform med on the former input tank of EUROCHEMIC. A total of 31 persons, representing 6 nationalities and 12 different institutes, contributed actively to the exercise. The raw data from all calibration runs were distributed among the partici" pants and the evaluation of these data is given in the appendixes. Finally, the international co-operation with experts in the field resulted in phase C of the exercise : the description of an "ideal input tank", its call-4
bration and operation. This part is described in a third chapter. This report describes this exercise without overlooking any important feature but also without digging too much into detail.
4
CHAPTER I
PHASE A : EVALUATION OF HISTORICAL DATA
A.I. THE DATA
Prior to the s tart c? the input tank calibration exercise the so cal led "historical data" were distributed among the participants for re^analysis . I t concerns data that were obtained between 1965 and 1968. They are reproduced in f u l l length in tables A.1. t o A.5. They had already been converted from individual weights to accummulated volu** mes, and from pressure reading on one or more instruments to millimeters of height in the tank. The reason for t h i s was to provide a standard se t of data to a l l participants and to avoid any disagreement that could be due to conversions between physical parameters of the tank.
Table A.1. : 221-4 TANK CALIBRATION RUN #1 25*10-65
SEQ. NR. HEIGHT MM VOLUME L
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
5. 204. 262, 353. 484, 509. 611, 705. 746. 961.
1181, 1395. 1621, 1832, 2047, 2264. 2477. 2690. 2906, 3122, 3272, 3337. 3363. 3461,
1 41 61
.90
.19
.91
3510.0
104.05 181.98 199.35 279.32 362.14 398.33 597.02 796.96 996.45
1196.93 1399.26 1598.61 1797.62 1995.71 2192.18 2391.49 2590.79 2729.19 2^87.49 2810.50 2901.76 2942.85
5
Table A . 2 . : 221-4 TANK CALIBRATION RUN #3 06-'11i'65
SKQ.JJR.
1 2 3 4 5 6 7 8 9
10 11 12 13 14 75 16 17 18 19 20 21 22 23 24 25 26 27
HEIGHT MM
77.1 134.2 179.2 228.2 279.4 336.4 390.5 442.5 527.6 580.7 634.7 692.8 918.1
1154.3 1387.7 1607.9 1842.0 2071.2 2302.2 2531.7 2761.8 2994.8 3236.3 3288.5 3362.7 3468.9 3508.7
VOLUMEJ
9.33 20.75 32.47 48.03 67.43 92.91
121.24 152.56 209.56 250.59 295.02 346.37 554.86 770.68 980.42
1191.53 1405.21 1617.37 1831.25 2043.65 2255.65 2470.77 2686.49 2735.50 2803.55 2902.61 2941.65
6
Table A.3 . : 221-4 TANK CALIBRATION RUN #4 07*11"65
SEQ._NR.
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
HEIGHT MM
19.0 75.9
133.3 173.3 214.2 262.7 321.6 395.5 538.3 621.2 673.1 783.0
1021.6 1259.3 1498.4 1733.3 1970.7 2211.1 2448.0 2691.4 2931.8 3180.8 3271.7 3348.7 3433.5 3503.4
VOLUMEJ
2.21 9.23
20.26 30.64 43.62 61.07 87.39
125.99 220.14 286.62 331.59 436.42 658.20 878.07
1093.27 1317.49 1538.42 1760.53 1983.69 2207.86 2432.33 2656.85 2742.67 2815.60 2894.68 2952.85
7
Table A. 4.
SEQ._NR.
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 . 39
: 22134 TANK CALIBRATION RUN #5 08*09-67
HEIGHT_MM
17.8 63.8
102.8 171.7 250.8 314.0 361.4 422.0 461.7 537.8 661.3 771.7 884.3 989.7
1209.7 1428.5 1646.2 1867.1 2087.3 2302.2 2530.4 27"»8.1 2966.3 3024.9 3036.7 3045.5 3058.9 3067.8 3079.6 3088.6 3100.4 3115.2 3162.6 3189.5 3250.2 3294.6 3346.4 3405.7 3507.8
V0LUME_L
2.50 7.94
14.35 31.02 56.90 83.75
107.17 141.04 166.57 219.69 319.94 421.63 523.09 623-27 825.52
1028.03 1230.15 1433.52 1635.44 1336.65 2048.81 2249.81 2451.74 2506.09 2516.39 2525.76 2537.57 2546.60 2556.53 2565.65 2575.73 2586.43 2626.24 2652.66 2709.95 2752.31 2799.80 2853.38 2962.72
8
Table A . 5 . : 221--4 TANK CALIBRATION RUN #6 09-»09»*67
SEQ. NR. HEIGHT MM VOLUME L
21.5 519.2 761.0 986.0
1207.2 1421.7 1644.2 1865.6 2087.0 2303.3 2521.7 2741.( 2962.2 318Ö.6 3403.3
2.80 206.08 411.99 618.49 823.92
1023.38 1228.77 1430.83 1637. £ 1839.77 2042.58 2245.28 2450.35 2652.54 2853.95
9
Table A.6. : 221*4 TANK CALIBRATION RUN #7 17"04*68
SEQ._NR.
1 2 3 J»
5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 ^4 25 26 27 28 29 30 31
HEIGHT MM
0.1 24.7 38.0 66.3 95.6
1 3 M 174.8 208.3 239.2 279.2 319.9 382.4 418.9 522.9 592.9 650.2 711.0 927.3
1135.3 1340.5 1551.7 1764.5 1990.9 2197.2 2410.3 2621.8 2836.7 3011.4 3231.9 3452.3 3499.7
VOLUME_L
1.16 3.15 4.54 8.07
13.04 21.30 31.94 41.94 51.74 67.73 85.64
117.17 137.86 206.43 258.72 307.76 360.48 559.05 749.92 939.30
1133.30 1328.65 1534.18 1727.04 1923.03 2117.13 2313.65 2474.53 2669.84 2879.94 3078.18
10
A.2. EVALUATION OF CONVERTED HISTORICAL DATA
A.2 .1 . The approach of Tokal works (Japan)
The data are evaluated by the PNC ana ly t ica l method r e su l t i ng in equations for thé non l inea r and l i nea r par t of the tank. The ana ly t i ca l procedure, the r e s u l t s and i t s discussion are summerized below.
A. 2 . 1 . 1 . A_nalytical_procedure
A graDhical representa t ion of the s ix runs i s shown in f igure A. I . From t h i s f igure i s concluded tha t a l l data a re acceptable , except point 31 of run 7. This point wi l l be excluded for the fur ther eva lua t ion . As the number of points in the non-'linear part of run 6 i s smal l , no equation i s calcula ted for that part of the run.
A. Estimation of t r a n s i t i o n reg ions . A f i r s t degree equation i s f i t t e d to a l l data of each run , and the r e s i d ual values are c a l cu l a t ed . The four lowest values of the r e s idua l s ind ica te the t r a n s i t i o n reg ion . An example i s given in f igure A.2. Considering a l l runs , the range of heights between which the break point i s s i tua ted : between 552.9 mm and 961.5 mm maximum, but a more narrow band can be deduced to be between 611.5 and 711 mm. The engineering review of the tank, reported in chapter I I s ta ted t h i s point at 709 rtm..
B. Study of the n o n l i n e a r p a r t . Polynominal regress ions from the f i r s t up to the th i rd degree a re ca lcu la t ed , assuming as break points the four values mentioned in A.2.1.1.A. An example i s given in the t ab l e A.7.
Table A.7. : Analytical Resul (Run #1) « Non l i nea r par t
Region
1 - 7 po in t
1 -» 8 po in t
1 - 9 po int
1 - 10 po int
I
Degree
1
2
3
1
2
3
1
2
3
1
2
3
T- tes t
0
0
X
D
0
X
0
0
X
0
0
0
F-test
0
0
0
0
0
0
0
0
o 0
0
0
Standard dev ia t ion
2.743463x10
2.309133x10"'
3.405776x10
6.107589X10""1
3.655880x10
1.363828
4.690787x10
8.379016
2.993271
11
In th i s table the 0 marks in the colums T-test and F-test represent s i g n i f i cant values. Finally for each run, the result ing smallest standard deviation i s accepted as a criterium to indicate the best suited equation, indicating in each run the equation of the second degree, and the lowest break point as upper l i m i t .
C. Linear part evaluation. The upper l imit of the non-linear part i s accepted as the lower l imit for the l inear part and polynominal regressions of the f i r s t *nd second degree are analyzed. An example of the resul ts i s shown in the table A.8.
Table A.8. : Analytical Results (Run #1) * Linear parts
Region
7 - 2 5 point
8 - 2 5 point
9 - 2 5 point
10 - 25 point
Degree
1
2
1
2
1
2
1
2
T-test
0
X
0
X
0
X
0
X
F**test
0
0
0
0
0
0
0
0
Standard deviation
2.691470
2.405738
2.400162
2.434708
According to the same procedure as for the non-linear part, the f i r s t degree equation i s accepted for each run.
12
t-. Presentation-of a l l equations. The resulting calibration equations for each run are represented in the table A.9.
Table A.9. - The resultant calibration equations '."cnverted data)
Run ?*o.
i R u " x' '
...
i I
Run #4
Run #5
Run #6
Run #7
Calioration equations
Non-linear part
Linear parts
V-6j:01l6x1(T',xHa2+6.27095xl(r2xHa+1.56256
V-9.2l876x10~lxHa'-2.89411x102
V-6.3^026x10~'xHa2+6.03990x10"2xHa+1.06644
'/-'J. ?w807x10'*1xHa-2.90325x102
V-6.39364x10~*xHa2+6.3i»572x10ii2xHa-t-6.28283x10"'
V-9.27084x10~lxHa-2.89499x10*
V-6.22891 x10",xHa2+7.24879x10"'2xHa-2.44574x10i*1
V-9.24975x10",xHa-2.93084x102
V-9.24909x10'1xHa-2.92342x102
V-6.266l5x10**%xHa2+6.37394x10*,2xHa+1.2l655
V-9.17993x10UlxHa-2.91245x102
Joi nt pc Vat
686.69
676.48
626.77
684.30
1
681.64
Standard deviation
2.3091 33x10"*1
2.691470
2.771255x10"'
2.096603
2.319537X10"1
2.381644
1.042276
3.050244
2.249891
3.202648X10'1
2.129246
The column "Joint point" is the calculated solution for both equations for each run. The residual values by the f i r s t degree equation are represented in figure A.3.
13
A.2.1.2. Evaluation_of th£ calibrations
A. Non-*linear part.
*• Each run results in a very good fit to its resultant calibration equa=» tions.
- Run 5 is not in agreement with the other runs.
B. Linear part
-* Each run results in a very good f i t to i t s resultant cal ibration equat ions .
* Run 6 and 7 are not in good agreement with the other runs.
A.2.2. The approach of the SCK/CEN (Belgium)
The Belgian Nuclear Research Centre, SCK/CEN, has adopted the approach communicated in [ l ] , to evaluate the historical data. This program i s not f i t t ed to treat the non-linear part of the tank, tut i t permits the subdivision of the l inear part in f ive sect ions . Each section i s treated s t a t i s t i c a l l y as i f i t were separate tanks, and the equations developped are applied only to the appropriate sect ion. Barlett's t e s t i s performed on the residual variance data to detect good or poor runs before combining the data from the different runs to obtain the best representation of the cal ibration. Fischer's t e s t i s performed on the combined data to detect s ignif icant differences in slopes of the individual calibration curves.
A.2.2 .1 . Est.imate_of transi^ion_reg^ons
The CUDS programme detects begin- and end-points which exeed the t e s t value and once that point deleted, i t s tar t s over and over the calculation until neither end"point contribution exeeds the criterion of l inear i ty . Operated as such, the whole run 1 was evaluated and a l l point3 below 705.5 mm were rejected. All values below that value wi l l not be considered as belonging to the l inear part for the evaluation öf the other runs.
A.2.2.2. The non^Hnearjjart £f_the_tan]<
The evaluation of this part of the tank i s not included in th is programme. L i t t l e effort has been devoted to that part as the tank i s practically never used in th i s region, except for measurements of the "empty" tank. This remaining height after transfer however i s very close to the dip-tube's end, but s t i l l measurable, and that volume i s usualy below two l i t e r s . (This i s true for transfers of l iquids of a density of about 1.5, but not for water. Therefore, during calibrations the emptied tank height will be somewhere between the end of the dip*tube and the bottom of the vesse l . )
14
A.2.2.3. The linear part of_the tank
Taking the 705.5 mm as the lower limit of height, a l l runs have been evaluated by CUDS individually. The following results per run were obtained :
Observation
Intercept a Slope b Resid. Variance Beta Variance Alpha Beta covar. Alpha Variance Degree of Freedom Upper Limit
Suspected points
Run 1
-288.09 Ö.9217 0.0409 0.0000 0.0105
36.^317 16
3461.0
1621.0 1332.5
Run 3
-291.56 0.9208 0.0216 0.0000
-0.0054 18.6742
14 3468.9
3236.3
Run 4
-289.97 0.9275 0.0247 0.0000
-0.0073 25.0791
13 3433.5
3180.8
Run 5
-290.82 0.9232 0.0701 0.0000
-0.0206 69.9920
26 3405.6
3045.5 3115.2 3162.6
Run 6
-291.31 0.9242 0.0309 0.0000
-0.0089 30.2976
12 3403.3
3188.6
Run 7
-292.92 0.9190 0.0081 0.0000
-0.0025 7.5812
11 3011.4
1990.9 2197.2
The programme also permits to make combinations of the different runs. Before making these combinations, i t is recommended to eliminate al l points formerly rejected as trespassing the upper limit of height per run because this i s a shortcoming in tne programme. The eliminated points in the individual evaluations are not rejected for the combined evaluation. The resulsts of the Barlet t 's tes t and F-test on the combined runs give the following results :
COMBINED SUNS
F- tes t between t o w i t h i n slopes
Corr .Chi Square Corr .Chi sq . P robab i l i t y Degrees of freedom Averaged lower Averaged higher a - Average b - Average Rand. Var. Average b Var. Average a Var. Average a-b Covar. Average
(1) Between slopes wi th p robab i l l t
1.3
0.0630
1.4327
i 0.10 30
699.15 3464.95 -289.82
0.9212 0.0319 0.0000
13.9587 -0.0040
1,3,4
3.6260
1.7096
2 0.10 43
(1)
1,3,4,5
2.1129
7.7881
â 0.10 69
738.25 3442.28 -289.94
0.9232 0.0449 0.0000
10.5607 -O.OO3I
variance greater than v ,y less than P • 0.10
1.3,4,5,6
2.1176
8.4223
<, 0.10 81
742.25 3434.48 -290.21
0.9234 0.0429 0.0000 8.1261
-0.0024
( i t h i n s l o |
1 ,3 ,4,5,6,7
3.5532
17.0737
£ 0.05 92
(1)
je variance
15
These tes t show the d i f f icul ty with run 7 and in a minor way with run 1.
The results of a l l runs mi-us run 7 i s accepted as a base of comparison for the future calibration r e s u l t s . Two facts are of importance for future comparisons :
a the densities of the increments were calculated out of the temperatures as measured in the feed drum,
- no buoyancy corrections were applied in those his tor ical cal ibrations.
A.2.3 The KflC-evaluations
A.2.3.1• Theoretical Approach
Four error models were applied to the his tor ical data :
Model I : both H and V, have errors
2 2 2 2
assumptions : i " < J u * 0 H ° v " ° V *• errors i n H and V, are uncorrelated 14 errors in H are assumed uncorrelated -* errors in Vi are assumed uncorrelated
2 2 - errors are of the same magnitude ° u " ° y
Model II : only V, i s accompanied with errors 2 2
assumptions : a a v - o v - errors in V, are uncorrelated (standard regression model)
Model III : only Hi i s accompanied with errors 2 2
assumptions : •* a jj "* ° H '•*- errors in Hj are uncorrelated
(inverse regression model)
Model IV : only Vt i s accompanied with errors 2 2"
assumptions : ~ ° AV " ° x û V i - errors in increments are uncorrelated - errors in V, are correlated,
(cumulative model)
The only way to identify which error model describes rea l i ty the best i s to combine the calibration data of several calibration runs and evaluate them as if they belonged to one run. This requires that no physical changes of the tank occurred and measurements are performed with the same instruments. These assumptions were made for th i s analys i s . Each calibration was evaluated separately with each error model as well as a combined evaluation with each model.
16
A.2.3.2. Results
-* The results might be improved by subdividing the linear region in three sections : 700 mm -+ 1800 mm + 3150 mm + 3500 mm.
This was not possible for the historical data by lack of points.
- Bi and Bi are determined.
** random and systematic errors were determined.
Model I : Table A.10. : Results obtained with model I
VA » B, • B.-Hj
RUN 1
RUN 2
RUN 3
RUN 4
RUN 5
RUN 6
RUN 7
RUN 1+7
Bx
-*292.30
-291.60
"288.40
-293.30
-292.20
-295.00
-292.00
02
0.9257
0.9257
0.9267
0.9251
0.9248
0.9279
0.9257
Var (V)s
for H - 3500
0.97
1.02
1.16
0.74
1.15
1.41
0.39
Var (V)r
for H - 3500
3.03
2.73
3.02
».. 26
2.26
2.39
6.65
o(VW^ar(V)3+Var(V)p
fer H » 3500
2.0
1.94
2.04
2.24
1.94
1.95
2.65
individual runs yield : - different intersections (B,) •* slightly different slopes (82) -* systematic a w 1L. -> random a _ 1.5 - 2.0L combined runs - systematic o w 0.6 L. (so smaller)
** random o , 2.6 L. (so larger) figure A-4 reveals that for the combined runs :
- the systematic deviation between the different runs is not adequately described by the very small systematic error,
*> the random error increases in this case because the systematic deviations between the different runs are treated as random errors
•* the 1 o bound is too narrow
17
Model II : Table A.11. : Results obtained with model II
Vt - B, • B2.H
RUN 1
RUN 2
RUN 3
RUN 4
RUN 5
RUN 6
RUN 7
RUN 1*7
6!
-292.31
-291.59
«288.43
-293.31
"292.15
-294.98
^291.95
6.
0.9257
0.9257
0.9267
0.9251
0.9248
0.9279
0.9257
Var (V) . f o r H - 3500
0.90
0.79
1.0
0.76
1.41
1.26
0.40
Var (V ) r f o r H - 3500
0.0
0.0
O.O
0.0
O.O
O.O
0.0
o ( V W V a r ( V ) + V a r ( V ) r f o r H - 3500
0.95
0.89
1.0
0.87
1.19
1.12
0.63
-> results of $,, B2 and og are almost identical to model I. ( model II is an extreme case of model I.) figure A"-5 illustrates that the systematic error is by far too small to describe the real situation.
Model III : Table A.12 : Results obtained with model III
V. - 6, • Ba.H.
RUN 1
RUN 2
RUN 3
RUN 4
RUN 5
RUN 6
RUN 7
RUN 1+7
Bi
-292.35
-291.61
-288.45
-293.37
-292.18
-295.00
-291.89
B2
0.9258
0.9257
0.9267
0.9251
0.9249
0.9279
0.9257
Var (V) . f o r H - 3500
0.90
0.79
1.00
0.76
1.41
1.26
0.40
Var(V)_ f o r H - 3500
6.16
'4.68
5.71
9.63
4.62
4.66
15.22
o ( V W V a r ( V ) + V a r ( V ) r f o r H - 3 5 0 0
2.66
2.34
2.59
3.22
2.45
2.43
3.95
- esults of Bit 02 ahd aa are almost identical to models I & II
(model III is the other extreme case of model I . ) - larger random errors are noted,
figure Afa6 ** same problems as with models I & I I . (o3 too small to describe
sat isfactori ly the systematic differences between the different runs.)
18
Model IV : Table A.13. : Results obtained with model IV
RUN 1
RUN 2
RUN 3
RUN 4
RUN 5
RUN 6
RUN 7
Bi
-287.98
-292.06
-287.56
-293.88
-291.19
-295.84
RUN 1+7I-291.45
62
0.9231
0.9261
0.92nS
0.9272
0.9240
0.9284
0.9256
Var (V)g for H - 3500
203.35
119.37
246.61
474.64
112.77
162.55
39.58
Var (V)r
for H - 3500
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o(V)-/Var(V)s+Var(V)r for H - 3500
14.26
10.93
15.70
21.79
10.62
12.75
6.29
• - resul ts of Bi and B2 are sl ightly different to models I , I I 4 I I I .
-> significantly increased <jg : , 10 - 20 L. - 0g significantly reduced for the combined runs t o , 6.3 L.
figure A-7 " almost a l l the points are within the 1 0 bound, when run 4 is
excluded.
A.2.3«3. Conclusions
•* Model IV does describe these six runs in the best way but one must remain aware of the assumptions made for this model;
- No further conclusion can be drawn before evaluation of the new calibration runs.
19
A.2.1. The ECN-Evaluations
A. 2 . 1 . 1 . Jheoreti£al Approach
The data were treated by the computer programme COMFIT [7] on a CDC CYBER 175/855 computer. This treatment permits f i t t i n g a straight l i n e to a ser ies of data points with the following modes :
1. uncertainties (unknown) only in y^direction; 2. uncertainties (known) only in yudirection; 3. uncertaintiea (unknown) only in x^direction; 1. uncertainties (known) only in x-*direction; 5. uncertainties (unknown) in both x^and y direction; 6. uncertainties (known) in both x-and y direction.
In the straight l ine f i t t i n g task the la t t er two modes have the following submodes :
-» parallel deviation vectors, yielding the so called orthogonal regression l ine;
-• non-parallel deviation vectors, yielding the regression l ine with non*par-< a l l e l i zed deviations.
The theory for the generalized regression l ine i s described in [8] and [ 9 ] .
The best f i t t i n g was obtained with a straight l ine above x< 600 mm in combination with a quadratic curve below x< 838 mm. The summary of the parameter data for the quadratic curve f i t t ing and the s tra i tht l ine f i t t i n g are presented in tables A.11 and A.15 respectively.
For reasons of convenience, we have also presented the weighted and the unweighted average for the s ix runs. Also are given the coeff ic ients of varia*-t ion V e x t and V i n t , derived from the external variance and the internal variance defined by the re lat ions .
1 2 I w i ( a i - a ) v ( n - 1 ) i n t " X i / ^ u j ) Sext Tvn^ "
v i n t - - ^ x 100Î v e x t - - | 2 £ x 100$
20
Table A.14. Summary of results of f i t t ing a quadratic curve for x < 838 mm.
Function : y » al*ai.x*ai.x2.
run
1 3 4 5 7
unw. aver . v ext F i n t
weighted average Vext Jint
combined runs
parameter
3 l
0.12977 E+1 0.84197 0.31549 0.71955 0.11105 E+1
O.985601)
1.01621)
0.91517
v ( a , )
49.4 $ 34.'4 $ >100 $ 58.7 $ 14.7 $
13.5 $ 13.3 $
1.0
9.2 $ 12.9 $ 0.5
23.6 $
a2
0.69176 EM 0.62621 E-1 0.68329 E-1 0.71547 E-1 0.65836 EM
0.67502 EM
0.65980 EM
0.66297 EM
v(a2)
6.4 $ 3.3 % 4.9 $ 4.8 % 2.4 %
2.3 % 1.6 % 2.0
2.1 % 1.6 % 1.6
2.7 $
a3
0.62564 E-3 0.63100 E-3 0.62828 E«3 0.61831 E*3 0.62157 E-3
0.62496 E-3
0.62534 E-3
0.62674 E-3
v(a,)
1.0 $ 0.46 % 0.74 % 0.84 % 0.42 %
0.36 $ 0.26 $ 1.9
0.37 % 0.26 $ 2.0
0.42 %
1) Values of run 4 not taken into account.
Table A.15. Summary of results of f i t t ing a straight l*ne for x > 600 mm.
run
1
3
4
5
6
7
unw. aver. Vext Vint
weighted average Jext Vint
combined runs
slope
orthogonal regression
0.92188 (0.066$) 0.92081
(0.056$) 0.92709
(0.062$) 0.92498
(0.068$) 0.924Ö4
(0.078$) 0.91800
(0.067$)
0.92293 0.15$ 0.03*
30.4
0.92279 0.15$ 0.03$
30.8
0.92360 (0.076$)
non-parall el i zed deviations
0.92188 (0.066$) 0.92081
(0.056$) 0.92709
(0.062$) 0.92498
(0.068$) 0.92484
(0.078$) 0.91800
(0.067$)
id
id
0.92360 (0.076$)
intercept
orthogonal regression
"0.28942 E+3 (0.55$) -0.29033 E+3 (0.46$) -0.28950 E+3 (0.51$) -0.29310 E+3 (0.61$) f»0.292l6 E+3 (0.59$) *0.29125 E+3 (0.50$)
-0.29079 E+3 0.19$ 0.22$ 0.80
^0.29096 E+3 0.21$ 0.22$ 0.93
"0.29186 E+3 (0.63$)
non-parallelized deviations
*0.28942 E+3 (0.51$) -0.29033 E+3 (0.43$) -0.28951 E+3 (0.47$) ^0.29310 E+3 (0.58$) -0.29216 E+3 (0.56$) -0.29125 E+3 (0.46$)
^0.29077 E+3 0.19$ 0.20$ 0.91
-0.29096 E+3 0.21$ 0.20$ 1.07
-0.29187 E+3 (0.59$)
21
A.2.4.2 . Results
The weighted aver.* value for the slope of the s t ra igh t l i n e equal to 0.92279 dmVmm witn a coeff icient of var ia t ion of 0.15 per cent agrees very well with Che expected value of 0.93061 dmVmm, mentioned in [ l ] .
In the tables the values of the parameters obtained in the separate runs are l i s t e d as well as those for the combined data s e t . In order to make a s t a t i s t i c a l comparison between the weighted average for the seperate runs and the r e s u l t s of the run with the combined data s e t , a proper analysis of covarian-ce i s requi red .
A.2 .4 .3 . Conclusion
A very good f i t t o the h i s t o r i c a l data in the ca l ib ra t ion runs for the EHRO" CHEMIC input tank was obtained by a combination of a quadratic curve (below x < 838 mm) and a s t r a i g h t l i ne (above x > 1000 mm.) Above x > 2000 mm one can predict from each ca l ib ra t ion run an y-*value with a r e l a t i v e standard deviation of 0.04 %.
A.2.5. The CE.A. Evaluations
A.2 .5 .1 . Theoretical Approach
When the tank was not emptied as in runs 5,6 and 7, the remaining volume was calcula ted by f i t t i n g a l inea r regression on the 4 points below 100 mm as obtained from the other runs .
CEA refer red to some d i f f i c u l t i e s about the pressure measurement techniques (combinations of H20"fllled U-tubes and TBE- f i l l e d U-*tubes and Wallace and Tiernan manometer, zero correct ion, averaging e t c . )
A.2.5.2. £esu2.t£
A l inear regression equation has been calculated to be H • 319.2 + 1.077xV and the differences with the measured data were plot ted on the graph, repre sented in f i g . Au8.
A.2 .5 .3 . Conclusions
•* Cal ibra t ion data a re not coherent between the runs; «• Tank i s not cyl indr ica l over the whole height .
*
22
A.2.6. The Brookhaven NL Evaluation
A.2 .6 .1 . Theoreti£al Approach
The data were s p l i t up in a non-linear and a l inea r part at a volume of 500 1 . The f i t of the lower part i s best accomplished with a polynomial of a high degree. A ninth power polynomial was t e s t ed . The l i nea r part i s very nearly a s t r a i g h t l i n e but a bet ter f i t of the data can be obtained using a 3rd or 4th degree polynomial.
A.2.6.2. Results
Non-linear part . even for the 9th degree, the p lot ted r e s idua l s show a pat-1* tern of reproducible " r i p p l e s " , and a spread in the data that i s „ 3 times greater than the run^to^run v a r i a t i o n .
Linear-part : the run-to-run va r i a t ion i s larger than any other e f fec t , and i s approximately 4 cm in height (0.8 % at volume of 2 530 l . ) see f igure A«-9.
A.2.6 .3 . Conclusions
Not too much ef for t should be put in to the analysis of these data because they are collected some time ago (1965) by methods that are somewhat behind today 's 3tate-ofa the«*art.
A.2.7. The DWK Evaluations
A.2 .7 .1 . Theore^icaJ. Approach
The c l a s s i c a l regression has been choosen, with x being the volume and y the he ight . The r e su l t s of the evaluations of a l l runs and averaging r e s u l t s i s given in table AH6.
Table A-16 : Linear fit Y - aX • b
with. : X-volume Y-height in mm water S-standard deviat ion on level in mm water
Run
1 3 4 5 6 7
( i ) ( j )
a
1.084526 1 .085999 1.077842 1.081708 1.081317 1.089405 1.083466 1.083388
b
314.1 315.3 313.3 316.1 316.0 317.2 315.3 315.4
S
1.60 2.28 2.23 2.28 2.25 2.40
( i ) Mean value over a l l 6 (J) Mean value without 4 and 7
23
In order to verify that ONE equation can or may be used over the entire height of the tank, the CUSUM'-diagrammes are consulted. An example is given in figure A-10.
Only run 5, given as example shows large differences in the slopes at diffe-1
rent heights in the tank.
A.2.7.2 Results
The volume below the level dipJtube is calculated tor each run out of all data below 345 liter, and ranges between 1.12 and 1.58 liter.
The equations are mentioned in the table.
The calculated height between the bottoa of the tank and the level dip- tube is ca. 45 mm instead of the by construction foreseen 20 nun.
A.2.7.3. Conclusions!
The problem with the level dip-tube can be caused by different effects :
- the level dip**tube is ei ther, not constructed as foreseen, or corroded or obliquely cut ted,
* the feed l ine had undetected dead volumes, *• or there existed a negative pressure at the s tar t of the calibration.
As long as the problem of the heel determination cannot be cleared, normalizing with new calibrations cannot be done.
The tank cannot be used for tracer techniques nor for emptying transfer measurements.
Due to the high standard deviations, in the point of view of todays exp^rien* ce, the calibrations are not satisfying to the norms of an accountancy input point, but acceptable for plant measurements only.
24
CHAPTER II
PHASE B : CALIBRATIONS AND RE"CALIBRATIONS OF AN ACCOUNTABILITY INPUT TANK AND ITS EVALUATIONS.
As th i s part of Ritcex cons i s t s of different sub jec t s , a subdivision has been made according to the following scheme :
- tank d i sc r ip t ion " preparatory work -i the ca l ib ra t ion by the wëigh-in method - the data evaluations - the calibration by tracer techniques
B.I. ENGINEERING REVIEW OF THE TANK
This review is based upon construction drawings, engineering flow sheets and photographs [3]. The figures B.1 and B.c give respectively a side and a top view of tank 221-4. These drawings enable the operator to predetermine the number and sizes of the increments required for proper calibration.
B.1.1. Transition Regions in the Tank
The tank as represented in figure B.1 is a construction to be subdivided in three different part?, due to the weldings. Part A consists of the region between 0 en 838 mm. It can itself be subdivided in :
- tne volume below level dip-<tube - the non linear part up to 709 mm •* the linear part between 709 and 838 mm.
Part B, between 838 and 2148 mm, is theoretically a totally linear part, as well as part C ranging from 2148 mm up to some distance below the overflow, located in the handhoie. It is obvious that the study of the internal piping can give rise to other transition regions.
B.1.2. Influence of Internal Piping
Figure B.3. i s the drawing of the a s -bu i l t in te rna l piping of the tank : the in ternal steam decontamination system Is however not indicated on t h i s d r a w ing, but detai led in f igures B.4. and B.5. The in terna l piping must be grouped in two di f ferent types : i ) the not vented l i n e s , which are normaly empty of solution during the
ca l ibra t ions as well as during operational input determinations, 11) the vented l i n e s , in which the l iqu id level stands at the same height as
in the r e s t of the tank.
To the f i r s t category, of not vented l i n e s , belong a l l instrument probes : level dip-*tube, density dip-tupe and in the higher region of the tank, the high level warning dip^tube. Indeed a constant a i r flow pushes the solution out of these tubes . A double influence i s a t t r i bu ted to the a i r sparge l i n e . After mixing the solut ion of input, the a i r remains in the ve r t i ca l part of the system in contradict ion to the horizontal part in which, due t o the a l t e rna t ive conf igurat ion of the ho l s s , th° a i r wi l l escape and be replaced by the so lu t ion . So the ver t ica l part be lor^j to the f i r s t category and the horizontal part acts as of the second category. All other l ines are vented e i the r by the op«n Jet exhausts in adjacent tanks (5 t ransfer l i n e s ) , e i the r by internal openings such as the decontamination system, or vent i la ted in the sampling b l i s t e r (3 sampling l i n e s ) .
25
The influence of the internal tubes will become clear after consultation of table B.1 T.ts influence on the slope in the linear part, on the total volume occupied in the tank, and on the mixing of the solution in the tank i s discussed. This means that the theoretical slope to be calculated in the next paragraph needs to be corrected for the following factors :
volume occupied by not vented l ines over 1 mm <"»f height (S2) volume occupied by the vented l ines over 1 mm of height (Sj)
Total
997.74 mm3
3337.51 mm» 0.004335 1/mm
Additional care has to be taken for the horizontal decontamination l i n e .
CODE
Table B.I -» (Ref.Fig. B.3*B.4*B.5)
FUNCTION ""O"" ®* 0 ;
mm nun mm 81
mm 62 2 mm
'S3 2
HO) mm
3B Level warning h igh 2A Density dip^tube 2B Level dip-'tube L Transfer sample l ine K Air l i f t sample l ine
eJ Transfer l ine I Transfer l ine H Transfer l ine F Transfer l ine E Transfer l ine
DH Air sparge horiz. DV Air 3parge vert ic . CVin Decont.line in vert. CVout Decont.line out vert . CH Decont.line horiz.
B Return sample l ine 1 Thermocouple Ü Feed l ine 0 Feed l ine N Feed l ine M Ventilation l ine T Feed cold H20 S T r f . hot H20 R Feed hot H20 P Tr f . hot H20
PM Hand h o l e 3A Reference dip*tube —l
13.5 13.5 13.5 13.5 13.5 42.4 42.4 26. 33 42 26 26 42 76 42
35 35 35 9 9 25 25 65 25 25 65 65 25 65 25
13.5 2.9
82.32 82.32 82.32 96.57 96.57
399.73 399.73 201.89 310.90 399.73 201.89 201.89 399.73 830.77 399.73
96.57
143 143 143 143 143
1411 1411 568 891
1411 568 568.32
1411.96 4548.41 1411.96
143.14
14 14 14 14 14 96 96 32 97 96 32
60.82 60.82 46.57 46.57
1012.23 1012.23
366.44 581.07
1012.23 366.44 366.44
1012.23 3717.64 1012.23
46.57
251 3250 3800 3250 2850 3550 3550 3500 3600 3650 10388 37^0 3728(2) 3054(2) 9890 3450
no influence on internal volume determination
Remarks
(1) i s the immerged length of the pipe i f the tank i s f i l l e d up to the overflow point in the handhole.
(2) bended part included.
26
B.1 .3 . Linear p a r t , s lope estimation
Figure B.1 l ea rns us that in the l i n e a r p a r t , the slope may be expected to be 0.93494 1/mm. The est imation of the volume of the in te rna l piping and the way of operating them, gives a reduction of the slopes of -* 0.004335 1/mm re su l t i ng in a f ina l theore t i ca l s lope of 0.93061 17mm. Consideration must be given however to the fact tha t the construct ion spec*» i f i ca t ions s t a t e d a "r ing thickness of 96 mm ± 2 mm and tha t a ve r i f i ca t ion by hydraul ic t e s t s should ind ica te 100 mm + 0 mm"
* 6 mm How a l l these f igures compare with the r e s u l t s of the h i s t o r i c a l data i s considered in chapter I I . In the l i nea r par t care should be given to th ree other reg ions , in addit ion t o those already mentioned in B . 1 . 1 . Namely a t the heights of 1000 mm and 2250 mm above the l eve l dip*tube, there ex i s t hor izontal tube supports of 20 mm x 4 mm over a lenght of 1350 mm, and, more important, at the height of 3115 mm i s located the in te rna l j e t decontamination l i n e with a t o t a l volume of 10.01 1 . over a height difference of 42 mm.
B . I .4 . " txlng Problem.
The study of the in te rna l piping revealed already a very important problem, not so much during ca l ib ra t ion opera t ions , but especia l ly during a rout ine inputmeasurement. Although the so lu t ion in the dissolver has already a c a r t a i n degree of homo** genei ty , due to the c i r cu la t ion i n the s lab tank and dissolver l e g , t h i s wil l again be destroyed by the not uniform d i lu t ion effect of the j e t t ransfer but especial ly by the th ree r ins ings of about 50 1 carr ied out in the dissolver and added t o the input tank, where the so lu t ion i s mixed and sampled before the volume measurement i s ca r r ied ou t . The normal operat ional volume, inclusive the th ree r ins ings i s about 2700 1 consis t ing of
150 1 of water added on top and 2550 1 of a mixture of concentrated so lu t ion di luted for about 7 % by
the steam j e t t r an s f e r . As the study revealed , the solut ion level in the decontamination l i n e , and in the five t r ans fe r l i n e s , wi l l increase together with the leve l of the r e s t of the tank volume. On the moment of adding the 150 1 of r ins ing solut ions they will contain about 30.4 1 of concentrated s o l u t i o n . (The hor izontal par t of the decontamination l i n e , 10 1 content , i s f i l l e d at t h i s h e i g h t ) . The r e s t of the tank volume wi l l be d i lu ted by the r i n s i n g s , then mixed and sampled. The sample wil l be represen ta t ive for about 2670 1 of so lu t ion , but not for the 30 1 in the piping. In the example here the concentration in the piping wi l l be C and in the r e s t
of the tank : fS222 x C 2670
This causes a biased input of about * 0.07 % per batch .
B.1.5. P o s s i b i l i t i e s offered by opening the handhold
All dimensions concerning the liandhole a re given in f igure B.6. The opening of t h i s hole permits :
M t o introduce the TDRasystem of leve l measurements + to introduce the acoust ic system of leve l measurement *» t o introduce the Eurochemlc camera t o make inspections in the tank.
However the review of internal piping, made e a r l i e r , revealed * d i f f i c u l t y .
27
As can be seen in figure B.4. , the upper part of the internal decontamination l i n e , occupies a large part of the in^tank surface at a height of 400 mm below the top of the tank. Of the thickness of the tank of 96 mm, the outer 50 mm are occupied by that tube. For the TDR and the acoustic systems, th is represents no problems because the camera can only be introduced down to that tube. Therefore the emptyness of the tank and the state of f i l l i n g has to be checked by using the zoom lens of the camera. The introduction of tracers via a funnel and a plast ic tube i s not impeded by this tube. The drawings of the handhole have been mailed to the participants concerned with TDR and acoustic probe level measurments.
B.I .6 . Temperature ef fects in dip-tube manometry
The system consisting of the tank and i t s probes i s calibrated in a retricted range of temperatures using a l iquid of density approximately equal to one. The temperature of each increment as measured in the feed tank, and that of the total volume as received in the tank to be calibrated, i s measured over the whole period of calibration. The range of these temperatures i s between 15° and 25° C. The effect of varying temperatures, up to 60° C to avoid crystal isat ion during normal opera-t ion , and l iquid densities up to 1.5 i s recognized as causing aberrations in the interpretation of calibration data. Former t e s t s , performed in th is tank during the years 1963-1968, did not reveal any substantial change in the batch weight determination at tempera-* tures varying from 19.5° C up to 61° C [4J. In those days readings of pres* sures were done by human eye on water or tetrabromoethane f i l l e d manometers. As however in the RITCEX, very advanced and much more precise instrumentation i s connected to the dip-tube system, those effects could be observed in principle. Unfortunately, the measurement of an identical mass at different temperatures, can not be performed due to the disconnection of the feed l ines to the heating/cooling jacket. A theoretical study [5] wil l be made. Special care however should be given to the annular shape of the tank, to the construction material (URANUS B 6 for the parts in contact with the input solut ion, AISI 304 L for the other parts) and especially to the fact that the input determination consists of a weight determination (V t xp t ) , minimizing in this way the density determination uncertainty in the tank.
B.2. PREPARATORY WORK
All deta i l s on the preparatory work are described in [ 1 ] . In great l ines however i t consisted of :
* select ing the scale to be used : different scales were tested during several calibration runs with well cert i f ied sta. ard weights, accepted by the Belgian and the F.R.G. authori t ies , and with standard weights of the scale fabricators. Evaluations on these calibrations can be consulted in [ 2 ] . Finally the Toledo-scale with dig i ta l indicator was selected and used during the whole exercise. The use of th is scale reduced the errors in the weighing of the increments to négligeable l e v e l s .
* humidification te s t s : two plast ic feed l ines to the tank were tested in the inactive zone in order to determine the draining time, the minimum slope and the volumes needed to humidify the tubes.
* i n s t a l l a t i o n of the level measurement instruments : the tank was provided with a three tube dip*tube system to which were connected :
** U-tube manometers f i l l e d with water or tetrabromoethane - a Meriam precision manometer type FA-187 - the complete Ruska system of the IAEA - the W & T portable , pneumatic calibrator, type FA-235
28
In addition, the Time Domain Reflector (TDR) of CNENH:asaccia and the acoust i c system of SCK-'CEN were introduced via the handhole inside the tank to measure the liquid heights independent from the dip-tube system. As far as possible an intercomparison of the instruments and leak te s t s on the systems were done.
* preparation of tracers and of the system for adding and sampling the tracers : a special sampling system, to be operated on top of the tank was constructed as the Eurochemic sampling system was out of order. The system was also used to add the tracers to the tank. Three tracer s o l utions and an Uranium solution were accurately prepared. The methods are described in B.5.
* preparation of data col lect ing forms, and tasks distr ibutions. Special forms were printed to col lect a l l data of scale calibrations and tank cal ibrat ions . The readings of a l l instruments was distributed among the participants.
B.3- THE CALIBRATIONS BY WEIGH-IN METHOD
Although i t was decided after phase A of Ritcex to perform three calibration runs, a fourth run was added in order do duplicate at l eas t one run. The runs 11 and 14 consisted of about 75 measurement points distributed according to the regions detected during phase A, while runs 12 and 13 only consisted of about 25 measurement points but use was made of these runs to t e s t the tracer technique. Before run 11, a visual check of the state of emptyness of the tank confirmed i t to be completely dry, so that this run could be considered as a f i r s t calibration run, a l l others being re*calibrations. The heel was estimated from phase A and confirmed by the constructrion draw" ings , to be l ess then 1.2 1 . Increments of about a quarter of a l i t e r were added, unti l bubbling of the air in the l iquid was noted. The draining time, determined during the preparatory work was taken into account. The f i r s t measurements were made after the l iquid "touches" the dip-tube. The in crements were choosen to make at l eas t ten measurements in the different regions observed during phase A, and small increments were added in the trans i t i on regions. The pre-designed incremental schedule was s t r i c t l y followed and a l l resulting data collected on th? forms, which, after each run were distributed to a l l participants. Although runs 12 and 13 consisted only of about 25 measurement points, a l l runs consisted of about 15 emptyings of a 200 1 . drum to the tank : for runs 11 and 14 more intermediate weighings and level measurements were performed, c ;her differences however can be distin-* guished between the two types : adding of tracers, mixing periods and samplings were performed during runs 12 and 13. In addition, the instruments introduced into the tank were different from run to run and as such no real Identical run e x i s t s . The aim of the exercise however was not to calibrate th i s tank but to look for an optimum procedure of the calibration technique. It i s obvious that for the calibration of a tank, at least three identical calibrations should be performed. Two additional runs were included in the exercise; comprising many t e s t s which normally had to be performed. Run 15 consisted of determining the volume loss by using the exist ing reagence feed l ine as the calibration l i n e , and to estimate the influence of changing the temperatures of the solution inside the tank. Run 16 f ina l ly consisted of a continuous f i l l i n g of the tank at a constant flow rate while making automatic measurements with the Ruska system a constant time interval . This resulted in 200 measurements performed in about 2 hours. The overflow height was also determined during this run.
29
In addition to this information, all basic data collection sheets are still available to all persons interested, but a warning should be give here because the runs are all somewhat different and could cause différer. approaches in data handling. Burochemic provided the opportunity to make a videofilm of the whole exercise. Although it has some imperfections due to the practical recording conditions, it has proven it's usefulness on many occasions.
B.4. SUMMARY OF RITCEX EVALUATIONS
Four calibration runs, numbered Run 11 to Rin 14, were performed during RITCEX. In Run 11 and Run 14 the same additions of liquid were foreseen. The other two runs were specially designed for the application of the tracer technique. The number of additions in both rurs was the same, but significantly less than in Runs 11 and 14.
The calibration data were used to investigate four different level measurement instruments namely the electromanometer (RUSKA), the liquid manometer using Tetrabromoethane (C2H2Br,,), the acoustic system (SONAR) and the time domain reflectometer (TDR). Unfortunately, the instruments could not all be installed in the tank before the beginning of the calibration runs. Thus, some instruments had to be installed between different runs, which resulted in run-to-run difference in the volume displaced by instrumentation. Table B.2 shows the instrumentation installed in each run.
Table B.2. : The instrument and technique used in each run is marked by X
Run 11 Run 1 2 Run 13 Run 14
RUSKA
X X X X
U-tube
X X X X
SONAR
X X X
TDR
X
TRACER
X X
The data were analyzed with respect to the precision and accuracy of each instrument. Good precision is necessary to identify systematic errors and for the accuracy to be evaluted.
The experiment showed (see Table II - Table V in RITCEX 12-B in volume II) that the TDR had the lowest precision. One of the reasons for the rather poor performance is that the signal of the instrument is plotted on strip charts. Each strip chart has then to be converted to a level measurement. This conversion was done by hand and this caused significant reading errors. Further development of tnis instrument is under way in which the signal is digitized so that the conversion to a level measurement can be done by a microcomputer. This will eliminate the reading error and will so hopefully increase the precision of the TDR.
The precision of the SONAR system is significantly better (compare Fig.3 and Figure 4 in RITCEX 12-B in volume II) than that of the TDR system, but the overall accuracy is only slightly better. It is interesting to note that the accuracy improves with an increase in the level. This might be an inherent feature of this system in which the complement of the level is actually
30
measured. There is some argument that the ventilation system of the tank caused a systematic measurement error due to an inadequate installation of the instrument. A better design of the SONAR system which avoids this effect seems to be possible so that the performance can hopefully be improved.
The shortcomings of the liquid manometer are mainly caused by the rather high reading error. This is especially true for the liquid manometer which wa3 used in this experiment. Because this was filled with Tetrabramoethane which has about three times the density of water. The rather poor measurement precision (see Fig. 2 in RITCEX 12^B in volume II) seems to be the dominating error.
The electromanometer (RUSKA) is known to have a very high measurement preci* sion. Though the precision was not directly measured during this experiment, it can be seen from the results (see Fig. 1 in RITCEX 12-B in volume II) that it is very high. But these results show also a significant systematic run to run deviation. The higher precision allows obviously to see effects which have been hidden in the measurement noise before. It would be interesting to identify the reasons for the systematic run to run deviation. But unfortunately these reasons cannot be identified by analysing the data presently collected during the RITCEX calibration runs. This can only be done in another experiment which is designed in such a way that possible reasons for the systematic deviation can be investigated. The existence of a systematic run to run deviation which turned out to be the dominating error is the most important result of RITCEX. One major contribution of RITCEX was thus to identify problems which need to be further investigated in order to increase the accuracy of the level measurements.
A reasonable estimate of the achievable accuracy of the volume determination via a level measurement with an electromanometer cannot be given because the calibration runs performed during RITCEX cannot be considered as an homogene-» ous sample. This is caused by a number of facts as for example the volume correction, which was necessary to correct for installed instruments between different runs, the different evaporation during the calibrations due to the different times needed to complete the various runs, the evaporation that occurred during extensive sparging in runs 12 and 13» the different tem" perature gradient in the liquid of the tank and the different pressure drop in the probes before the beginning of each run. A test for the homogeneity of the runs was performed, (see RITCEX 12*A in volume II) which confirmed that the runs should not be considered as a homogeneous sample. Therefore, an estimate of the systematic run to run deviation cannot be given.
The standard error models used for tank calibration assume that either the random error in measuring the level or the random error in measuring the volume is dominant or that both random errors have to be considered. Another error model, known as the "cumulative model", is also used in tank calibra^ tion (see e.g. RITCEX 12-E in volume II). This model assumes that the random error in measuring the volume of each increment is dominant, i.e. the addition of increments causes a systematic error in the volume measurement. We should be aware that a random error in the measurement device is the basic assumption on all these error models. There could be other error sources however, which have nothing to do with the measurement device, such as e.g. leaking valves or evaporation. Whether the systematic run to run deviation is caused by such systematic errors or by the inhomogeneity in the calibration data needs further investigation. It is obvious (see e.g. RITCEX 12*B in volume II) that the observed systemitic run to run deviation exceeds by far the size of the random errors in the measurement device.
Therefore, estimates fbr the accuracy in the volume determination via a level measurement as given in RITCEX 1 2"A to 12-E in volume II are inadequate.
31
The achievable accuracy in determining the volume of a tank via a liquid manometer measurement is usually assumed to be about 0.5 %. Tne evaluation of the historical calibration data of this tank confirmed th?L statement, [lO], There is some indication that the accuracy achieved in the RITCEX calibration runs might be slightly better than 0.5 %. The achievable accuracy in determining the volume via electromanometer measurements should be considerably better than that. This seems to be the case also in the RITCEX calibration. But the achievable accuracy could be improved still significantly, if the reasons for the systematic run to run deviation are better understood and hence actions could be undertaken for their reduction or elimination. Numerical analysis values are given in tables B.3i B.4, B.5, B.6, B.7.
Table B-3 : The Resultant Cal ibra t ion Equations (single data se t )
Data Set
Ruska (Run #11)
U-tube (Run #11)
Ruska (Run #1U)
U-tube (Run#14)
Acoustic (Run #11)
TDR (Run#14)
Region- !
V=6.40859x10—xHa* •5.96374x10~*xHa •8.35U67X10"1
V-6.23120x10~"xHaa
+6.51506x10a*xHa •7.01885x10*»
V=6.40476x10"-HxHa* •6.0'»210x10' i2xHa •8 .51818x10" 1
V=6.27935x10""*xHaa
+6.53887x1 O^xHa •6.59970x?O"1
V=3-95062x10~sxHa2
• 3.97839x1044lxHa +6.98818x10""
Region-2
V=6.20331x10" ixHa2
+7.7526lx10"*xHa -2 .82094
V=5.76l48x10 i ,*xHa2
• 1.22576x10*MxHa -1 .38779x10
V-6.17408x10"*-xHa* •7 .91203x10 - 2 xHa -2 .761 . °
V-6.07889x10**-xHaa
+8.98732x10-*xHa -5 .23964
V=5.40865xl0 ' -xHa 2
• 1.3041 OxlO^'xHa -1 .11566x10
V=4.56835x1O^-xHa* +3.46206x10~'xHa -2 .20412x10
Region-3
V-2 .946l1x10"*xHa 2
+9.20567x10~ lxHa -2 .90494x10*
V=9.27198x10~ lxHa . -2.93803x10*
V-2.27317x10" i 8xHa ï
• 9.68822x10 - i sxHa* +9. l4 l40x10~ 1xHa -2 .88836x10*
V - 9 . 432x10 i i ,xHa -2.92988x10*
V=1.89689xlO"sxHa2
+8.64458x10~ lxHa -2 .69116x10*
V-8.93072x10 i* ,xHa -1 .96716x10*
Region-4
V-1.13876x10~"xHa ,
^.OSoOSxIO^xHa* +1.l6833xHa -5 .02446x10*
V-9.29344x10~'xHa "2.96556x10*
V-1.06844x10"»xHa» H8.2364lx10"sxHa* +1.l4030xHa -4 .76789x10*
V-9.30100x10 f c lxHa -2.99537x10*
V-9.37309x10~»xHa2
+8.89777x10~'xHa -«2.79828x10*
V-8.99084x10~ lxHa ^2.05203x10*
Region-5
V-8.53l41x10~ lxHa "6.14495x10
V-8 .5 l689x10" 'xHa -5.81888x10
V-8.53553x10u ,xHa -6 .37943x10
V-8.56569x10 _ lxHa "7.39303x10
V-8.62765x10" lxHa -1.06791x10*
Region-6
V-9.32633x10 i i ,xHa -3 .12384x10*
V-9.35552x10_ , ,xHa -3.237?9x10*
V~9.33019x1O^'xHa -3 .14260x10*
V«9.3l825x10"'xHa -3 .11410x10*
V—3.13229x10-*«xHa' •3.11711x10~*xHa2
-1 .0236lx10*xHa +1.13656x10*
Table B-4 : The Resultant Calibration Equation (combined data set)
Data Set
Ruska vRun #11 and #11)
U-tube (run #11 and #11)
Ruska (Run #11 t o #14 )
U-tube (Run#11 t o #14)
Acoustic (Run#12 to#14)
Region-1
V=6.39567x10""xHa2
+6.03621x10~2xHa +8 .27" )4 lx l0 - 1
V-6 .25531* lO ' -xHa 2
•6.524*.oxK *xHa +6.88469x10"*1
V-6.38736x10""*xHa2
+6.04057x10~2xHa +8.27952x10"-
V-6.27978x10"sxHa2
+6.4l296x10~*xHa •7.09760x10**1
Region-2
V=6.18612x1O^-xHa2
+7.85931x10 - 2xHa -2 .86106
V-5.91447x10w -xHaa
•1.06924x10"'xHa -9 .76048
V - ô . l i g ^ x I O ^ - x H a 2
+8.17005x10~axHa ^•3.64001
V-6.21564x10 l*HxHa2
•7.48497xlO"**xHa -2 .04270
V-4.79471x10_ , ,xHa2
+ 1.82432x10* i IxHa -2 .18323x10
Reglon-3
v-g^Teiexio^-xHa -*2.94708x104-2
V-3.52907x10'"»xHa2
+9.17264x10*-xHa --2.87705x102
V-2.50705x10-*xHa2
+9.21193x10""xha -2 .91337X10 2
V-4.47747x10 k , xHa 2
+9. l4655x10- i l xH* -2.8637»»x102
V-3.99570x10"sxHa2
TÔ.07482x10_' lxHa -2 .41603X10 2
Reglon-4
V"9.30251x10 - 1xHa -2 .98804x10*
V-9.29721x10~ lxHa -*2.98040x10a
V-9.30657xlO" ,xHa -3 .00272x10*
V-9.30223x10*"-xHa - '2.99855x10*
V-9.43192x10~'xHa ~3<56298xl02
Region-5
V-8.48l87x10 l* ,xHa ••4.64057x10
V-8.43966x10u ,xHa -3.11885x10
V-8.37627x10 i* IxHa ••1.37912x10
V-8.29124x1O^'xHa +1.16299x10
V-8.08314x1Ow,xHa +6.19039x10
Reglon-6
V-9.32842x10~'xHa •-3.13367x10=
V-9 .3366lx10 u ' xHa -*3.17484x102
V-9.30882x10*"'xHa -•3.07108X102
V-9.32261x10u ,xHa -3 .13025x10*
V»-2.96991 x lO^xHa» +2.93720x10"2xHa2
*9.57803x10xHa +1.05700x10*
Table B-5 : Data Point(D.P.), Degree (Deg.) and Standard Deviation (C.;., of each calibration equation
Data Set
Ruska (Run#11)
U^tube (Run#11)
Ruska (Run#14)
U-tube (Run#l4)
Acoustic(Run#14)
TDR (Run#14)
Ruska (Run#11 and#l4)
U-tube (Run#11 and#l4)
Ruska (Runf l l t o # l 4 )
U-tube Cun#11 t j # 1 4 )
Acoustic (Run#12to#l4)
Region-1 D.P. Deg. S .D .
13 2 0.084
13 2 0 . 2 U
11 2 0 .051
11 2 0 .271
9 2 2.384
23 2 0 .101
23 2 0 .291
29 2 0.134
29 2 0 .311
Region-2 D.P. Deg. S .D.
9 2 0 .061
9 2 0 .761
9 2 0 .061
9 2 0.484
7 2 1.904
10 2 5.^64
18 2 0.104
18 2 0 .681
31 2 0.304
31 2 1.174
17 2 3-234
Region-3 D.P. Deg. S .D.
17 2 0.254
17 1 0.724
17 3 0.194
17 1 1.104
17 2 1.034
15 1 7.754
33 1 0.624
33 2 0.824
50 2 0.844
50 2 1.334
35 2 9.414
Region-4 D.P. Deg. S .D.
21 3 0.224
21 1 1.034
20 3 0 . 3 U
20 1 0.814
20 2 0.744
20 1 7.224
40 1 1.024
40 1 1.064
50 1 1.244
50 1 1.654
30 1 5.194
Region-5 D.P. Deg. S .D.
5 1 0.654
5 1 0.784
5 1 0.784
5 1 1.284
5 1 0.754
9 1 0.754
9 1 0.674
11 1 1.014
11 1 1.424
5 1 2.1*74
Region-6 D.P. Deg. S .D.
13 1 0.064
13 1 1.034
13 1 0.074
13 1 0.384
11 3 0.334
25 1 0.324
25 1 0.794
29 1 0.804
29 1 1.374
16 1 2.074
Table B-6 : Comparison of Volume calculated with each calibration equation at the typical value
Data Set
Ruska (Runf l1 )
U-tube ( R u n f l l )
Ruska (Runf l4 )
U-tube 'Runfl 4)
Acoustic(Runfl 4)
TDR (Runfl 4)
Ruska (Run#11 a n d f ' 4 )
U-tube (Run#11 and#14)
Ruska (Run#11 t o f 1 4 )
U'-tube (Runf l l t o f l 4 )
Acoustic (Runf l2 to f 14)
Regioo-1 H* » 200 mm
3 8 . 4 0 K - 0 . 0 6 l )
3 8 . 6 6 K O . 2 0 l )
38 .561 (0 .101 )
3 8 . 8 6 K 0 . 4 0 4 )
81 .851 (43 .391 )
3 8 . 4 8 K 0 . 0 2 l )
3 8 . ? 6 K 0 . 3 0 £ )
38 .46*
3 8 . 6 5 K 0 . 1 9 t )
Region-2 Ha - 500 mm
1 9 1 . 0 2 K 0 . 0 8 l )
1 9 1 . 4 5 K 0 . 5 1 l )
1 9 1 . 1 5 K 0 . 2 1 t )
1 9 1 . 6 7 K 0 . 7 3 t )
l 8 9 . 2 6 K - 1 . 6 8 t )
2 6 5 . 2 7 K 7 4 . 3 3 t )
1 9 1 . 0 9 K 0 . 1 5 t ) *
l 9 1 . 5 6 K 0 . 6 2 t )
190.941
1 9 0 . 7 7 K - 0 . 1 7 t )
1 8 9 . 2 5 K - 1 . 6 9 * )
Region-3 Ha - 1500 mm
1 0 9 6 . 9 9 K 0 . 9 0 1 )
1 0 9 6 . 9 9 K 0 . 9 0 t )
1096 .501 (0 .41 t )
1 0 9 6 . 6 6 K 0 . 5 7 1 )
1 0 7 0 . 2 5 K - 2 5 . 8 4 t )
1142.891(46.801)
1097 .021 (0 .93 t )
1096 .13K0 .041 )
1096.091
1 0 9 5 . 6 8 K - 0 . 4 1 1 )
1 0 5 9 . 5 2 K - 3 6 . 5 7 1 )
Region-4 Ha = 2500 mm
2 0 2 8 . 4 3 K 2 . 0 6 1 )
2 0 2 6 . 8 0 K 0 . 4 3 1 )
2 0 2 6 . 1 3 K - 0 . 2 4 1 )
2025 .711("0 .661)
2 0 0 3 . 2 0 K - 2 3 . 1 7 1 )
2042.511(16.141)
2026 .821(0 .451)
2 0 2 6 . 2 6 K - 0 . 1 1 1 )
2026.371
2 0 2 5 . 7 0 K - 0 . 6 7 1 )
2001 . 6 H K - 2 4 . 6 9 t )
Region-5 Ha » 3100 ram
2 5 8 3 . 2 9 K 0 . 4 4 1 )
2 5 8 2 . 0 5 K » 0 . 8 0 1 )
2 5 8 2 . 2 2 K - 0 . 6 3 t )
2 5 8 1 . 4 3 K - 1 . 4 2 1 )
2 5 6 7 . 7 8 K - 1 5 . 0 7 1 )
2 5 8 2 . 9 7 K 0 . 1 2 1 )
2 5 8 2 . 1 1 K - 0 . 7 4 1 )
2582.851
2 5 8 l . 9 1 1 ( - 0 . 9 4 t )
2 5 6 7 . 6 8 K - 1 5 . 1 7 1 )
Region-6 Ha - 3300 mm
2765.301(0 .501)
2 7 6 3 . 5 6 K - 1 . 2 4 1 )
2764 .701 (^0 .10 ! )
2763.611(^1.191)
2 7 5 2 . 8 7 K - 1 1 . 9 3 1 )
2 7 6 5 . 0 1 K * 0 . 2 1 1 )
2 7 6 3 . 6 0 K - 1 . 2 0 1 )
2764.801
2763 .44K- .1 .361)
2756 .44K- -8 .361)
Note ( ) : The difference between the volume of each calibration equation and that of Ruska (Runfl1to#14).
Table B-7 : Comparison of Volume calculated with each ca l ib ra t ion equation at break point
Data Set
Ruska (Pun#11)
U-tube (Run#11)
Ruska (Run#14)
U-tube (Run#11)
Acoustic (Run#11)
TDR (Run#11)
Ruska (Run#11 and#11)
U-tube (Runf l l and#11)
Ruska (Run*11 to#11)
U-tube (Run #11 to#11)
Acoustic (Run#12 to#11)
Region-1 Region-2 Region-»3 Region-1 Region*5 Region-6 Ha = 350 mm Ha = 700 mm Ha = 2000mm Ha = 3070 mm Ha » 3160 mm
100.211 100.301 3 5 5 . t U 356.29£ 1562.121 1561 .871 2557. 17* 2557.69* 2631. 18* 2631.71* ( 0.09*) ( 0.881) (-0.55*) (0.22*) (0.26*)
99.81* 99.60)1 351.21* 355.15* 1560.598. 1562.591 2556.53* 2556.50* 2633.15* 2632.18* (-0.21*) ( 1.00*) M ,51*) ("0.03*) (-0.67*)
100.16* 100.56* 355.15* 355.03* 1560.01* 1559.83* 2556.81* 2556.61* 2633.13* 2631.08* ( 0.10*) (-0.12*) (-0.18*) (-0.20*) (0.65*)
100.17* 100.68* 355.51* 355.51* 1559.88* 1560.66* 2555.87* 2555.71* 2632.83* 2633-16* ( 0 .2U) (-0.03*) (0.78*) (-0.13*) (0.33*)
315.15* 315.30* 1535.68* 1537.22* 2510.13* 2511.90* 2619.55* 2619.53* ( 0.15*) (1.51*) (1.77*) («0.02*)
111.78* 155.09* 111.15* 128.13* 1589.13* 1592.97* (10 .3U) (15.72*) (3.511)
100.30* 100.13* 355.27* 351.76* 1560.93* 1561.70* 2557.07k. 2557.53* 2633.87* 2631.11* ( 0 . 1 3 * ) ( - 0 . 5 U ) (0.77*) (0.16*) (0.51*)
100.15* 100.12* 351.89* 356.11* 1560.91* 1561.10* 2556.20* 2556.79* 2632.71* 2632.88* (-0.03*) ( 1.22*) (0.56*) (0.59*) ( O . ï l * )
100.22* 100.28* 351.86* 351.73* 1561.08* 1561.01* 2556.81* 2577.72* 2633.11* 2631.18* ( 0.06*) (-0.12*) (-0.01*) (0.88*) (1.37*)
100.08* 100.30* 351.92* 356.08* 1560.85* 1560.59* 2555.93* 2557.01* 2631.66* 2632.92* ( 0.22*) ( 1.16*) (-0.26*) ( U U ) (1.26*)
310.81* 313.21* 1533.19* 1530.09* 2539-30* 2513.13* 2616.18* 2617.28* ( 3.60*) (-3.10*) (1.13*) (1.10*)
Note ( ) : The difference between the volume of upper Region and that of lower Region.
37
B.5. RESULTS OF THE USE OF TRACER TECHNIQUES
B.5.1. Introduction
During the Reprocessing Input Tank Calibration Exercise the feasibility of measuring the weight of solution in a typical reprocessing input tank by the use of tracer techniques has been evaluated. In addition the tracer versus the uranium concentration ratio in the solution can be used as an independent method for the assay of the uranium inventory in the tank. The principles, the recent applications and the experience obtained with the tracer technique has recently been reviewed in a workshop, organised by the ESARDA working group on Reprocessing Input Verification [il]. According to the ensuing recommendations the purpose of the use of tracer techniques in the RITCEX experiment has been defined as follows :
1. to demonstrate the feasibility of the tracer technique for assaying the uranium inventory in a typical tank used for reprocessing input measure-* ments;
2. to obtain data on the accuracy of the uranium assay in the reprocessing input tank using tfci tracer techniques;
3. to demonstrate the feasibility and assess the accuracy of the tracer tech-» nique for remote tan'< volume calibrations.
The number of tracers used in the experiment has been limited to three i.e. lutetium, lead and neodymium. Together with the tracers a quantity of uranium has been added to the tank. Because of the operational constraints at the Eurochemic plant and the nonavailability of the Thorex sampling system a special recirculation and sampling system had to be installed on the tank inside the hot cell because direct transfer of liquids from the decontaminated tank outside the cell was considered as a potential hasard. Each sampling operation thus necessitated an intervention into the shielded cell. This fact sevei'ly reduced the number of samples taken during the actual experiment with respect to the original planning. The investigation of the homogenisation as a function of sparging time was canceled.
B.5.2. General Design of the Experiment
The tracers were added in the runs 12 and 13 of the RITCEX experiment. Lutetium anj lead were added in run 12, neodymium in run 13- Simultaneously a nominal quantity of about one kg of uranium was added in each of the runs. Figure B.7. shows the general design of the experiment. The tracers and the uranium were added when a nominal volume of 500 1. was reached in the calibration procedure. Before the addition of the tracers a blank sample B was tak?n. After addition of the tracers and the uranium the solution in the tank was stirred by air sparging for homogenisation during 30 minutes. After sparging sample I was taken from the solution. The calibration run was then continued until a nominal volume of 1600 1. was reached. The solution was then stirred again by air sparging for 30 minutes and sample K was taken. A similar operation at the nominal volume of 2600 1. yielded sample L. The three samples and the blank having each a volume of about 250 ml were weighed and transferred to the laboratory for subsampling and distribution.
38
The labora t ies pa r t i c ipa t ing in the experiment received th ree subsamples from each of the samples B, I , K and L. Two of the samples were we*ghed into 5 ml glas3 v i a l s , sealed with a rubber l i d and an aluminum cap. The th i rd one was weighed in to a 5 ml p l a s t i c v ia l closed with a screwed cap. The purpose of the sample in the p l a s t i c v ia l was to be en t i re ly free of interference from lead or neodymium which coula be released from the glass v ia l s in acid sol-» u t ion . I t was ant ic ipa ted that only concentration r a t i o s could be measured in the p l a s t i c v ia l s and that actual concentrations would dif fer from the o r i g inal ones due to evaporation l o s s e s . In addit ion each laboratory received a duplicate sample of the or ig ina l t r a cer solutions and of the uranium so lu t ion , in t h i s way seven s e t s of samples have been d i s t r ibu ted to d i f ferent l abo ra to r i e s , but only five reported measurement r e s u l t s for evaluat ion.
B.5.3. Tracer quan t i t i e s and c e r t i f i c a t i o n
The t racer and the uranium solu t ions to be introduced in to the tank have been carefully prepared and character ised in accordance with the ant ic ipated high level of accuracy of the ma3s spectrometric measurements. No correct ions for a i r buoyancy have been applied t o the weights.
Lutetium oxide. The lutetium oxide was obtained from Fluka (pur i s s . 99.99 %). I t was heated for 2 hours at 900°C in a porcelain crucible under a i r . The powder was brought in a pyrex beaker and cooled in a des icca tor . A weight of 19.48770 g was dissolved in 2.16 M n i t r i c acid af ter gent le boil ing during 3 hr i r s . The solut ion was quant i ta t ive ly t ransferred in to a 1 1 p l a s t i c b o t t l e . The net weight of the solut ion was 771.25 g . About 100 ml have been taken into a 100 ml p l a s t i c b o t t l e . The remaining solut ion (656.85 g) was added to the tank. From the 100 ml fract ion a 50 ml glass ca l ibra ted f lask was f i l l e d to the mark containing 51.99672 at 20°C. The density of the so lu t ion at that temu
perature i s thus 1.03993 S cnT3 . On the basis of the pur i ty and a stochiome^ t r i e factor of 0.87938 the concentration of the lutetium in the solut ion i s 22.218 mg gMl and the quanti ty added to the tank i s 14.5939 g.
Lead metal wire. The lead metal wire of 1 mm diameter was obtained from Johnson Matthey Chemicals Ltd. The material was c e r t i f i e d with a t o t a l impurity content of 15 ppm. The metal wire was weighed (47.17906 g) and dissolved in a pyrex beaker by heating in 2 M n i t r i c acid for s ix hours. The so lu t ion was t ranferred to a p l a s t i c bo t t l e and di lu ted to 768.38 g, yielding a lead concentration of 61.401 mg g*1. About 100 ml have been t ransferred t o a p l a s t i c bo t t l e and the remaining solut ion weighing 650.48 g and containing 39.940 g of lead was added to the tank. From the 100 ml fraction 50 ml have been t ransferred into a ca l ibra ted f l a sk . The weight was 55.0607 g and the density of the lead solut ion thus 1.101231 g cm"', a t 20°C.
Neodymium oxide. The neodymium oxide was obtained from Johnson Matthey Chemicals Ltd. The material was ce r t i f i ed with an impurity content of 120 ppm. After drying at 120°C for 18 hours and calc ining under a i r at 900°C for 3 hours, the material was cooled in a des iccator . A weight of 21.64610 g Nd203 was t ransferred in to a pyrex beaker and dissolved in 2.16 M n i t r i c acid by gent le heat ing. The solut ion was t ransferred in to a p l a s t i c bo t t l e and d i lu ted to 750.78 g. On the basis of 99.99 % pur i ty and a stoichiometric factor of 0.85735 the neody» mium concentration in the solut ion was 24.716 mg g**1. About 80 ml were t r a n s ferred in to a 100 ml b o t t l e . The remaining so lu t ion , weighing 669.78 g and containing 10.5544 g of neodymiuum is t ransferred in to the tank. From the 80 ml fraction 25 ml were t ransfer red in to a ca l ibra ted f l a s k . The weight of the solution was 26.17776 g and the density thus calculated was 1.04711 g enr" at 20«C.
39
Uranium oxide. Depleted uranium oxide (nuclear grade) was recovered from a stock of fresh fuel pins. A quantity of p e l l e t s , weighing 2317 g yielding a tota l solution weight of 10468 g. The solution ha3 been subdivided in two 5 1 plast ic bott les containing 5095 g and 5221 g to be added respectivel into the tank during run 12 and 13- Part of the solution was transferred to calibrated f lasks for density determination and confirmatory analytical measurements. On the basis of a stochiometric factor of 0.8815 and an impurity content.content lower than 100 ppm a concentration value of 195.11 ng g"11 was expected. The value of 195.46 rag g*1 as obtained by potentiometric t i t ra t ion was retained as the reference value. The reference uranium quantities introduced into the tank during run 12 and 13 thus respectively 995.87 and 1020.50 g. The la t ter value has to be corrected for the uranium in the heel of the tank remaining from run 12. The corrected reference value i s 1020.89 g .
B.5.4. Experimental results
B. 5. M. 1. Integr£ty of_the_samples
In order to have some indication on the integrity of the samples after shipment the gross weight of a l l shipped sample bottles has been recorded and i t was asked to the participating laboratories to report their weighings on the data sheets . Obviously differences were observed in the weights of the plas4* t i c bottles due to evaporation of the l iquid during shipmont and storage. The weight differences recorded for the glass v ia l s were small and mainly pos i t ive , which i s probably due to the different re la t ive humidities at the time and place of sample preparation (February 84) and during analys is . The average weight differences and their standard deviations are presented in table B.8. The largest single difference observed would correspond to a weight change of the sample solution of • 0.2 %. However in view of the posit ive sign of a l l changes, i t was concluded that no evaporation losses oc* curred in the samples transported in glass v ia l s and no corrections have been applied. The v ia l s containing uranium tracer solution however showed v i s ib le attack of the rubber cap after some months of storage and the integrity of th is series of samples i s quest ionable . Those resul ts therefore have not been considered in th,e evaluation.
Table B.8. Gross Weight Changes of the Sample v ia l s between Preparation and Analysis.
Laboratory Number of Vials Weight Changes in 10"*' g Mean value and standard deviation
SCK/CEN 8 0.12 ± Ü.74 JRC 4 1.63 ± 0.86 ITREC 8 5.19 ± 1.30 EUREX • 4 2.89 l 0 .92 ECN 22 1 . 1 0 ± 0 . 8 3
B.5.4.2 . Cone ent ration Data_for_the_Tracer Solutions
The concentration data for the tracer solutions reported by the different laboraties are presented in table B.9. The table shows the difference of the mean value with respect to the reference value given in section B.5.3 and the standard deviation (single measurement) calculated from the reported measure* ments.
no
Table B.9. Concentration Results for the Tracer So lu t ions . Difference of the mean value with respect t o the reference value and standard dev i a t i o n . (All data expressed in percent . )
Tracer Laboratory
A
B
C
D
E
Lutet ium
- 0.27 ± 0.027 - 0.76 ± 1 . 2 8 + 0.068 ± 0.10 * 0.27 ± 0.032
e»
Lead
- 0.19 ± 0.05 • 0.12 ± 0.13
~*
"•
- 0.54 ± 0.07
Neodymium
-
• 0.58 ± 0.19
™
—
• 0.83 t 0.11
The r e s u l t s ind ica te t ha t res idual systematic e r ror components are more im* portant than the random uncer ta in t ies expressed by the standard dev ia t ions . The in te r labora tory standard deviat ion i s 0.34 % for lu te t ium, 0.49 % for lead and 0.18 % for neodymium. Only in the case of neodymium the systematic difference with respect to the reference value i s of s ign i f i cance .
8 . 5 . 4 . 3 . Homogenei_ty_ of_the_Solution in_the_tan]<
The operat ional r e s t r i c t i o n s during the experiment precluded the study of the homogeneity in the tank as a function of a i r sparging durat ion. On the other hand homogeneity of the so lu t ion in the tank i s an essen t ia l feature of the t racer technique. In t h i s experimental se tup , the t r a c e r s were introduced s e quent ia l ly into the tank during the r e c a l i b r a t i o n procedure and th ree differ-1
ent l eve l s of homogeneity can be discerned :
a) homogeneity of the sample so lu t ion dispatched to the di f ferent labora* t o r i e s ; t h i s so lu t ion was col lected as a s i n g l e quantity and al iquoted in the laboratory in a way that homogeneity at t h i s level has been achieved.
b) homogeneity of the t r ace r solut ions mutually; t h i s homogeneity i s achieved a f te r su f f i c i en t mixing in the tank and can be control led by comparing the r a t i o s of t r ace r concentrations in the d i f fe ren t sanples .
c) homogeneity of the t r a c e r s in the tank so lu t ion ; t h i s l eve l of homogeneity i s disturbed at each addi t ion of l iqu id during the ca l ib ra t ion procedure and has not been control led during the experiment because of the opera t ional r e s t r i c t i o n s .
The mean concentrat ion r a t i o s for the d i f fe ren t elements measured by the individual l abora to r ies are shown in Table B.10. The use of the element concentrat ion r a t i o s allows incorporation of the data obtained on the p l a s t i c sample v i a l s in to the evaluat ion.
Ml
Table B.10. Element Concentration Ratios
Mean values and Standard Deviation
Run
Reference
Sample I
Sample K
Sample L
Uranium Lutetium
12
68.239
67.318 ±0.752 67.797 ±0.707 68.333 ±0.587
Uranium Lead
12
24.931
23.978 ±0.150 24.640 ±0.128 24.715 ±0.223
Lutetium Lead
12
0.3654
0.3598 ±0.0011 0.3659
±0.0030 0.3620
±0.0026
Uranium Neodymium
13
61.669
57.249 ±0.457 61.724 ±0.534 61.777 ±0.360
From the resul ts i t can be concluded that homogeneity of the different tracers in sample I has not been achieved at the lower than 1 % l eve l . Probably the a i r sparging during 30 minutes at the relatively low liquid level of 500 1. causes insufficient turbulence for adequate homogenisation of the solution. The effect is reproducible in both runs 12 and 13. Much better homogeneity has been achieved in sample K and particularly in sample L which i s close to the normal operational level of the tank where air sparging is probably most effective. The inhomogeneity observed in the sample I leaves them unsuitable for the calculation of the quantity of liquid in the tank.
B.5.4.4. Accuracy _and_Precision_of £he £oncentration Data_for_the_Solution in the Tank
The standard deviations shown in Table B.10. contain not only the random variations of the concentration measurements of each element by the laboratories but also the potential systematic deviations in a particular labora-1
tory for a particular element. A different way to evaluate the data is to calculate the concentration rat ios of different samples for a single element. This procedure eliminates systematic effects, such as spike calibrations from the resul ts and yields a better estimation of the ultimate precision of the technique. Proper identification of the systematic error sources by appropriate calibration procedures should eventually convert this precision into accuracy. This evaluation of the data i s i l lustrated in Table B.11., com" paring for each element, the interlaboratory standard deviation calculated from the mean values of ihe reported concentration results with the lnterla* boratory standard deviation on the concentration rat ios in different samples.
42
Table S.11. Interlaboratory standard deviation for the reported element concentrations and for the concentration rat ios of a single element.
Values in percent.
Run 12
Sample I Sample K Sample L Ratio K/I Ratio L/I Ratio L/K
Run 13
Sample I Sample K Sample L Re Mo K/L Ratio L/I Ratio L/K
Uranium
1.25 0.94 0.83 0.43 0.58 0.34
Uranium
1.03 1.12
0.73 0.086 0.31 0.39
Lutetium
1.52 1.77 1.74 0.32 0.43 0.23
Neodymium
0.089 0.16 0.15 0.096 0.095 0.002
Lead
0.20 0.37 0.23 0.56 0.41 0.15
I t can be seen that systematic error sources significantly contribute to the interlaboratory standard deviation for the measurements of uranium and lutetium. The data for lead and neodymium are based on the results of only two laboratories and the contribution of systematic components to the inter-1
laboratory difference seems to be much smaller. The in t r ins ic capability and limitation of the tracer technique resulting from the mass spectrometric measurements i s best represented by the inter*1
laboratory standard deviations on the concentration r a t ios . The spread on the concentration results however shows that unidentified systematic error sources significantly contribute to the overall uncertainty of the measure-4
ments.
B.5.4.5. Calibration £f_the_tan]<
In the calibration of the tank by the use of the tracer technique the calculation of the weight has been preferred to the calculation of the volume because the l a t t e r would introduce additionnai error sources related tc the density and temperature measurements of the samples and the liquid in the tank. Moreover the weight of the liquid introduced into the tank has been carefully recorded whereas the volume is inluenced by the temperature and density gradients observed during the experiment. Comparing the reference weight of the solution with the weights calculated from the tracer concentrations yields the results presented in Table B.12. Because of the homogeneity problems reported in section B.5.4.3, low results are obtained by a l l labora -
tories at the 500 kg level in both runs.
43
Table B.I2. Weight of Solution in the Tank calculated from the different
Tracers (values in kg).
Run 12
Reference Lutetium Laboratory
Lead Laboratory
Run 13
Reference Neodymlum Laboratory
A B C D
A B
A B
Level I
505.85
482.44 478.72 479.11 482.41
471.57 472.89
Level I
512.84
451.38 452.00
Level K
1605.96
1620.82 1607.08 1611.96 1620.37
1611 .04 1602.79
Level K
1616.80
1610.19 1614.59
Level L
2609.16
2652.47 2677.29 2642.86 2651.99
2655.76 2647.84
Level L
2621.35
2625.60 2632.70
At the 1600 kg level in run 12 the mean solution weight based on the lutetium measurements differs by 9.1 kg from the reference weight (0.57 %) with a standard deviation of ± 6.7 kg. The corresponding values for lead are 0.96 kg (0.06 %) with a standard deviation of ± 5.8 kg. At the 2600 kg level high results are obtained for both tracers differing respectively by 47 kg (± 15 kg) and 43 kg (± 5.6 kg) from the reference weight. This result is understood as a lack of homogeneity in the tank solution due to the addition of water although the tracers themselves are mutually homogenised. The results ob" tained during run 13 and based on the neodymium data are better in this respect although the homogenisation and sampling techniques used were the same as for run 12. The weight difference with respect to the reference weight is 4.4 kg (0.27 %) with a standard deviation of ± 3.1 kg at the 1600 kg level and at the 2600 kg level the corresponding value is 7.8 kg (0.30 %) with a standard deviation of ± 5 kg.
B.5.4.6. Uranium inventory_ in_the_tanj<
The design of the experiment allowed to assess the capability of the tracer technique for the verification of the uranium inventory in the tank using the measured concentration ratios in the samples in combination with the known quantity of the tracer. The results are presented in Table B.13. for the samples taken at 1600 and 2600 kg where homogeneity of the tracers and uranium had been achieved.
44
Table B.13. Uranium Inventory in the Tank calculated from the Concentration Ratios (values in g ) .
Run 12 Reference inventory 995.87 g
Lutetium Lab A Lab B Lab C Lab D
K-level 989.51 978.55 1002.63 990.05
L^level 989.37 1001.57 1006.61 987.87
Lead
K-level 981.06 987.84 L-level 993.52 993-73 Run 13 Reference inventory 1020.89 g
Neodymium Lab A Lab B
K-level 1015.71 1034.39 L-level 1018.31» 1030.97
It can be concluded that the average uranium inventory calculated from the measurements i s within 0.5 t of the reference inventory in most cases. The results however show an interlaboratory standard deviation of ± 1 % which i s mainly due to the systematic error component in the individual concentration measurements. No s ingle tracer element can be selected as being preferable on the basis of those resu l t s . Surprisingly, the resu l t s for those elements which have i s o -topic reference materials available for the calibration of mass spectrcmetric measurements (uranium and lead) are not very different from the results obtained for neodymium and lutetium, where no reference materials are readily avai lable.
B.5.5. Conclusions of the tracer experiments in Rltcex
The conclusions obtained on the use of tracer techniques during the Ritcex experiment can be summarized as follows :
a) Considerable care should be taken in the design of the tank to achieve homogeneity of the solution, also at intermediate l iquid l e v e l s , i f tracers are envisaged for the recallbration of the tank.
b) The three tracers , neodymium, lead and lutetium performed equally well in the experiment. The interlaboratory standard deviation on the concentra-» tion measurements i s mainly due to element speci f ic systematic error sources in the measurements. Proper calibration and operating procedures could reduce the spread by a factor 'of about three.
c) When satisfactory horoogenisation i s achieved the weight of the l iquid in the tank can be measured by the tracer technique with an accuracy of 0.3 to 0.5 t
d) The uranium inventory in the tank can be measured by the use of the tracer technique with an accuracy of 0.5 %.
It should be remembered that the calibration experiments and measurements have been performed on a real reprocessing input tank but in a decontaminated environment where handling of the solutions and samples presented no radia» tion hazards. Implementation in active conditions might affect the perfor*
M5
mance and accuracy of the technique, although interlaboratory measurement and evaluation programmes generally show that the effects on the measurement performance due to radioactivity in the solutions are small [12,13]• The present results however are felt to be representative of the state of the practi e in this particular field and are sufficiently promising to encourage the fu. ;her development of tracer techniques for the recalibration of reprocessing input tanks and for the verification of input inventories as part of safeguards implementation.
46
CHAPTER I I I
PHASE C : DESIGN PRINCIPLES AND OPERATIC \L PROCEDURES FOR AN IDEAL ACCOUNT* ANCÏ INPUT TANK
C . 1 . INTRODUCTION
One of the aims of the Ritcex exercise i s to describe the design and opera* t ion procedures of an "ideal input accountancy tank" with respect to safeguards. No considerations wi l l be given to safety a spec t s . Neither w i l l there be any discussion about operat ional r e s t r i c t i o n s or n e c e s s i t i e s , mechanical aspects or f inancial impacts of the design or operat ion of i t . We also believe " tha t the overa l l concept of an Ideal tank design i s ra ther simplifying the r e a l i t y s i n c e , by necess i ty , the design process i s of a high** ly complex nature .ind must consider many di f ferent f a c t o r s , most of which w i l l inevi tably be f a c i l i t y s p e c i f i c . As such i t i s impossible to produce a meaningful yet deta i led descr ip t ion of an inut tank which woula be judged to be universal ly i d e a l " . However quite a number of general design and opera* t iona l pr inciples can be iden t i f i ed , and these wi l l be discussed in t h i s chapter . The contr ibutions t o t h i s part of the report were made ava i lab le t o the Ritcex organisation by UKAEA and BNFL of the United Kingdom, the BNL of the United S t a t e s , the KFK of the Federal Republic of Germany, Euratom DCS Safe" guards at Luxemburg and the SCK/CEN of Belgium. I t s content was 'li^cussed a t the f ina l meeting about Ritcex at Mol, December 19 to 21, 1984.
C.2. THE DESIGN OF THE TANK
During th i s work we wil.1 consider a 3000 1 annular tank, s imilar t o the one ca l ib ra ted during Ritcex, and wil l transform i t s design in to the " idea l " one. This example can of course be transposed to some of the ex i s t ing input tanks and serve as a reminder for future construct ions .
C . 2 . 1 . The shape of the tank
The tank under considerat ion i s ful ly described in chapter I I .
C . 2 . 1 . 1 . Heel J>elow_Ins£rumen£ation_and_transfer h 0 ® 1 !
The heel below the lowest dip-tube was determined during ca l ib ra t ion run 11, a t the moment the tank was completely empty. I t was found to be 0.83 1 . with an uncertainty of 0.05 1 . In addi t ion, t h i s tank was designed in such a way that the l iqu id height af ter emptying of the tank was s l i g h t l y above the lowest dlp*tube and thus measurable. Since the systematic error on a measured heel determination i s in the same direct ion for a f u l l and an empty tank, as the input measurement AS made by difference, the influence of t h i s uncertainty i s neg l ig ib l e .
RULE : 1 Minimize the heel below the lowest dip-* tu be RULE : 2 Emptied t rans fe r tank volumes should always be measurable
C.2 .1 .2 . The non**nnearj>art °f_t]2e_ta.nJS
As can be seen from the construct ion drawings and as a r e su l t of the differ* ent ca l ib ra t ion runs , the non-*linear part of t h i s tank reaches up to a height of about 700 mm above the lower dip- tube. Prac t ica l ly t h i s region of the tank i s not important for accountancy measurements ~* not even during physical inventory taking •* but i t s influence on measurements on a ful l tank i s ra ther important .
47
Indeed, the volume occupied by th-» input solut ion, in the linear part (or parts) of the tank i s expressed by the following equation :
(1) A • B x h where : A,B are constants and h i s the height in mm of the solution level above the end of the leve l dip^tube
Moreover
Finally usol
0301
AP _D h'
where : AP i s the differential pressure
between leve l and reference dip--tube and psol i s t n e so lut ion's density
where : APJJ i s the differential pressure between leve l and density dip-*tubes and h' i s the physical height between the t ips of those dip-tubes
(2) or A • B x AP, xh'
APr
As the volume changes as a function of the density of the solution (or its temperature) it is preferable to determine the input on a mass basis. In addition, the laboratory primarily determines the concentrations of the nuclear materials in g of nuclear materials.
Tne order of magnitude of the different factors of equation (2) are for a full input tank (paol - 1-5) :
V • 3000 1
A » -300
B « 1
The two factors determined with the largest uncertainty are APn and h', resulting in a poor density determination in the tank.
If however the weight of solution is determined, equation (2) is transformed in, equation (3)
APL
APD
h'
m
m
m
5000
360
2U0
(3) W - V x APr AP
A x — E • B x iPr
It will be seen that the measured density of the solution i s only influencing the intercept A which has a smaller influence than B x APL in equation ( 3 ) . Of course APL - h x P 9 0 i» . but in t h i s cas p s o l i s the real density of the solution distributed a l l over the height of the tank. Of course, a smaller intercept, wil l result in a smaller error on the sol* ution's weight determination. To decrease th is intercept, the non^linear part should tend to a zero volume.
RULE : 3 : Minimize the non-linear part of the tank.
C.2.1.3. The Unear_part £f_the_tank
I t i s obvious that this region, and especially the upper part of i t * together with the heel region, i s the most important part for accountancy mass determinations. For this reason i t would be s t r i c t l y advisable to construct this portion of the tank as a straight l inear par t . During Ritcex, i t was observed that the internal decontamination l ine could cause many problems for input measurements. In addition the slope should be minimized in order to increase the response of small variations in liquid heights.
RULE : 4 : Minimize the surface in the l inear part (or a l l over the tank) and the slope.
RULE : 5 : Avoid any disturbance to the l inear i ty in the area of input measurements.
C.2.1.1*. General considerations
Deformations of the tank resulting from the introduction of liquids should be minimized and for a given volume, any deformations should be independent from the density of the l iquid, and as much as possible also from the temperature of the l iquid. I t would also be desirable to have the tank heated and cooled in a manner that could be described by a linear expansion equation. Tanks should not have bottom transfer l ines nor bottom located valves. (C.5)
RULE : 6 : Tank should have sufficient strength to avoid deformations at higher liquid densit ies.
RULE : 7 : Heating/cooling deformations must be controllable. RULE : 8 : No bottom transfer l ines must be used.
C.2,2. The Instrumentation features in or on the tank
C.2.2.1. Weighing_possibilities
Due consideration should be given to alternatives to concentration-nrolume me* thods, such as weighing the tank and i t s contents. In the United Kingdom, British Nuclear Fuels pic (BNFL) are currently design*» ing and constructing a reprocessing plant for thermal oxide fuels (THORP), which should be commissioned by the early 1990's. An important feature of the accountancy system in THORP is the proposal to ins ta l l both weighing and traditional pneumercator systems for the Head End (Input) post-'clarif ication accountancy tanks and for the post-evaporation plutonium concentrate storage tanks. Pneumercdtors have been included as a f a l lback system and for opera-* tional level control and indication.
The input accountancy tanks are vertical cylindrical Jacketed stainless s tee l vessels with dished ends. Each tank is f i t t ed with pulse j e t tubes for mixing the maximum liquor weight of 3^.5 tonnes. One essential design difference between weighed and volumetric accountancy i s the need for the weighed tanks to be freely suspended. The proposed method of instal lat ion ot the input tanks is shown" schematically in Figure C.1. Each tank is suspended by four hanger rods which pass through the weighing room floor and connect with a support structure which bear3 down on the platform weighing system located on the cell roof. This design has been selected to fac i l i t a te maintenance of the weighing system as well as providing a means of calibrating and verifying the
U9
system by using independently verifiable check weights. A total of 53 tonnes of weights (possibly TOO x 530 kgs) will be required for a full-scale call-1
bration and these will be 3tored in a room adjacent to the weigh platform. Weights will be moved by an electric hoist travelling on an overhead track. During the design and development of the weighing system major engineering problems will have to be faced and overcome. In this context, the UKAEA are currently undertaking generic development work on weigh accountancy tech^ niques with particular emphasis on Fast Reactor Fuel reprocessing aecountan** cy, and BNFL will be pioneering the work on weighing large accountancy vessels. Engineering solutions will have to be found which :
a) reduce the influence and restraint on the weighing system from process pipework, (see Figure C.2)
b) account for any movements of the tank caused by the energy input from pumping and mixing systems,
c) define the minimum clearances necessary between vessel supports, cell roof liners and seismic restraint features to ensure that the weighing operation is not affected by frictional losses,
d) account for changes in the centre of gravity during filling opera-1
tions, e) examine the effect of thermally-induced expansion in tank pipework,
and f) ensure that the weigh platform design and performance i3 optimised.
The performance of the weighing system is difficult to predict. Theoretically, a gyroscopic force balance system should be able to achieve a precision of better than ± 0.005 % (one standard deviation, random error), but given the engineering complexity of the accountancy tanks it is unrealistic to suppose that precisions of this order will be achieved. At present the target value for precision is ±0.1 % and this figure forms the basis for modelling the nuclear material accountancy of the THORP weighing system. Of course, errors which occur in the chemical analysis of liquor samples and in relating the sample composition to the bulk liquor volume (heterogeneity of the batch) will add to this figure, as will any systematic errors, but overall the system is expected to perform significantly better than a pneumemator based accountancy method. The United Kingdom Atomic Energy Authority (UKAEA) are currently conducting a series of experimental trials which should help to resolve some of the engineering problems listed above. The work is being done at the Springfields Nuclear Laboratory (SNL) and is scheduled over three phases. The first two phases have examined various industrial weighing machines and a weigh machine has been selected on the basis of :
(i) a vertical platform displacement of the order of 0.5 mm, (ii) readout stability and (iii) resolution and ease of calibration.
Subsequently the project has concentrated on the minimisation of pipework re" straint due to weigh platform displacement and temperature differences between the pipework and the surroundings. A computer analysis of framework, pipework and shells using the finite element stiffness matrix method is being conducted in parallel with experimental work to optimise pipework geometry. Initial studies have led to the specification of suitable "hairpin" pipework geometry.
50
Pipework arrangements which could also eliminate tank swing are also being examined. Fig. C.3. shows the weighing t e s t fac i l i ty which will be constructed at SNL during phase three of the project. A fluidic RFD pump and a f luidic diverter will be attached to the prototype accountancy tark for liquor mixing and transfer operations. In addition to the reduction c' aerosols transferred to the plant vessel ventilation system during mixing, RFD pump3 have been shown to be much more effectived than 'air*sparge* systems for the mixing of accountancy tank liquors - not only have higher degrees of homogeneity been attained, but operational mixing times have also been reduced. In conclusion, therefore, the UK have a major commitment to develop weighing systems which should improve the precision and accuracy of nuclear materials accountancy in both input and output accountancy tanks. Development work in conjunction with detailed engineering design studies are actively in progress in BNFL and the UKAEA prior to the ins ta l la t ion of weighing systems on accountancy tanks in the THORP complex and probably future fast reactor reprocessing plants. It should be noted that the development programmes are in addition to our intention to ins ta l l and further improve the t radi t ional pneumercator based system of accountancy.
C.2.2.2. Di£-tub_e_probe£ and rel_ate£ instruments^
Some general aspects related to the dip-tube system are taken from the con-tributions of the part icipants.
RULE : 9 : dip-tubes (as a l l other piping i'n the tank) should be solidly mounted
RULE : 10 : dip-tube diameters and connecting tubing diameters should be sufficiently large so that flow generated pressure drops are not significant, i . e . 8 - 10 mm or larger
RULE : 11 : temperature sensors should be located at different points on and in the tank.
The conventional concept of the present dip-tube system consists of a reference dip-tube on top of the tank (not plunging in the l iqu id) , possibly a high level warning/alarm dip-tube, a density dip-tube and finally a level dipr*tube. The future concept that Ritcex propagates consists of a bundle or even bundles of dip-tubes. The distances between each dip-tube is measured physically after construction outside of the tank. The tubes are internally fixed one to the other and then introduced into the tank. This system permits several auto-controlling level and density (and as such homogeneity) measurements, at different levels in the tank. If use is made of more bundles, not only a vertical but also a horizontal control can be performed. The use of an eleotromanometer system, equipped with a 12 port pneumatic scanner, will permit to measure a l l the pressures of a l l tubes and the software of the on-line computer can give a l l information, including alarm s ta te ments and intercomparisons of a l l measurements. In addition th is instrument i s able to control and regulate the air-flow to each of the dip-tubes, sufficiently well so that the air-flow is not affected by changing tank liquid levels . Further work should be performed on scannivalves before their use can be recommended for operational use.
C. 2.2.3. Redundant i ns truments
In the past the differential level pressure between the reference dip-tube and the level- dip-tube as well as the differential density pressure between the density and the level dip-tube was measured by means of U**tube manometers .
5T
As described earl ier [1] , the density U*tube manometer was f i l led with water and the one for level measurements with tetrabromoethane (CjHjBr,, or TBE). This TBE was used to keep the U*»tube length within reasonable l im i t s . I t was obvious that the resul ts obtained during Ritcex highly recommend the electrom anom eter as primary pressure measurement instrument. In addition to i t s sens i t iv i ty , i t offers a number of secondary data permitting cross-checks on the different pressure measurements. Some additional hardware and software would permit a s t r i c t control of the air*flow to the dip^tubes. If the system with bundle(s) as described above i s used, i t i s possible to replace the TBE by H20, gaining already a factor of 3 in the uncertainty of reading the pressures. In addition not al l dip-tubes need to be equipped with U*tube manometers.
Up to now th is seems the simplest, cheapest and most re l iable control instru-ment for the electromanometer. Other instruments, tested out during Ritcex, such as the acoustic system, and the time domain reflectometer (TDR) look promising but need further invest i gation before competing with the systems mentioned above. Surely other systems are available on the market but we limit ourselves only to instruments tested during the exercise.
C.2.3. The Internal and other piping of the tank
I t i s evident that in the case of weighing the input tank the influence of the piping connected to the tank can be of great influence to the weighing capabil i ty. This i s being studied by the plant operators who are intending to use weighing as a routine accountancy method, and i s discussed in section C.2.2.1.
Of more importance in the case of volume (mass)/ concentration input determinations is the influence of the internal piping. The internal piping can be subdivided in different categories :
A : pipes always empty (instrument lines) B : pipes part ial ly f i l led ( i . e . spare exit pipe with blind flange) C : pipes to ta l ly fil led (exit pipe).
Sketch C.4. shows the different types.
Type B pipe can also represent pipes whose valves are closed without venti lating the tube ( i . e . sparging l i ne , internal decontamination l i n e ) . As a principle, for safeguards reasons, i t must be possible to empty a l l piping from solution before and during mixing. With that respect, pipes of type A will not cause problems. More diff icul t , but with a solution, are pipes of type B. Most of the time i t is possible to empty these pipes by blowing a i r through i t and after mixing ventilate i t to the tanksystem. No solution however i s seen for the problems caused by type C pipes. An example, calculated on the tank of the Ritcex, i l lus t ra ted the importance of th is piping. The resul ts are described in C3«
During Ritcex a systematic error on the input measurements of about -0.1 % was observed.
52
RULE : 12 : Inse r t in the tank only pipes , provided with an evacuation system during mixing of the so lu t ion , wherever t h i s i s posa
s i b l e . S t r i c t l y minimize a l l other p ip ing.
Furthermore, in agreement t o RULE 5 a l l piping should be d i s t r i bu ted a l l over the length of the linecj* p a r t ( s ) of the tank . I f a horizontal l i n ing up i s unavoidable, such as for mixing and decontaminaton l i n e s , t h i s should be located in the non^operational zones of the tank.
C.2 .4 . Piping and provis ions for c a l i b r a t i o n and r eca l i b r a t i on
A special l i n e , which could a l so be the reagent feed l i n e , should be foreseen to be used as the ca l i b r a t i on or r e c a l i b r a t i o n l i n e .
RULE : 13 : The ca l i b r a t i on l i n e should be sho r t , d i rec t and slope d i r e c t l y in to the tank. Any hold-up must be avoided.
This l i n e however must not reach t o the bottom of the tank in order to obser* ve RULE 12. For very spec ia l occasions such as heel deter jii nat ions or t r a c e r techniques, where the increments are so small or where any s p i l l on the i n s ide walls of the tank would cause an important e r r o r , use could be made of one of the instrument l i n e s , going deeper ins ide of the tank. The diameter of the spec ia l c a l l brat ion/reagent feed l i n e depends on the t o t a l content of the tank.
As t h i s pipe should not have hold-*up, or at l e a s t a controlaDle hold-up, i t would be needed to place the end of the pipe on the inac t ive s ide in to a kind of glove-'box (shielded or not) and provided with connections to the water or n i t r i c acid feed l i n e and t o the feed drum for adding incremental weights. This box should ta equipped with the p o s s i b i l i t y to enter bo t t l e s with t r ace r l i q u i d s . The other end of t h i s l i n e , ins ide of the tank, should not be in the neigh* bourhood of the off gaz system or the possible overflow l i n e in the tank.
C .2 .5 . Additional concepts
These ideas are not pa r t i cu l a r to safeguards and the re fo re , although very important, they wil l be touched only b r i e f l y . I t i s obvious that a good mixing device i s i n s t a l l e d on the tank. Whether the system i s equipped with an a i r sparging system, a r e c i r c u l a t i o n pump or a s t i r i n g device i s not pr imordia l , as long as the r e s u l t s are acceptable . Promising r e s u l t s are being obtained with RFD pumps in the UK.
Concerning tne sampling system, the prac t ice in the past was to sample only in one point in the tank . I t goes without 3aying tha t sampling at d i f ferent spots would be preferab le . A study should be made how much the sample i s evaporated using a Thorex system (vacuum + a i r l i f t ) . The off gas system a lso can play an important ro le during ca l ib ra t ion or input meaurements. The eva5* porat ion of solut ion during these operations should be avoided. The ef fec ts of mixing in adjacent tanks should not influence any measurement in the accountancy tank.
All valves in s t a l l ed to operate steam j e t s need t o be t i g h t l y closed during measurements and c a l i b r a t i o n s , t o avoid any leakage t o the tank during these opera t ions .
53
All lines of type B should be ventilated'during these operations in order to permit the entrance of solution to the same level as in the tank. The a i r used to operate the instrumentation lines should be free of oil to avoid disturbances of the flowmeters. On the other hand i t i s advisable to humidify that a i r to avoid plugging at the end of the dip-'tubes due to crysta l isat ion. All transfer l ines should be keyoperated in order to avoid a simultaneous transfer to and from the tank. Ideally, a l l operations should be under a comprehensivs computer controlled logic control system. The overflow-line should be routed back to the feed tank of the input tank. All points described above are i l lus t ra ted in figure C.5. The instrumentation lay out is represented in figure C.6 and the inactive part of the recalibration l ine is shown in figure C.7.
C.3. PROCEDURES TO CALIBRATE THE INPUT TANK
As an example of the calibration of an input tank, the features described in C.2. are used, but each input tank would probably be different . Nevertheless, a l l steps will be described in detail in such a way that adaptations to the real input tank can be made.
C.3 .1 . Preparative control
" Earlier we have defined three types of tube entering into the tank. In relation to the operation and calibration of the tank, a fourth type must be considered. These are the tubes not entering the tank but either feeding i t with scrutions or ventilating the tank. The operator should be assured that , during the whole period of calibra** tion, no uncontrolled addition of liquid can happen. All valves on steam-lines should be t ightly closed. The ventilation of the tank should be under normal working conditions. Operations in adjacent tanks should be avoided during the whole calibration period.
*• The instrumentation system should be in optimal working condition. Possible calibrations of the manometers should be performed in advance. Liquids in U-ltube manometers should be renewed and their density determined with high precision. All instruments needed to make accurate calibrations should be on the spot before s tar t ing the operations. A summary of these instruments and their use is given in table C.I.
TABLE C.1. Instruments needed for calibration
instrument
«* scale -» standard weights - scale cal ibr . forms
- thermometer 1
" hygrometer * barometer - thermometer 2
•» tank cal ibr . forms
used for
weighing accurately the increments calibration of the scale predesigned forms on which a l l results of the scale calibrations are recorded. placed close to the scale; needed for calculating the air-buoyancy idem idem placed close to the liquid f i l led U-tubes predesigned forms to record al l data
collected during tank calibrations
54
- The scale calibration should be performed just before starting the tank calibration. It should be transported to the spot where it will be used, so that no additional transportation of this instrument is needed • before, during and after scale calibration, the temperature, humidity and pressure readings are recorded on the scale calibration form. As in the case of this tank calibration, a scale with an overall range of 200 kg with digital graduations of one gram is suited for the work. Tho standard weights, with certified deviations and uncertainty with respect to the nominal weight, needed for this operation would be 1 weight of 10 kg, 2 weights of 20 kg and 3 or 1 weights of 50 kg. An upward and a downward calibration of the scale is performed. In the case of a perfect response (see the Toledo results during Ritcex) one up- and downwards run can be sufficient. If the results are not satisfying, a number of runs are performed so that tht. scale response can be trusted to the requested degree. During upwards calibration, care must be taken to approach the next higher weight from below, and during downwards calibration the approach should be from a weight above. The example below will visualize this in a better way.
Operation
0 add 10 remove 10 add 20' add 10 remove 10 add 20* add 10 remove all add 50' etc.
Scale indication
0 10 (0) 20 30 (20) 40 50
50
Weights used : 10,
* 10 ^ 20' 20' + 10 20' 20' • 20* 20' • 20* * 10 -50'
20', 20*,
record record
record record
record record
record
50' kg
The operation is done Ir. this way in order to detect any hysteresis effect of the scale. The example of a downwards calibration i s given below :
Operation
50' add 10,20',20* remove 50' remove 10 add 10 remove 20* remove 10 add 10 remove 20' remove 10
Scale indication
50 (100) 50 40 (50) 30 20
• (30) 10 0
Weights used
50' 50',10,20',20* 10,20',20* 20',20* 10;2O',20* 10,20' 20' 20',10 10
••*
record
record record
record record
record record
55
If the scale i s used for the f i r s t time, additional t e s t s should be performed. As the calibration consists of weighing in fact 15 gross increments of 200 1 - some of them can of course consist of 10 x 20 1 -1 i t is worthwhile to study the behaviour of the scale during such a number of weighings. So 15 cycles of on the one hand 200 kg standard weights and on the other hand of no standard weights are performed and recorded without making any zero or other adjustement of the scale. Finally i t s sensi t ivi ty can be checked at different intervals of weighing by adding small standard weights in the order of magnitude of 1 to 5 gradu1' ations. This scale calibration operation should also be repeated as described above after the tank has been calibrated.
*> Leakage tes ts on the pneumatic system. The pneumatic instrument l ines are equipped with a valve just outside the active area of the plant. The tightness of the metal tubing to the tank should be carefully checked during commissioning of the plant and ;he parts where connections are made for instrumentation should be cont.-oiled for tightness before each calibration (and measurement). Unfortunately for th i s control, the electromanometer must be disconnected because the operatior or the scannivalve is consuming some air pressure. In any case the lining-up can be checked unt i l th is point as well as to the total U-tube instal lat ion by putting an a r t i f i c i a l pressure to the system and controlling i t for a possible decrease as a function of time. A simple and effective system to detect possible leaks is to use a soap solution and look for bubbling formations on tubes, connections and system val ves.
-* Pressure drop determination should be performed several times with the tank empty. At th is moment i t i s also recommended to investigate the influence of changing air-flows to the different instrument lines on the pressure measurements. I t is worthwhile to spend enough preparational work on these tests at th is moment as they, most probably, will be unique in the history of the tank's l i f e . These tes ts will probably demonstrate that the air-flow to the different instrument lines must be controlled in a s t r i c t manner. In the case that air flow rotameters are used, i t will demonstrate that these control instruments must be very clean, and kept clean, during the whole measurement period.
C.3.2. Heel determination
Although during Ritcex, an accurate heel recalibration could be performed on a tank which had been in active use, th is should not be seen as a normal possibility for future recal ibrat ions.
Usually i t should be considered that a heel calibration can only be performed during one period, and this is when the tank i s s t i l l inactive and a vis ible check of the emptyness of the tank can be performed. This stresses the import tance of this operation. All lines of the tank however should already be installed and preferably the off^gaz system functioning. The possibi l i ty should s t i l l exist however to open the handhole.
56
The sequence of operations would be :
(a) Check v'.a the handhole that the tank i3 completely empty. If not, clean the tank and empty completely i.e. by heating and evaporation.
(b) Prepare a feed line of small diameter, to be introduced into the tank at a level just above the level dip*tube. Before introduction, the inside of this feed tube is wettened to such extend that a 100 gram increment to the tube is also collected at the other side of the tube, within the weighing error. The draining time is also recorded.
(c) Introduce the tube in the tank.
(d) Accurately weigh an amount of water, enough to reach the level of the dip-tube, and take its tomperaturt. It should be arranged that the temperature of the feed solution is the same as the tank temperature.
(e) Feed a little quantity of water, of about 1/10 of the expected heel volume into the tube.
(f) Wait a sufficiently long time to permit complete draining of the water into the tank, (respect the recorded draining time)
(g) Observe the level measurements on the electromanometer (and its standard deviations).
(h) If no change to the previous level measurements occurs, repeat steps (e), (f), (g) until a change occurs, otherwise continue with (i).
(i) Make several level measurements and weigh accurately the remainder of the feed liquid; record its temperature.
(j) Add another 9 small increments to the tank, still observing the draining time and taking the level measurements and the remaining weight of the feed liquid at each time.
(k) Repeat the operations (a) to (j ) until at least three satisfactorily agreeing results are obtained.
The case of heel recalibration will be treated in C3.6.
57
C.3-3* Shape determination
It has been remarked in the past that a theoretical linear part in a tank is in reality composed of several linear or almost linear parts. Therefore it is of great importance to know at which heights the transition regions are loca-* ted. The answer to this problem was given by run 16 of Ritcex :
* a contineous, well controlled flow is added to the tank while the electro-manometer is in "draining mode". This draining mode permits an averaging of n measurements over a short period of time During Ritcex this were 100 measurements in 20 seconds. The constant flow and n and t are chosen in such a way that some 200 to 300 measurements are made over the total height of the tank. Plotting the resultant level measurement points versus a constant incremental increase of volume will result in a detailed picture of the internal form of the tank. The constant flow needs even not exactly to be known, although this is of course preferable. The only imperative is that the flow is really kept constant. How the set-»up would look like is illustrated in figure C.8.
A typical response is shown in figure C.9 which was obtained during Ritcex. Not considering the height below 1000 mm, this picture would inform us about the transition regions. In addition, some strange points, to be observed with a detailed investigation are indicated. According to this result the tank could be subdivided in seven regions each of them being calibrated by some 10 points withing the regions and detailed calibration has to be performed at the transition points. This method informs the operator of any non-linear behaviour over the height of the tank which would not be noticed if only batches of 200 1 were used. This method could also be used as a recalibration check as will be suggested in C.3.6.
C.3.1*. Full calibration
After the heel was determined carefully and the investigation on the shape of the tank has been performed, a detailed full calibration of the tank can s t a r t . The tank is emptied as far as possible and possibly heated in order to eva-» porate the remaining l iquid. I t is possble that the level dip-tube is s t i l l touching the liquid and bubbling can be observed. This is then the s tar t ing point for the calibr-a-» t ion. The volume remaining in the tank must be calculated using the equation resulting from the heel calibrations and the pressure as measured at th is moment. If no bubbling can be observed, the liquid level is below the level dip-tube. Small carefully weighed increments are added to the tank, respecting the draining time, until bubbling i s observed and the f i r s t measurement performed. The volume in the tank before s tar t ing the addition of increments i s calculated, again by means of the equations resulting from heel cal ibrat ions, using the pressure as measured at th is moment. The calibration performed for the determination of the shape of the tank has given the operator a l l information about the transit ion regions. Each region should be covered by at least ten measurement points and smaller increments should be used around the transi t ion points in order to localize them carefully. Of course points of interest for the operation of the tank should also be investigated (minimal volume for sampling, overflow volume with and without sparging, alarms e tc . )
5ÏÏ
Some general remarks are worthwhile to note here :
- F i l l in careful ly the p redes igned ca l ib ra t ion records mentioning in fu l l d e t a i l s a l l observations such as :
* gross and t a r e weights of the increment =* a i r conditions c lose to the feed drum - temperatures of the feed water which should be as close as poss ib le to
the temperature of the tank to be ca l ibra ted - l e f t and r igh t readings of the l egs of a l l U^tube manometers - a l l recordings of the electromanometers ( i n c l . time) •* a l l indicat ions of the air-f low con t ro l l e r s to the dip-tubes - temperatures close to the U-tube manometers (checked on top and bottom
of the U*tubes) - any event which could or could not influence the c a l i b r a t i o n r e s u l t
(sparging, sparging in adjacent tanks , v e n t i l a t i o n reduced, disconnect i on of instruments, a i r - f low adjustments, e t c . )
- Respect absolutely the draining t ime. This can eas i ly be checked on the electromanometer in "draining mode"
J Avoid any sp i l of so lu t ion , or r e s t a r t -1 Avoid any evaporation of so lu t ion in the tank ( i . e . by leaving the
handhole opened, excess of sparging) - Before and a f t e r pauses, l imi ted t o a minimum, a measurement should be
made without increment addi t ion a Be sure a l l data a re col lec ted before entering the next increment
The f u l l ca l ib ra t ion should be repeated at l e a s t th ree times following exact ly the same procedures. After each c a l i b r a t i o n , the tank should remain f i l l e d un t i l an estimation can be made about the normal evaporation r a t e in the tank. This factor could be taken in to account for correc t ion of the incre-* ments as a function of t ime. Additional t e s t s should be performed when the tank i s f i l l e d , in order to t e s t the t ightness of the closed va lves . The valves are opened one by one and the corresponding changes in the leve l p re s sures a re noted for evaluation of the volume changes. After emptying the tank by the normal operat ional procedure, a se r ies of measurements should be performed to determine if the t rans fe r heel (with H20), i s measurable or not , and to ca lcu la te the remaining volume. If no agreement i s reached a f t e r t h ree runs but the t r a n s i t i o n points are well determined, increments of l a rge r volumes can be added in order to reduce the ca l ib ra t ion time. Advantage should be taken from the f i l l e d tank to inves t iga te the behaviour of the tank and i t s instrument l i n e s at d i f ferent temperatures. Heating and cooling of the solut ions wil l answer the quest ions. Concerning ca l ib ra t ions with higher density so lu t ions , we would l i ke to refer to C.3.6. ( r eca l lb ra t ions ) although ca l ib ra t ions could be performed, exactly in the same way as described before .
C.3.5. Calibration of special volumes
By specia l volumes are meant minimum sampling volume, operat ional volumes, alarm volumes, e t c . As the intermediate volumes a re ot no i n t e r e s t to the opera tor , e i the r large weighed increments could be added with or without level measurements un t i l the point to inves t iga te has been reached. Another and more appropriate method would be to use the shape ca l ib ra t ion method supplemented at the poin t (s ) of i n t e r e s t by applying the t r ace r method.
59
The tracer method i s a t t ract ive because i t allows an independent verification of the mass of f i s s i l e material in the tank which can then be compared to ••he quantity derived from the volume and concentration measurements. The use of the tracer technique i s also possible during a recalibration of the tank if a number of conditions are fu l f i l l ed . In a batch-dissolver system the best place to introduce the tracer of course is in the dissolver and not in the tank i t se l f . Recal oration of à tank by the tracer technique iepends on the following conditions :
- the reagent feed lines should be designed to ensure and verify complete introduction of the tracer solution into the tank.
" the volume contained in open tubes dipping into the solution is not necessari ly mixed with the bulk of the tank and depends on the operational sequence .
- adequate mixing of the liquid in the tank must be ensured to homogenise the tracer 0>lution, but th is i s a normal requirement of the tank.
- the normal sampling system of the tank should also accomodate the samples taken for recalibration by the tracer technique.
C.3.6. Recalibratlons
The easiest and fastest method of recalibration is the one described in the paragraph on shape determination. If for a l l recal l brat ions as well as for the shape determination, identical procedures are applied, th is method can detect sufficient physical points inside the tank to indicate that something has changed inside the tank or in the instrumentation.
I t i s sufficient to carefully locate the t ransi t ion points, the moments of touching different dip-tubes, the lenght and 3lopes of the transit ion r e gions, to be able to verify if former calibrations are s t i l l valid. The end point of such a calibration should always be close to the overflow height or even exceed i t . The temperature influence can be re-investigated. A possible corrosion of dip^tubeCs) can be detected immediately.
The advantage of this recalibration method is that i t can be performed in a very short period of time and i t gives an overall picture of the tank. Collecting the data and their evaluation could easily be performed within one working day.
If th is system however i s not sat isfactory, a repeated full recalibration of the tank, similar to the described full calibration has to be performed, possibly supplemented by the use of tracer techniques.
One of the very f i r s t and most interesting recalibratlons however will be performed during the cold or start-up tes t s of the plant. A well determined amount of unirradiated or very sl ightly irradiated fuel will be dissolved and the input determined. As this fuel i s VERY well known by the fuel fabricators data and either no burn-up or a very low burn-up occurred, i t is the best possible check on the behaviour of the input tank and i t s instrumentations under operational temperature and density conditions. Special care must be taken during these input measurements to clarify any problems.
CM. OPERATING PROCEDURES OF THE TANK
All efforts performed during calibration or recalibration of the tank can be annihilated by improper operational procedures. Some of these points will be touched in the following paragraphs.
60
C.4.1 . Feeding the tank
A tank, equipped with many type B and type C pipes (see C.2.3.) . and not equipped with a system to empty these pipes before mixinj the solution can cause serious systematic errors during input measurements [5 ] . Part of the influence of these pipings can be reduced by following certain operational procedures. Before transferring the solution to the input tank, a sufficient homogeniza-* tion should be performed in the feed tank. Any transfer of r inse solution on the top of the bulk transfer should be avoided. If even th i s i s inevitable, mixing the input solution should be performed before s ta r t ing and during a l l feeding transfers . After completion of the transfer, a se t t l ing time would be recommended in order to latect the se t t l ing of undissolved par t i c les . Indeed, a slowly but continuous increase of the level pressure would be an indication of part ial ly plugging of the dip-tube by undissolved particles (most input solutions however are clarified before being transferred to the input tank).
C.4.2. Mixing and sampling
Mixing time should be determined before the start-up period. The presence of a direct calibration l ine could help the test ing operations. In addition, the following procedure could provide a supplementary tes t on the cal ibrat ions. After f i l l ing up the tank with a well known volume up to the operational volume, an exactly known amount of uranium in the form of a weighed solution of uranylnitrate is entered via the calibration l ine ; weighed amounts of rinse solutions are added. Mixing for intervals of time followed by samplings are performed. From the measurements the time needed to make the solution homogeneous can be determined and in addition the influence of internal piping can be investigated. After mixing of the solutions in the tank, the existence of a bundle or bundles of dip-tubes in the tank would permit a check on the homogeneity of the solution in the tank. Due to the existence of internal temperature probes a comparison could be made with the density as determined in the laboratory.
CM.3. Emptying of the tank
The emptying of the tank should allow a small but s t i l l measurable amount of solution remaining in the tank after transfer of the bulk to the process area. Operated in such a way tne volume and the concentration of the remaining heel are known and can be deduced from the next full tank content to determine the next input quantity. This heel volume however should be determined immediately after the transfer happened because possible evaporation could produce a significant change on such a small volume and even make i t unmeasurable after some time.
C.5. RECOMMENDATIONS FOR DESIGN OF ACCOUNTABILITY TANKS BUL (Brookhaven National Laboratory)
The following recommendations for design of accountability tanks are based on the experience obtained during the RITCEX exercise and experience gained at the Idaho Chemical Processing plant. The recommendations are intended to help the designer provide a tank whose contents can be measured accurately and incorporate design features that should eliminate common problems.
61
1. ASSUME THAT THE LEVELS AND DENSITIES IN THE ACCOUNTABILITY TANK WILL BE MEASURED WITH BUBBLER PROBES.
Bubbler Probe measurements of level and density are current practice. The probes are metal tubes. The associated instrumentation can be located at some distance from the tank in low radiation areas. Current accuracy for bubble measurements is superior to other techniques. Attempts to use direct weighing have so far not been successful for tanks of a size used in reprocessing plant. The principal problem with bubbler probes is plugging. While troublesome, it can be overcome by periodic cleaning or partially by using humidifiers on the bubbler probe air supplies.
2. ACCOUNTABILITY TANKS SHOULD BE DESIGNED WITH SUFFICIENT STRENGTH SO THAT THE HYDROSTATIC LOAD OF THE MOST DENSE CONCEIVABLE LIQUID WILL NOT PRODUCE A SIGNIFICANT INCREASE IN TANK DIMENSIONS.
It would be difficult to provide a reliable calibration if the volume for a given liquid height was a significant function of the liquid density. It would be doubtful that elastic deformation of the tank would be sufficiently reproducible and stable with time to permit a calibration as a function of density.
3. THE ACCOUNTABILITY TANKS SHOULD BE MOUNTED SUCH THAT TEMPERATURE CF'.NGES WILL NOT RESULT IN DEFORMATION (ELASTIC OR INELASTIC) 0? THE TANK.
Tank mounting should allow the tank to expand and contract without introducing sufficient force to deform the tank. Tanks that "oilcan" under thermal stress would be awkward to calibrate.
4. THE ACCOUNTABILITY TANK SHOULD BE MOUNTED IN ITS SHIELDING CELL SO THAT THE TANK IS IN A UNIFORM FLOW OF VENTILLATION AIR.
It would be desirable to have a tank volume which heats and cools in a manner that could be described by a linear expansion equation.
5. IF POSSIBLE, THE TANK SHOULD NOT HAVE A COO'ING JACKET.
This is desireable for the same reason given for # 4. However, because of the need for a rapid dissolution and large tank sizes, this may not be possible.
6. ASSUME THAT LARGE ACCOUNTABILITY TANKS WILL BE CONSTRUCTED WITH SPARGE RINGS OR LINES (FOR MIXING) AND TRANSFER JETS (FOR REMOVING LIQUID), ADDITION LINES, DECONTAMINATION LINES OR HEADERS, AND AN OFFGAS (VENTILA** TION PORT)
These fittings are current practice. Small accountability tanks, as in Plutonium product areas, ma' not require all these lines.
7. ACCOUNTABILITY TANKS SHG'JLD NOT HAVE BOTTOM LOCATED VALVES.
A leak^proof valve designed for chemical service has not yet been built.
8. ADDITION LINES INTENDED FOR CALIBRATION USE SHOULD BE SHORT, DIRECT, AND SLOPE DIRECTLY INTO THE TANK.
The essential assumption in a calibration is that all the liquid added rapidly enters the tank. Long addition routes or routes with multiple bends and sections that hold up liquid are undesirable.
62
9 . ACCOUNTABILITY TANKS SHOULD HAVE TEMPERATURE SENSORS FOR TANK AND TANK LIQUID TEMPERATURE MEASUREMENT.
I t i s des i rab le t o know both the tank and the l i q u i d temperature for very accurate measurements.
10. INTERNAL STRUCTURE IN THE ACCOUNTABILITY TANK SHOULD BE SIMPLE, WITH MINIMUM VOLUME AND SHOULD NOT HAVE BRACES OR OTHER DISCONTINUOUS FEATURES AT LEVELS NORMALLY USED FOR MEASUREMENT.
It i s desirable to have a linear volume-height curve over the l eve l s of the tank used for measurements. If structures were present, i t would be necessary to do a more complex cal ibration.
11. BUBBLER PROBES AND SPARGE LINES SHOULD BE SOLIDLY MOUNTED.
Sparge l i n e s v ibra te i n u s e . This could cause premature f a i l u r e . The spacing between the l e v e l and dens i ty bubble probes i s an assumed constant (except for temperature changes) used for dens i ty c a l c u l a t i o n s . Loosely secured bubbler probes could introduce error i n the d e n s i t y measurement.
12. TANK SAMPLERS AND SAMPLING PROCEDURES MUST PROVIDE A REPRESENTATIVE SAMPLE OF THE TANK LIQUID.
A valid sample i s essential for accurate accountability measurements. Samplers that introduce bias into concentration measurements by évapora" tion in an a i r - l i f t or by slow cleanout of dried sol ids or l iquid from a previous sample are undesirable.
13. ACCOUNTABILITY OFFGAS (VENTILATION) SYSTEMS SHOULD BE STABLE DURING MEASUREMENTS.
Tank offgas system that allow the tank head pressure t o vary during measurements introduce pneuratic no i se i n t o l e v e l and dens i ty measur ments. The offgas systems should have s u f f i c i e n t capaci ty and s t a b i ' .cy to prevent significant changes in the tank headspace pressure. It i s also desirable that sparging in adjacent tanks should not generate s ignif icant differences in tank headspace pressures between the accountability tank and other connected tanks.
11. INTERNAL LINES SUCH AS SPARC". LINES, SAMPLER LINES, AND DECONTAMINATION JETS SHOULD BE ARRANGED SO THAT LEVELS IN THESE LINES MATCH THE TANK LEVELS WHEN THE LINES ARE NOT IN USE.
Trapped air in such l ines or closed valves can cause the liquid leve ls in these l ines to be different from the tank l e v e l . While normally small, this difference in level may introduce a measurable error into tank con" tent measurements.
15. BUBBLER PROBE AIR SUPPLY PRESSURES SHOULD BE SUFFICIENTLY HIGH THAT THE AIRFLOW IS NOT AFFECTED BY CHANGING TANK LIQUID LEVELS.
Bubbler Probe air supplies should be clean, (no dirt or o i l ) and the pressure should be suff ic iently high so that the increased back pressure that occurs when a tank f i l l s does not greatly affect the airflow into the bubbler probes.
63
16. BUBBLER PROBE TUBE DIAMETERS AND CONNECTING TUBING DIAMETERS SHOULD BE SUFFICIENTLY LARGE THAT FLOW GENERATED PRESSURE DROPS ARE NOT SIGNIFY CANT.
Pressure drops generated by flow restriction can be significant (for very precise measurements) if small tubing (internal diameters of 6 mm or less) are used or there are collapsed bends or cell wall block valves nearly closed. If pipe or tubing with inside diameters of 8-10 mm or larger is used, the pressure drops should be no larger than a few tenths of a millimeter of water. This saould not be significant.
17. TANK DESIGN SHOULD PREVENT STEAM CONDENSATION FROM ENTERING THE ACCOUNTABILITY TANKS.
Good quality steam valves should be used and the header design should prevent steam condensation from leaky valves from draining into the accountability tanks.
18. ACCOUNTABILITY TANKS SHOULD BE DESIGNED WITH THE INLET OF THE DISCHARGE JET LOCATED AT THE LOWEST POINT. THERE SHOULD BE NO INTERNAL STRUCTURE TO RESTRICT FLOW TO THE INLET.
The jet transfer should be as complete as possible. Since there may be solids in the liquid, baffles or support structures that would catch solids are undesirable. If the discharge jet inlet is not located nea.' the lowest part of the tank, solids buildups might occur which may bias the transfer measurement and, in the case of plutonium or enriched uranium accountability tanks, present a criticality danger.
C.6. RECOMMENDATIONS FOR DESIGN OF ACCOUNTABILITY TANKS BNFL - UKAEA
Further to the request for contributions concerning the design and operation of an "ideal input accountancy tank" the UKAEA ana British Nuclear Fuels pic wish to make the following comments ; We think that it is most important to make clear during phase C of RITCEX that the contributions concerning the design and operation of an "ideal input accountancy tank" only address those aspects of design considered important to 'safeguards'. We believe that the overall concept of an ideal tank design has to be erroneous since, by necessity, the design process is of a highly complex nature and must consider many different factors most of which will inevitably be facility specific. Consequently we do not believe it possible to produce a meaningful yet detailed description of an input tank which would be Judged to be universally 'ideal'. For example, BNFL are at present actively pursuing the goal of designing the ideal input tanks for the THORP repro* ces3ing plant but it is surely appreciated that, on the basis of capacity alone (23 m'), the proposed design would be quite unsuitable for use at Euro-1
chemie, Mol. Since the capacity and planned throughput of the tank are prime factors controlling the tank's design and operation, detailed recommendations concerning ideal design/operation become impossible. We would agree, however, that a number of general design principles can be identified and these are listed below :
1. FEED SOLUTIONS -
It is essential that feed solutions to the tank are well clarified, ie the insoluble 'fines' removed.
6U
2 . PHYSICAL DESIGN OF TANK
- For accountancy systems based on the volume/concentration method, the uncertainties in volume/liquid level calibration should be minimised and constant over the operating regions of the tank. Due consideration should also be given to alternative accountancy systems such as weighing the tank and its contents. The aim should be to reduce accounting errors to a minimum by employing the most appropriate techniques.
- Provision should be made to homogenize the tank contents. ~ The volume of tank heels should be minimized •» Provision should be made to verify that homogenization is complete. - Provision should be made to measure the temperature of the tank contents
at several locations. " Facilities for recalibrating the tank should be provided. a Provision should be made to obtain representative samples of the tank
con* jnts. -< P ision should be made for the introduction of tracers if appropriate. - Ti.o design should avoid obstructions or recesses within the tank in which air or gases can accumulate.
* Deformations of the tank resulting from the introduction of liquids should be minimized and for a given volume, any deformations should be independent of the density of the liquid, and to the maximum extent possible the temperature of the liquid.
3. OPERATIONAL REQUIREMENTS
u The design and ins ta l la t ion of a comprehensive logic control system is v i t a l . Amongst other functions this should ensure that the tank cannot be f i l led and emptied simultaneously and that samples cannot be removed until homogenisation i s complete.
-* The sampling technique should minimize the contamination of a sample by traces of previous samples.
-» Calibration of the tank should be performed under conditions as closely duplicating operational conditions as possible e.g.
•» with fac i l i ty for décrémentai volume changes •* diK-tube3 a l l purged of liquor ** 3imilar temperature of contents •» using liquids of similar density (e.g. n i t r i c acid) - covering the operational range of volume changes
H The dip^tubes should be purged of liquor to ensure complete homogeniza-1
t ion.
4. RECOMMENDATIONS
It is recommended that a study be made of error propagation in the volume/concentration methods of determining the contents of accountancy tanks.
65
CHAPTER IV
CONCLUSIONS
Conclusions have been presented throughout the tex t on the occasion of the discussion of the d i f fe ren t t o p i c s , notably in B.1*. and B.5 .5 . where they can be consulted in fu l l d e t a i l . The most important points a r e repeated he re .
Conclusions of the welgh-ln methods
The c a l i b r a t i o n data we-e used to inves t iga te four d i f fe ren t l eve l measure-» ment instruments namely the electromanometer (RUSKA), the l i qu id manometer using Tetrabromoethane (C2H2BrH), the acoust ic system (SONAR) and the time domain ref lectometer (TDR).
The data were analyzed with respect to the precis ion and accuracy of each instrument. A quan t i f i ca t ion of precis ion and accuracy of the d i f fe ren t systems can be found in volume I I . They a re only t r e a t e d in a q u a l i t a t i v e way. The experiment showed that the TDR had the lowest precision. One of the reasons for the rather poor performance is that the signal of the instrument is plotted on strip charts.
The precision of the SONAR system is significantly better than that of the TDR system, but the overall accuracy is only slightly better. It is interesting to note that the accuracy improves with an increase in the level. This might be an inherent feature of this system in which the complement of the level is actually measured.
The shortcomings of the liquid manometer are mainly caused by the rather high reading error. This is especially true for the liquid manometer used in this experiment which was filled with Tetrabromoethane. So the rather poor measurement precision seems to be the dominating error.
The electromanometer (RUSKA) showed to have a very high measurement preci-1
sion. But these results show also a significant systematic run to run deviation. The higher precision allows obviously to see effects which have been hidden in the measurement noise before. It would be interesting to identify the reasons for the systematic run to run deviation, which turned out to be the dominating error.
A reasonable estimate of the achievable accuracy of the volume determination via a level measurement with an electromanometer cannot be given because the calibration runs performed during RITCEX cannot be considered as an homogeneous sample. This is caused by a number of facts as for example the volume correction, which was necessary to correct for installed instruments between different runs, the different evaporation during the calibrations due to the different time needed to complete the various runs, the evaporation that occurad during extensive sparging during runs 12 and 13, the different temperature gradient in the liquid of the tank and the different pressure drop in the probes before the beginning of each run.
The achievable accuracy in determining the volume of a tank via a liquid manometer measurement is usually assumed to be about 0.5 %• There is some indication that the accuracy achieved in the RITCEX calibration runs might be slightly better than 0.5 %. The achievable accuracy in determining the volume via electromanometer measurements seems to be better than that based on liquid manometer measurements. But the achievable accuracy could be improved significantly, if the reasons for the systematic run to run deviation are better understood and hence actions could be undertaken to reduce or eliminate these.
66
Conclusions of the tracer experiments
The conclusions obtained on the use of tracer techniques during the RITCEX experiment can be summarized as follows :
a) Considerable care should be taken in the design of the tank to achieve homogeneity of the solution, also at intermediate liquid levels, if tracers are envisaged for the recalibration of the tank.
b) The three tracers, neodymium, lead and lutetium performed equally well in the experiment. The interlaboratory standard deviation on the concentra* tion measurements is mainly due to element specific systematic error sources in the measurements. Proper calibration and operating procedures could reduce the spread by a factor of about three.
c) When satisfactory homogenisation is achieved the weight of the liquid in the tank can be measured by the tracer technique with an accuracy of 0.3 to 0.5 %.
d) The uranium inventory in the tank can be measured by the use of the tracer technique with an accuracy of 0.5 %•
It should be remembered that the calibration experiments and measurements have been performed on a real reprocessing input tank but in a decontaminated environment where handling of the solutions and samples presented no radia* tion hazards. Implementation in active conditions might affect the perfor" mance and accuracy of the technique, although interlaboratory measurement and evaluation programmes generally show that the effects on the measurement performance due to radioactivity in the solutions are small [12,13]. The present results however are felt to be representative of the state of the practice in this particular field and are sufficiently promising to encourage the further development of tracer techniques for the recalibration of reprocessing input tanks and for the verification of input inventories as part of safeguards implementation.
67
REFERENCES
F. Franssen Status Report n° 1, RITCEX, BSPSI n° 3 " November 1983
F. Brunelli, L. Olivi, P. Parisi Procedure of Estimation of the Accuracy and Precision of a Set of Weighing Scales Proceedings 6th Annual Esarda Symposium Venice » 1984.
Private Communication Eurochemic (nov. 1983)
F. Franssen, W. Frenzel Input tank calibrations at the Eurochemic Plant ETR * 236 (Feb. 1969)
B. Keisch, S. Suda Temperature ef fects in dip-tube manometry BNL *» 28015 (1980)
L.G. Andersen and C.W. Lewis : "CUDS : A computer program for processing cumulative data s t a t i s t i c s " , Report DP-1327. (E.I. du Pont de Nemours 4 Co, Aiken, July 1973)
W.L. Zijp, and J.K. Aaldijk, : "COMFIT. A computer program for determining best f i t t i n g curves", Report ECN 117 (ECN, Petten, May 1982).
W.L. Zijp : "Generalized l eas t squares principle for straight l i n e f i t t ing" , Report ECN*83^093 (Petten, June 1983).
W.L. Zijp : "Generalized method of l eas t squares", Report ECN-83-161 (Petten, October 1983).
D. Sellinschegg, G. Nâgele, F. Franssen, "Evaluation of Tank Calibration Data in RITCEX", Proc. 6th annual Symposium of Safeguards and Nuclear Material Management, 14*18 May, 1984, Venice, ESARDA «-Report 17, pp 223-230
G. Guzzi, P.R. Trincherini, "Determination of the Volume of Reprocessing Input Solutions by Tracer Techniques", ESARDA Bullet in, 6, pp 6-8
W. Beyrich, W. Golly, G. Spannagel, P. De Bievre, W. Wolters, "The IDA80 Measurements Evaluation Programme on Mass Spectrometric Isotopic Dilution Analysis of uranium and Plutonium", KFK«3760 (1984)
W. Beyrich, E. Drosselmeyer, "The Interlaboratory experiment IDA-72 on Mass spectrometric Isotopic Dilution Analysis" KFK-1905 (1975)
TASTEX * Tokai Advanced Safeguards Technology Exercise IAEA - Technical Reports Series N° 213 (1982)
P86-05
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TANKS (BNFL)
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FIG. C-2 : PROPOSED PIPEWORK ARRANGEMENT FOR THORP
ACCCUNTANCV TANKS (PMFL)
Calibratton ^etflnbridge .Tiebar
f l 6 , « : TEST «>GH.NG F K I U T Y (SNÜ
ALWAYS Ut
STEAM
ALWAYS OPEN TO ADJACENT TANK WITH EOWL OP. UNEQUAL VENTILATION
A B C
FIG. M : TYPES OF INTERNAL PIPING
PRACTICAL OPERATION AREA FULL TANK
' T R 1 PRACTICAL . .^OPERATION
— -y. HREA " *— "— • - • w n, EMPTY TANK
STR1
F I G . C-5 : INSTRUMENTATION LAY-OUT
f A"
%fâF m MI ' nr-Tiacs
STR SUfAGE TO». K t ITR «TONAL TOT. MX
STB ma STM
"ïTir (TRI STB rm
MKSSUKSOF MMUSflP 0P-1UKS
Jl
Tl"l
«•ROW CtMTML
USMéJ
1 1
1/1
2/3
n r r
i 1
„J
» i
FIG. C-6 : INSTRUMENTATION LAY-OUT
Tractr addition ConntcHon to rfyO fttd Unt • rinct lint y I fted Unt weigh drum
Vatvt-A
FIG, C-7 : RECALIBRATION SET-UP
OVERFLOW WITH NGOAHETEft
7777
HjOFttJ
A - VALVC
X.
2:
ORIFICE
VALVE
7: 2:
7:
ELECTftOHAMOMETER SYSTEH
'ZZA
FIG, C-8 : SHAPE DETERMINATION SET-UP
4VILI
2_
RUN.: 16 VARIABLE : LP V« -292.08 • 0.92735 H
<t% . 0.4489 b «0.00020
*VH « 18538
fLOWRATE : 0638 LiK"1
-1
-1
-1
- 1
starting up of Nit sysrtn
T T 1000 2000 3000
FIG. C-9 : RESPONSE CURVE OF ELECTROMANOMETER DURING FILLING OF THE TANK AT CONSTANT RATE
H (mm)
9 mof i l
S T U D I E C E N T R U M V O O R K E R N E N E R G I E
C E N T R E
D' E T U D E
D E
REPROCESSING INPUT TANK CALIBRATION EXERCISE (RITCEX)
Volume 2 : DETAILED STATISTICAL EVALUATIONS OF THE MEASURED DATA
L' E N E R G I E
R. CARCHON, P. DE REGGE, F. FRANSSEN
N U C L E A I R E
June 1986
E. Plaskylaan 144. 1040 BRUSSEL BLG 588 144, avenue E. Plasky, 1040 BRUXELLES (BELGIË) (BELGIQUE)
REPROCESSING INPUT TANK CALIBRATION EXERCISE (RITCEX)
Volume 2 : DETAILED STATISTICAL EVALUATIONS OF THE MEASURED DATA
R. CARCHO t, P. DE REGGE, F. FRANSSEN
June 1986
BLG 588
iABLE OF CONTENTS
VOLUME 1. FINAL REPORT
Abstract 1
Introduction 2
Chapter I . Phase A - Evaluation of Historical Data 4
A.1. The data 4 A.2. Evaluation of converted h is tor ica l data 10
A.2.1 . The approach of Tokai Works (Jap ) 10 A.2.2. The approach of the SCK/CEN (Belgium) 13 A.2.3. The KFK evaluations 15 A.2.4. The ECN evaluations 19 A.2.5. The CEA evaluations d] A.2.6. The Brookhaven NL evaluation 22 A.2.7. The DWK evaluations 22
Chapter I I . Phase B - Calibrations and re-cal ibrations of an accountability input tank and i t s evaluations 24
B.1. Engineering Review of the Tank 24 5.2 . Preparatory work 27 B.3. The calibrations by weigh-in method 28 B.4. Summary of RITCEX evaluations 29 B.5. Results of the use of tracer techniques 37
Chapter I I I . Phase C - Design Principles and operational procedures for an an ideal accountancy input tank 46
C.I. Introduction 46 C.2. The design A the tank 46
. C.3. Procedures to cal ibrate the input tank 53 C.4. Operating procedures of the tank 59 C.5. Recommendations for design of accountability tanks
Orookhaven National Laboratory) 60 C.6. Recommendations for design of accountability tank
(BNFL-UKAEA) 63
Chapter IV. Conclusions 65
References 67
Figures (reproduced from copies provided by the authors) 68
VOLUME 2. DETAILED STATISTICAL EVALUATIONS OF THE MEASURFO DATA
RITCEX 12-A Evaluation of RITJEX a data/ENEA » Casaccia M. Aparo, M. Dionisi, C. Vicini
RITCEX 12^B Evaluation of calibration data of RITCEX/KfK Karlsruhe D. Sellinschegg
RITCEX 12*C IAEA evaluation of RITCEX Calibration Data/IAEA * Vienna H. Shimojima, S. Suda, K. Gharwal
RITCEX 12- D Evaluation of RITCEX converted data by PNC Analytical Methoa/PNC Japan T. Uchida, Y. Murakami
RITCEX 12-E ITREC evaluation of RITCEX Calibration Data/ENEA - ITREC CRE -TRISAIA * G. Arcuri
EISEÜ RITCEX 1 2 - A
Dipartimento ciclo dal combustibil*
EVALUATION OF RITCEX DATA
M.APARQ, M.DIONISl .(COMB-MEPIS CR. E. CASACCIA ENEA)
C.VICINI (DIPARTIMENTO Dl ENERGETICA - UNIVERSITA' DEGLI
STUDI "LA SAPIENZA" - ROMA)
ENEA SXllSiïX* .»Huppo S.P. An,ulll.r.... 301 T. . . , f . to: CASACCIA • ENEA Z'M.£££ 00100 Aom.A.D. C . M . . . Po.1.1. N. 2*00
Page 1
- DATA ANALYSIS PROCEDURE
The general procedure for the analysis of tank
calibration data is outlined in fig. 1. Our analysis
starts from step 4, data fitting for each calibration
run with different procedures, using data suggested in
RITCEX report, dated 28 may 1984. The partitioning of
the tank into six regions is based on the break points
as agreed during the last meeting held in Luxemburg.
As far as the statistical tests (analisys of
covariance and Bartlett's test) are concerned, we
stopped our data analysis when at least one hypotesis
could be rejected.
- MODEL ASSUMPTIONS IN DATA FITTING
A part the regions 0-350 mm and 350-700 mm, our
general calibration model was:
Yi + Eyi » A • B# < Xi+ Exi ) +Et
where A e B are the intercept and the slope
respectively and
Xi » "true" liquid level
Yi » "true" volume
Ex - random error associated with liquid level
measurements
Pan*'-- Z'
Ey = random error associated with volume measurements
Et = -fixed error due to tank imperfections or
instrument non linearity
In thp analysis of RITCEX data we have taken into
consideration four different error models, derived
from the general formula, and we have assumed the error
associated with lack of fit to be negligrble.
Error model A
We suppose that E>: = 0 (i. e. the true values for the
level can be observed) and Ey is normally distribuited,
indipendent of i and uncorrelated with other ones.
Yi = A + BXi + Eyi
Error model B
We assume that Ey = 0 (i.e. the true values for volume
can be observed) and Ex is normally di stribui ted,
indipendent of i and uncorrelated with other ones.
Yi « A + B< Xi + Exi )
Error model C
The approach is that both Ex and Ey are different from
zero, and they have the same mean and the same
varianc». We also suppose the errors to be uncorrelated
with Be:h other and to be indipendent of i.
Yi » A + B: Xi + Exi ) + Eyi
Error model D
We suppose that Ex « 0, but now we consider the
variable Yi as a sum of successive increments and the
associated errors Eyi as a sum of errors of the same
increments:
Paqe 3
Eyi = sum Eyj
so that we assume Eyi as a cumulative error having a
normal distribution with mean zero and variance
proportional to i.
The regions 0-350 mm and 350—700 mm are -fitted with
the least square model (errors in y direction) with a
second degree equation. We carried out the data
evaluation for these regions by using polynomial model:
Yi = A + SXi + CXi + Eyi
The results of the data eva. ation, with different
models,, are summarized in the tables from 1 to 16. The
standard deviation of the overall error in predicted
volume, presentee! in the last column of the tables, is
given in its minimum value as far as models A, B, C are
concerned, while for the cumulative model is presented
in both the ma>:imun and minimum value. The plots of the
volume residuals versus the observed val we of the level
are also reported, togheter with the confidence band
calculated at J.c .
RITtEX EXERCISE INSTRUMENT MEASUREMENT
RWH1 RUN 12 I RUH13 RU* 14
1) RAW DATA PROCESSING
X 2) DATA NORMALIZATION
3) PRELIMINARY ANALYSIS AND PARTITIONING
4) DATA FITTING WITtf DIFFERENT PROCEDURES
DATA RECOMBINATION COVARIANCE ANALYSIS BARTLETT'S TEST
END OF
ANALYSIS
"ARE THE 3 HYPOTESIS
»T£
OVERALL
CALIBRATION
TABLE 1°
RfcGIÜNE O - 350
V = Ào + A l * h • A2 * h' 2
j n s t r . RUN Ao S<Ao> Ai S(Ai> A2 S(A2> R-ss.Var
RÜSKA » 11 .8355 . 04471 „05964 6 . 7 E-4 Ô.4 E-4 2 . 0 E-o S.ó F 3
« 14 ,S33S .04003 .06089 4 . 8 E-4 Ô..4 E-H 1.3 E-o 1.6 E-' .
U-TUBE. « 11 ..6982 .12010 ,0653b 1.8 E-3 6 . 2 E-4 5 , 2 E-6 .0406
* 14 .6823 .28965 .06481 3 , 4 E-3 f . .3 E-4 9 „ 3 E-ó .0833
TABLE t"
RhGIONfc 350 - 700
•s) = fyp + A l * h + A2 * h"2
!.nstr. RUN Ao St An) At 81A.D A2 S^A2> H es. Var
RUSKA « 11 -3.289 .35823 ,07921 3,2 E-3 6,2 E-4 2.9 E-6 3,8 E-3
« 12 -5,372 1.50095 .087*1 5,9 E-3 *-l E 4 5.7 E-ê 1..2 E-P
M t3 -3.794 .85490 .08194 3.3 t-'A 6.2 E-4 3.1 E-6 3,5 E-3
« 1 4 -2.762 .50499 .07912 2.0 E-3 c, 2 F-4 1,9 F-6 ^.3 E-3
ii-TUBE « .11 -J.6.8/8 J.J..S/75 ..13335 .042*0 5. 7 E-4 3,9 E-5 , Ö 7 2 8
tt 12 12.953 14.4873 ,.01.902 ,.05695 A.7 E-4 5,4 E-b .090b
« 13-15.011 4.1492 .12215 .01599 5..RF-4 1,5 E-5 , 0ÖJ3
« It - 5.240 4.2*63 .08987 .01677 6.1 E-4 1,6 E-b „2320
TABLE 3»
RUN l i
Vi = 371.40 l i t r e s
Vf = J 545.99 l i t r e s
RUÜKA
U-TUBE
A
B
C
D
A
B
t;
D
INTERCEPT
-295.2102
-295.2115
-295. .il 10
-294.5748
-293.6560
-293.6591
-293.6570
-294.0516
S(INT)
,34947
,34947
.34947
1.37851
.5480
.5460
.5468
4.2339
SLUPE
.9^8508
.928509
.928508
.928265
.927109
.927111
.927110
.927730
S(SI
2.52
7 5?
2.52
1.16
3.94
3.94
3.94
3.55
L0>
E-4
F-4
E-4
SD(V)
.479
.478
.359
E-3 1.55-2.58
E-4
E-4
E-4
.750
.749
.563
E-3 4.78-7.95
RES.VAR.
.2155
.2155
i.69 E-3
.5287
.52U7
1.60 E-2
TABLE 1°
RUN 11
Vi = 1595.43 l i t r e s
Vf = 2557.72 l i t r e s
RUSKA
U-TUBE
A
B
C
D
A
B
C
D
INTERCEPT
-295.2301
-295.2371
-295.2334
-298.4254
-295.9088
-295.9358
-295.9213
-297.7441
S(INT)
.98591
.98591
.98591
? 04365
1.9417
1.9417
1.9417
14.8074 .
SLOPE
.929233
.929235
.929234
.930289
.929115
.929125
.92911y
.929507
S(SLO)
3.67
3.67
3.67
1 ft
7.23
7.23
7.23
5.92
t-4
E-4
t-4
E-3
E-4
E-4
E-4
E-3
-•
2
l;
SD(V>
.541
.541
.404
.49-3.06
1.066
1.065
.796
2.2-14.9
RES.UAR.
.2790
.2790
1.53 E-3
1.0816
1.0G16
/'.63 t-2
TABLE 5°
RUN 11
Vi = 2577.72 l i t r e s
Vf = 2616.47 l i t r e s
RUSKA
U-TURE
A
B
C
D
A
E
C
\
INTERCEPT
13,7381
12.4690
13.2410
13.2130
50.S579
50.4004
50.5043
50.6711
S(INT)
So.0110
58.0405
58.0160
71.0760
21.0063
21.0078
21.0066
25.7262
SLOPE
.828983
.829390
.829142
.829232
.816828
.816879
.816845
.816821
S(SLO)
1.86
1.86
1.86
2.28
6.74
6.74
6.74
8.25
E-2
E-2
E-2
E-2
E-3
E-3
E-3
E-3
l;
4,
SD(V)
.710
.710
.592
2.3-12.4
.261
.261
.218
.47-4.50
RES.VAR.
.,3785
.3786
2.43 E-2
.0511
.0511
3.23 k-3
TABLE 6°
RUSKA
RUN 11
Vi = 2636,38 litres
Vf = 2907.21 litres
INTERCEPT S(INT) SLOPE B(SLO) SD(V) RES.VAR.
A
B
C
D
-312.3839
-312.3851
-312.3845
-312.1.801
.52943
.52943
.52943
2.55460
.932633
.932633
.932633
.932578
1.59
1.59
1.59
7.73
E-4
E-4
fc-4
E-4
.061
.061
.046
1.04-1.09
3.49
3.49
1.74
E-3
E-.Î
E-4
U-TUBE A -325.7604 9.2509 .935552 2.77 E-3 1.066 1.0562
B -324.0604 9.2518 .935642 2.77 E-3 1.066 i.0563
C -323.f?y97 9.2511 .935594 2.77 E-3 .002
D -312.3250 77.0714 .932129 2.33 E-2 31.6-33.0 .1580
TABLE 7°
RUN 12
Vi = 359.05 l i t r e s
Vf = 1408.02 l i t r e s
R1JSKA
U-TUBE
SONAR
A
B
C
D
A
B
C
D
A
B
C
D
INTERCEPT
-294.6333
-294.6338
-294.6335
-294.0881
-293.9825
-293.9963
-293.9888
-290.1040
-297.6491
-298.2461
-297.9152
-286.3624
S(INT)
.27545
.27545
.27545
1.06007
1.5Î90
1.5190
1.5190
9.7593
10.0008
10.0062
10.0019
25.0598
SLOPE
.926792
.9P6792
.926792
.926450
.925492
.925504
.925497
.923589
.896753
.897261
.896980
.895448
S(SLO)
2.30
2.30
2.30
9.31
1.27
1.27
1.27
8.58
8.07
8.07
8.07
2.15
E-4
K-4
E-4
E-4
E-3
E-3
E-3
E-3
E-3
F-3
E-3
E-2
SD(V)
.279
.278
.213
1.2-1,9
1.539
1.538
1.177
10.8-17.6
10.010
10.102
7.820
27.9-45.2
RES.VAR
6.98 E-
6.98 E-
9,B3 E-
2.1263
2.1263
B.37 E-
91.547
91.599
.5396
TABLE 8 e
RUN 12
Vi = 1609.49 l i t r e s
Vf = 2 4 1 5 . 0 1 l i t r e s
INTERCEPT S<JNT) SLOPE S(SLO) SD(V) RES.VAR.
RUSKA A
B
C
D
-299.2040
-299,2074
-299.2056
-300.2114
1.61400
1.61402
1.61402
3.03457
.929728
.929729
.92972B
.930033
6.44 E-4
6.44 E-4
6.44 E-4
1.24 E-3
.403
.483
.37b
2.3-2.8
.1948
.1948
1.33 E
U-TUBE A
B
f.
D
-298.1003
-298.1074
-298.1036
-299.3534
2.3441
2.3441
2.3441
4.7999
.927999
.928002
.928000
.928286
9.35 E-4 .703
9.35 E-4 .702
9.35 E-4 .550
5.76 F-2 3 .7 -4 .4
. 4 1 1 3
. 4 1 1 3
3 . 3 3 E-3
SONAR A
B
C
D
-•402.8226
-403.7560
-403.2695
-422.8596
27.6012
27.6118
27.6036
52.5161
.958425
.958795
.958602
.964117
1.09 t-2
1.09 E-2
1.09 E-2
2.11 E-2
7.917
7.918
6.137
39.6-46. fl
53.232
52.253
.3714
TABLE 9°
RUN 12
Vi = 2616.25 l i t r e s
Vf = 2904.23 l i t r e s
INTERCEPT S(INT) SLOPE S(SUT) SDCV) RES„VAR.
RUSKA A -304..2574 2.32080 .929648 6.99 E-4 .184 2.47 E-2
B -304.2582 2.3208.5 .929648 6.99 h-4 . i83 2.47 Ï-2
C -304.2573 2.3208Ö .929648 6.99 E-4 .149
D -304.7219 3.23286 .929808 9.82 E-4 1.36-1.43 2.99 fc~4
U-TliPE A
P.
C
D
-305.6111
-305.6137
-305.6120
-306.2443
3.1563
$.1562
3.1562
4.3y81
.928930
.928931
.928930
.929148
9.50
9.50
9.50
1.33
h-4
E-4
E-4
E-3
. 250
.24 y
.202
1.86-1.95 5
.0456
.0456
.52 E
TABLE 10°
RUN 13
Vi = 366.39 l i t r e s
Vf = 1419.11 l i t r e s
INTERCEPT S ( I N T ) SLOPE S(3L0) SD(V) RES.VAR,
RUSK A
U-TUBE
SONAR
A
B
C
D
A
B
C
D
A
B
C
D
-29b.3502
-295.3512
-295.3507
-294.5670
-293.7110
-293.7192
-293.7147
-292.4397
-305.3991
-305.4644
-305.4288
-306.5925
.39854
.39854
.39854
1.94321
1.1897
1.1897
1.1897
9.6919
3.3302
3.3304
3.3302
61.1357
.926941
.926942
.926941
.926658
.926683
.926690
.926686
.926038
.914600
.914656
.914626
.917595
3.31
3.31
3.31
1.69
9.8B
9.08
9.80
8.45
2.70
2.70
2.70
5.21
E-4
E-4
E-4
L-2
E-4
E-4
E-4
E-3
E-3
E-3
E-3
b-2
.402
.<t01
.30/
"•' *?-3 5
1.201
1.200
.918
10.7-17.3
3.328
3.327
2.560
67.5-108
.1448/
.14487
3.25 b -3
1.2944
1.29<t4
.0812
9.9441
9.9497
3. J.ÖB7
TABLE 11»
RUN 13
Vi = 1620.86 litres
Vf = 2427.4c litres
INTERCEPT SCINT) SLUPt S(SLO) SO(V) RES.VAft
RUSKA
U-TÜBE
A
B
C
[)
A
B
C
D
-301.2439
-301.2483
-301.2460
-302.5314
-300.9170
-300.9267
-300.9215
-301.9318
J.86971
1.86970
1.86970
3.39198
2.7616
2.7616
2.7616
5.05Ó1-!
.930283
.930285
-930204
.930667
.9^0598
.930602
.930600
.931215
7.42
7 „42
7.42
1.38
1.10
1.10
1.10
2.05
E-4
E-4
E-4
E-3
E-3
E-3
E-3
E-3
.357
.557
,436
2.6-3.1
.823
.823
.644
3.9-4.6
.25890
.25890
1.64 E-3
.5650
.5650
3.66 E-3
SONAR A -357.2324 4.9933 .943927 1.97 E-3 1,454 1.7619
B -357.2634 4.9934 .943939 1.97 E-3 1..454 1.7619
C -357.2470 4.9933 .943933 1.97 E-3 1.133
D -358.8914 8.7513 .944087 3.52 E-3 6.7-7.9 .0106
TABLE 12°
RUN 13
Vi = 2629.19 l i t r e s
Vf = 2C- 06.64 l i t r e s
INTERCEPT 5(INT) SLOPE S(SLO) SD(V) RES.VAR.
RUSKA
U-TUBE
SONAR
A
B
C
D
A
B
C
D
A
B
C
D
-313.6535
-313.6527
-313.6530
-313.7451
-352.5844
-352.6025
-352.5926
-350.8166
-545.5438
-547.7294
-546.6364
-527.7967
.39717
.39716
.39716
.57723
7.6669
7.6669
7.6669
11.1004
85.4424
05.4984
85.4564
119.7682
.932198
.932198
.932198
.932229
.944237
.944243
.9442^0
.943643
1.000171
1.000827
1.000499
.994195
1.19
1.19
1.19
1.75
2.30
2.30
2.30
3,36
<L • JO
2.56
2.56
3.62
t-4
E-4
E-4
E-4
E-3
E-3
E-3
E-3
E-2
E-2
E-2
E-2
.030
.030
. 024
,23-.25
.500
.579
.470
4.6-4.8
6.070
6.071
4.834
48.1-50.2
6.73 k
6.73 E-
y.09 E-
.?445
.2445
3.32 t-
26.938
26.955
.3649
-4
•4
•6
3
TABLE 13°
RUN If
Vi = 372.19 litri Vf = 1509-91 litri
RUSKA
- •
A
B
L
D
_INTFRLEPT_
-294.3461
-294,3462
-294.3461
-29.1.9707
.SiJNJEi
.13385
.13385
.13385
.69497
...SLOPE.
,927222
,927222
.927222
.9^6912
S_(SLQ2.
9.92 fc-5
9.72 F-5
9.92 b-5
5.OB E-4
SD(V) RES.VAR.
.i7f .02923
.1.76 .02923
.132
78-1.26 4.24 F.-4
U-TUBE H
B
C
I)
-293,1345
-293.1427
-293.1380
-29.1.7517
.9154
.9154
.9154
4.9690
.926504
,9265JO
,926507
,926180
6.79 F.-4 1.208
6.79 F-4 .1.208
6.79 F.-4 .910
4 .2 i F-3 5 .6 -9 .2
1,3696
i .^696
.0218
SüNAR A
..-
i.
D
-299.3580
-299.401.7
-299.3780
-29*.4946
2.1.134
2.1134
2.1134
7,5302
.915383
.915417
.915399
.916636
1-54 E-3 2/777 7.2311
1.54 E-3 2.777 7.2313
1.54 E-3 2.101
6.27 E-3 8 .4-13.9 ,04b,'<
TOR A
B
C
I)
-190.5331
-191.0009
-190.7396
-199.8178
6.6675
6.6702
6.6680
61.7828
.889085
.889471
.889255
.899383
5.14 E-3 9.533
5.14 F-3 9.539
i.14 E-3 7.302
i.62 E-2 71-121
85.267
85.304
3.994
TABLE 14°
KUN 14 Vi = 1561.07 1 i t r i Vf = 2547 .44 I i t r i
RUSKA
-
A
B
C
D
_INJERÇEPT.
-301.3344
-301.3367
-301.S355
-302-6611
_.iiINi>.
.5500
. 5500
. 5500
1.55*2
__SLQPE_
.930887
.930808
.930887
.931381
5iSL0> >D(V>
2 ,08 E-4 .322
2 .08 E-4 .322
2rOB E-4 .240
6 .29 E-4 1 „ 3 - 1 . 6
.RES.. WAR.
.09873
.09873
4 .19 E-4
U-TIJBF
B
C
D
-299 .5228 1. .412H
-?.99.bS; 1.4120
-299.3585 12.5591
,930090 5 .33 E-4 .828 .6524
.930096 5 .33 E-4 .823 .6524
,930073 5 .33 E-4 .616
,929731 5 . 0 / F-3 1 0 . 5 - 1 2 . 9 .0273
SONAR A -340.6889 2 .1531 . 9 3 7 9 8 i
B - 3 * 0 . 7 2 2 0 ?..153l . 9 3 , 9 9 3
C - 3 4 0 , / 0 4 4 2 .1531 „937987
D -339,7453 11.3769 .y38229
8.06 E-4 iv241 1.4c6.i
8 .06 F.-4 1.240 l .<niol
8..06 E-4 „923
4 .55 E-3 9 . 4 - 1 1 . 6 .021R
TOR A -203,6201 .1.1.2434
B -204.5721 11.2479
C -204.0451 11.2443
D -226.5555 94.3571
898156
898520
898319
907^24
4.26
4.26
4.26
3.84
E-3
E-3
E-3
E-2
6.850
6.850
5.192
79.6-99.1
44.6S0
44.700
1.607
TABLE 15°
RUN 14 Vi = 2566.95 1 i t r i Vf = 2627.28 I i t r i
INTERCEPT S(TNT) SLOPE SiSLQ) SDvV) RES.VHR.
RUSKA
U-TUBE
SuNAR
A
B
C
D
A
B
C
D
A
B
L
D
- 20.3377
- 21.1617
- 20.6878
- 24„3299
9.1862
8„7872
9.0265
6.7929
- 61.1776
- 61.7548
- 61.4298
- 67,3155
32.5J97
32.5298
32.5214
50.4128
22.8670
22.8705
22.8675
35.1988
27.2561
27.2619
27.2571
44.1168
.839007
.839930
.839779
.841071
.830022
.830150
.830073
.830877
.848266
.848450
.848347
.850317
1.04
1.04
1.04
1.62
7.33
7.34
7.M
1.13
8.70
3.70
8.70
1.41
E-2
E-2
E-2
E-4
E-3
E-3
E-3
E-2
E-3
E-3
E-3
E-2
10
7,
9.
.640
.640
.528
.7-10.9
.455
.455
.377
.5-7.6
.528
.528
.435
,3-9.4
.31420
.31430
.0187/'
.1589
.1590
.0093
,2140
.2141
.0141
TDR A -1817.858 98.5667 1.428192
B -1820.132 98.6162 1.428930
C -1819.407 98.5890 1.428690
D -18i7.668 120.7148 1.428214
3.20 E-2
3.20 E-2
3.20 E-2
.731
.730
.514
3.91 E-2 16.2-16.3
.4004
.4006
.0429
TABLE 16°
RUM 14
Vi = 2645.68 litri
Vf = 2906.79 l i t r i
INTERCEPT S ( I N T ) SLOFf. SOLO) SD(V) RES.VAR.
RURKft A
B
C
D
-314.5062
-314.5078
-314,5070
-316.1652
667?
6672
6672
4304
., 933092
.93,5092
„933091
.933603
2.00
2.00
2.00
7.34
F-4
E-4
E-4
E-4
.073
.073
.055
..97-1,02
.00496
.00496
1.51 E-4
U-TUBE A
B
C
\)
A
B
C
D
-310.5501
-310.5942
-310.5703
-311.1501
-536.7430
-537.2172
-536.9784
-517.8371
3.7291
3.7291
3.729:1
32.5528
14.1006
14.1026
14.1011
65.3051
.931571
.931585
.931578
.931837
.997525
.997667
.997595
.992022
1.12 E-3 .410 ,1553
1.12 E-3 .410 .1553
1.12 E-3 .31.0
9.83 E-3 13.1-13.7 .0027
SONAR 4.21 E-3 1.461 J.S91Ô
4.21 E-3 1.461 1.8915
4.2i E-3 1.091
1.V7 E--2 25.5-26.5 .1020
F'eae A
- ANALYSIS OF COVARIANCE FOR THE COMPARISON OF THE FOUR
CALIBRATION RUNS
In the tables hereinafter reported the calibration
lines referred to the four runs are compared to the
analysis of covariance as given by Brownlee.
Furthermore, the result of Bartlett's test for
homogeneity of the variance of the residuals are also
presented.lt ir.ust pointed out that the data treatment
has been performed using only the data evaluated by
model A.
TABLE 17»
ANALYSIS OF COVARIANCE, RUN 11-14 U-TUBE 2OO0-3O70
SOURCE OF VARIANCE
DESREES OF FREEDOM SUM Or SQUARES MEAN SQUARES
BETWEEN B E BH
DEVIATION OF GROUP M. AbAUT RE6RESS!ON
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
42
48
1
61.4*66138
31.593689
2.71337B91
34.1428223
129.227539
4763214.87
61.4466138 «84
13.7968443 -S3
.904439635 -82
.81292434 «SI
S2/S1 - 1.I1260002 DISTRIBUTED AS F< 3,42 1
S3/S1 - 19.4321214 DISTRIBUITED AS Ft 2,42 >
S4/S1 - 75.5871252 DISTRIBUITED AS Fl 1,42 >
BARTLETT TEST I I.3759040S
ANALYSIS OF COVARIANCE, RUN 11-14 U-TUBE 700-2000
SOURCE OF VARIANCE
DECREES OF FREEDOM
BETWEEN B E BM 1
DEVIATION OF GROUP h. 2 ABAUT REGRESSION
BETWEEN INDIVIDUAL 3 SLOPES
ABOUT INDIVIDUAL 41 LINES
ABOUT OVER-ALL 47
DUE TO OVER-ALL 1
SUM OF SQUARES
20.1B7816
11.1279602
2.55126953
49.1572266
83.0410156
8001836.01
MEAN SQUARES
20.I87BI6 -S4
5.5639801 -S3
.850423177 -S
1.19895675 -S
S2/S1 - .709302634 DISTRIBUITED AS F< 3,41 >
S3/SI - 4.6406846 DISTRIBUITED AS F( 2,41 >
S4/S1 - 16.8378185 DISTRIBUITED A3 Fl 1,41 >
BARTLETT TEST I 4.08927812
TABLE 18°
MNALVSIS OF COVARIANCE, RUN 11*13*14 U-TUBE 7OO-20O0
SOURCE OF VARIANCE
PESREES OF FREEDOM
BETWEEN B E BH
DEVIATION OF GROUP H. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
38
1
SUN OF SOUARES
1.84477513
.221313477
.614257813
34.2724*1
36.9853516
6770163.04
MEAN SQUARES
1.84477513 -S4
.221313477 -S3
.307128906 -82
1.00801336 -SI
S2/SI - -304687277 DISTRIBUTED AS F « 2,34 )
S3/S1 - .2I9S34067 DISTRIBUTED AS F< 1,34 >
S4/S1 « 1.B3010944 DISTRIBUTED AS F( 1,34 >
BAKTLETT TEST I 1.84194072
ANALYSIS OF COVARIANCE, RUN 11-14 U-TUBE 3160-TOP
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETWEEN B E R 1 1
DEVIATION OF GROUP ». 2 ABAUT REGRESSION
BETWEEN INDIVIDUAL 3 SLOPES
ABOUT INDIVIDUAL 23 LINES
ABOUT OVER-ALL 29
DUE TO OVER-ALL 1
SUM OF SOUARES
28.6266046
10.4164587
7.14822388
13.4610901
60.0615845
313723.376
MEAN SQUARES
28.6266046 •=
5.20822936 •
2.38274129 -
.585264786 -
S2/S1 - 4.0712193 DISTRIBUTED AS F< 3,23 )
S3/SI - B.B9B92B3 DISTRIBUTED AS Ft 2,23 >
S4/S1 - 48.9122279 DISTRIBUTED AS F( 1,23 )
BARTLETT TEST i 4.7470390*
TABLE 19°
ANALYSIS OF COVARIANCE, RUN 11*13*14 U-TUBE SIAO-TOP
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETWEEN B E M l I
DEVIATION OF GROUP M. 1 ABAUT REGRESSION
BETWEEN INDIVIDUAL 2 SLOPES
ABOUT INDIVIDUAL 22 LINES
ABOUT OVER-ALL 26
DUE TO OVER-ALL 1
SUM OF SQUARES
.0136276321
-.607942951
S.416931IS
13.413431
18.7429199
269422.663
MEAN SQUARES
.0136276S21 -S4
-.607942391 -S3
2.70846938 -82
.609793229 -SI
S /SI - 4.44161307 DISTRIBUITED AS F< 2,22 >
S3/S1 • -.996969073 DISTRIBUITED AS F( 1,22 >
S4/S1 - .0223479883 DISTRIBUITED AS F( 1,22 >
BARTLETT TEST » 3.61333492
ANALYSIS OF COVARIANCE, RU 11*13*14 U-TUBE 2000-3070
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETNEEN I E W
DEVIATION OF GROUP M. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
39
43
1
SUT1 OF SQUARES
.6.29344497
9.801B34I1
I.43339379
32.9086914
49.7948B28
4279494.22
MEAN SQUARES
6.25944497 -S4
3.80133411 -S3
.716796879 -62
.8438126 -SI
S2/S1 - .849474012 DISTRIBUITED AS F( 2,39 >
S3/S1 - 6.8797377 DISTRIBUITED AS F< 1,39 )
S4/S1 - 7.41331021 DISTRIBUITED AS Ft 1 39 >
BARTLETT TEST I .713417137
ANALYSIS OF COVARIANCE, RUN 11-14 RUSKA 2OOO-307O
TABLE 20°
SOURCE OF VARIANCE
DEGREES OF FREEDOH
BETWEEN B E M
DEVIATION OF 6ROUP H. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
42
SUM OF SQUARES
47.170462
13.34'4478
3-OSAI5234
B.13844727
74.2504883
47*3269.84
MEAN SQUARES
47.170462 -S4
7.77322388 -S3
t.0187174S -S2
.194248744 -SI
S2/S1 - 5.^4439636 DISTRIBUTED AS Fl 3,42 >
S3/S1 - 40.0168332 DISTRIBUTED AS F 4 2,42 I
S4/Sk • 242.835331 DIBTRlBUlTED AS F« 1,42 >
BAKTLETT TEST a 3.37204398
ANALVSIS OF COVARIANCE, RUN 11-14 RUSKA 700-2001»
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETWEEN 8 E BM
DEVIATION OF GROUP M. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
41
47
I
SUM OF SQUARES
24 .8728881
3 .43956*21
4 .68359373
4 .89794922
37 .9599609
8001881 .09
MEAN SOUARES
24 .8728881 -S<
I .729782J - S 3
1 .56119792. - S ;
.119462176 -SJ
S2/S1 - 13.068S541 DISTRIBUTED AS F l 3 , 4 1 >
S3/S1 • 14 .4797472 DISTRIBUTED AS F< 2 , 4 1 >
S4/S1 - 208 .207224 DISTRIBUTED AS F( 1 ,41 >
BARTLETT TEST i 9.81908619
TABLE 21°
ANALYSIS OF COVARIANCE, RUN 12-14 SONAR 7OO-20OÖ
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETWEEN > E W
DEVIATION OF GROUP H. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
27
31
I
SUM OF SQUARES
1522.90572
8*3. "t3S96
361.104492
804.44336
3553.72703
4931783.I
MEAN SQUARES
1322.90372 -84
863.233396 -S3
180.332246 -S2
29.7941983 -SI
S2/S1 - 6.03997997 DISTRIBUTED AS F< 2,27 )
S3/S1 - 29.0404O3I DISTRI8UITED AS F( 1,27 >
S4/S1 • S1.114169B DISTRIBUTED AS F< 1,27 >
BARTLETT TEST < 9.94469812
ANALVSIS OF COVARIANCE, RUN 11-14 RUBKA 3160-TOP
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETWEEN B E BK
DEVIATION OF GROUP M. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
23
29
1
BUM OF SQUARES
9.71373424
12.6207616
.449249268
.113189697
22.3676148
3,13761.07
MEAN SQUARES
9.71373424 -S
6.31038002 -S
.149749756 -6
4.921291I9E-0
S 2 / S I - 30 .4289566 DISTRIBUTED AS f < 3 , 2 3 >
S 3 / S I - 1 2 8 2 . 2 6 1 2 ! DISTRIBUTED A8 F( 2 , 2 3 )
S4/S1 - 1973 .81823 DISTRIBUTED AS F < 1,23 I
BARTLE1r TEST I 1 .90697877
TABLE 22°
ANALYSIS OF COVARIANCE, RUN 13-14 SONAR 2000-3070
SOURCE OF VARIANCE
DEGREES OF FREEDOM
BETWEEN B E BH
DEVIATION OF GROUP M. ABAUT REGRESSION
BETWEEN INDIVIDUAL SLOPES
ABOUT INDIVIDUAL LINES
ABOUT OVER-ALL
DUE TO OVER-ALL
24
2G
1
SUM OF SQUARES
208.84963
198.995719
136.913574
188.370361
733.942383
2901923.IB
MEAN SQUARES
208.84983 »S4
198.955719 -S3
78.4367871 »S2
7.B4B76S04 -SI
S2/S1 - 9 .99606779 DISTRIBUTED AS F< 2 , 2 4 )
63 /S1 - 2S.34B6694 DISTRIBUTED AS F< 1,24 t
8 4 / 8 1 - 26 .6087504 DISTRIBUTED AS F ( 1,24 >
BARTLETT TEST > 13 .915924
F f C P
I n t h e a n a l y s i s of c o v a r i a n c e t h e f o l l o w i n g hypoteses
are t e s t e d :
HI : S2 /S1 t h e l e a s t - s q u a r e s e q u a t i o n s f o r each of d a t a
s e t s can be regarded as p a r a l l e l .
H2 : S3 /51 t h e group means can b . r e g a r d e d as l y i n g on
a l e a s t squares l i n e .
H3 : S4/S1 a s i n g l e ? i n e , t h e o v e r a l l r é g r e s s i e z l i n e ,
i s an adeguate f i t af a l l c a l i b r a t i o n r u n s .
The r e s u l t s of t h e a n a l y s i s of c o v a r i a n c e a r e t h e
f o l l o w i n g s :
RUN 1 1 - 1 2 - 1 3 - 1 4 U-TUBE r e g i o n 7 0 0 - 2 0 0 0 mm
- h y p o t h e s i s HI i s accepted
- h y p o t h e s i s H2 i s r e j e c t e d a t t h e 0 . 0 2 5 l e v e l
- h y p o t h e s i s H3 i s r e j e c t e d a t t h e 0 . 0 0 1 l e v e l
RUN 1 1 - 1 2 - 1 3 - 1 4 U-TUBE r e g i o n 2 0 0 0 - 3 0 7 0 mm
- h y p o t h e s i s HI i s accepted
- h y p o t h e s i s H2 i s r e j e c t e d a t t h e 0 . 0 0 1 l e v e l
- h y p o t h e s i s H3 i s r e j e c t e d at t h e 0 . 0 0 1 l e v e l
RUN 11-12-13-14 U-TUBE region 3160-top
- h y p o t h e s i s HI i s r e j e c t e d a t t h e 0 . 0 2 5 l e v e l
- h y p o t h e s i s H2 i s r e j e c t e d a t t h e 0 . 0 0 1 l e v e l
- h y p o t h e s i s H3 i s r e j e c t e d a t t h e 0 . 0 0 1 l e v e l
I n s p e c t i o n of t h e p l o t of t h e r e s i d u a l s suggested
t h a t run 12 might be t h e source of t h e r e j e c t i o n s of
i •' ii a e t>
the hypothesis. Analysis o-f covariance has been
repeated with calibration run 12 omitted.
RUN 11-13-14 U-TUBE region 700-2000
the three hypothese? are accepted and a -fitting o-f the
overall data has been done.
RUN 11-13-14 U-TUBE region 2000-3070
- hypothesis HI is accepted
- hypothesis H2 is rejected at the 0.025 level
- hypothesis H3 is rejected at the 0.025 level
RUN 11-13-14 U-TUBE region 3160-top
- hypothesys HI is rejected at the 0.025 level
- hypothesis H2 is accepted
- hypothesis H3 is accepted
An overall calibration has been done and presented for
the two upper regions as well.
RUN 11-12-13-14 RUSKA
in the ana lys is of covariance for Rusfca data , the
hypotheses H I , H2, H3 for the d i f f e r e n t regions are
always r e j e c t e d at the 0.001 l e v e l . I t could be due t o
understimation of the pooled var iance abêut the
ind iv idua l l i n e s .
Page 7
RUN 12-13-14 SONAR
the hypotheses of the analysis of covariance are
rejected at the 0.001 level.
An overall fitting of RUSKA, U-TUBE, SONAR data has
been carried out, even if with the analysis of
covariance we obtain results so that the hypothesis of
being a single line, fitting of all groups, was
rejected. Hereinafter the results obtained are
presented together with the residuals plot.
The RUSKA data have been also divided in two groups
and the overall fitting re presented as follows :
a) overall fitting of runs 11 and 14
b) overall fitting of runs 12 and 13
TABLE 23°
U-TUBE REGION 7 0 0 - 2 0 0 0 MM
RUN NUMBER INTERCEPT S ( I N T ) SLOPE S(SLO) RES. VAR
RUN 11
RUN 12
RUN 13
RUN 14
RUN 11-12-
RL'N 11-13-
•13-14
14
-293.6560
-293.9825
-293.7110
-293.1345
-293.9344
-293.5756
.5480
1.5190
1.1897
.9154
.5702
.4682
.927109
.925492
.926683
.926504
.92687
.92687
3.94E-4
1.27E-3
9.88E-4
6. 7911-4
*r.35E-4
3.50E-4
.5287
2.1263
1.2944
1.3696
1.7648
.97048
U-TUBE REGION 2 0 0 0 - 3 0 7 0 MM
BUN-NUHiEB INIERGIEI ÜIMI1 SLQEI SiSLQI RES.._yôR
RUN 11
RUN 12
RUN 13
RUN 14
-'95.9088
-298.1003
-300.9170
-299.5228
1.9417
2.3441
2.7616
1.4128
.92915
.92799
.930598
.930090
7.2oE-4
9.35E-4
1.10E-3
5.33E-4
1.0816
.413
.56sr0
.6524
RUN 11-12-13-14 -299.8491 1.8523 .93022 7.02E-4 2.7156
RUN 11-13-14 -298.5687 1.2441 .92989 4.69E-4 .1.0889
TABLE 24°
U-TUBE REGION 3160-TOP
RUN NUMBER
RUN 11
RUN 12
RUN 13
RUN 14
INTERCEPT
-323.7604
-305.6111
-352.5844
-310.5501
S(INT)
9.2509
3.1563
7.6669
3.7291
SLOPE
.93555
.928930
.944237
.931571
S(SLO)
2.77E-3
9.50E-4
2.30E-3
1.12E-3
RES. VAR.
1.0562
.0456
.2445
• 1553
RUN 11 -12 -13 -14 -321 .4192 8 .0381
RUN 11-13-14 -322 .7314 5 .1226
,93473
.93523
2 .41E-3
1 .53E-3
2 .0864
.72642
RUSKA REGION 700-2000 MM
SUN-NUMBER INI£BÇE,PI I H N H SLOPE i i i L Q l BESi.VARj
RUN 11
RUN 12
RUN 13
RUN 14
-295.2102
-294.6338
-295.3502
-294.3461
.34947
.27545
.39854
.13385
.928508
.926792
.926941
.927222
2.52E-4
2.30E-4
3.31E-4
9.92E-5
.21552
6.98E-2
.14487
.02923
RUN 11-12-13-14 -295.2919 .38633 .92789 2.94E-4 .80821
RUN 12-13 -294.9821 .31254 .92685 2.60E-4 .17903
RUN 11-14 -294.8545 .33247 .92794 2.42E-4 .37602
TABLE 25°
RUSKA REGION 2000-3070 MM
RUN NUMBER INTERCEPT S (INT) SLOPE S(SLO) RE'i. VAR.
RUN 11
RUN 12
RUN 13
RUN 14
-295.23^1
-299.2040
-301.2439
-301.3344
.98591
1.6140
1.86971
.5500
.929233
.929728
.930283
.930887
3.67E-4
6.44E-4
7.42E-4
2.08E-4
.27902
. 1948
.25890
.09873
RUN 11-12-13-14 -300.2724 1.3966
RUN 12-13 -300.1624 1.4499
RUN 11-14 -298.8041 1.2995
.93065
.92998
.93025
5.29E-4
5.77E-4
4.87E-4
1.5434
.31307
1.0384
RUSKA REGION 3160-TOP
RUN_NyMlgR
RUN 11
RUN 12
RUN 13
RUN x4
NIERQEPI__
312.3839
304.2574
313.6535
314.5082
__§iINIi
.52943
2.3208
.397171
.6672
__§L.QPi
.932633
.929648
.932198
.933092
S1S.L.Q!
1.59E--4
6.99F>4
1.19E-4
2.00E-4
-Biii-VOBi
3.49E-3
2.47E-2
6.73E-4
.00496
RUN 11-12-13-14-312.7948 4.9095 .93255 1.47E-3 .78276
RUN 11-14 -313.3671 2.0589 .93284 6.17E-4 .09994
RUN 11 U-TUBF " DEG
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RUN 12 RUSKA NOD. A
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RUN 13 RUSU MOO. A
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RUN 11 U-TUBE HOD fl
RUN I I U-TUBE HOD. C
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RUN 12 U-TUBE MOD. A
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RUN 1 3 U-TUBB NOD. D
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RUN 14 U-TUBE / A
RUN 14 U-TUBK MOD. C
J RUN 14 U-TUBE MOD. D
RUH 12 SONAR MOD. A
RUN 1 2 SONAR MOD. C
• « . -4. •4. •7. • t .
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RUN 14 SONAR MOD. B
HUH 14 SOUR HDD. D
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12
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II
II
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RUN 14 TDR HOD. B
ir- T -^—r i
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I I
IS
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3
I OVERALL CALIBRATION U-TUBE RUN U + 1 2 * 1 3 * l i
J.
« I RUN 11
• » RUN 12
•- » RUN 13
* V RUN 14
I « RUN 1 2
« « RUN 1 3
Y f RUN 1 4
• RUN 11
m • un PII i
OVERALL CALIBRATION RUN 12 - 13 RUSKA
* » RUN 12
• • • • • RUN 13
* RUN 11
• RUN 14
OVERALL CALIBRATION RUN 11*13+14 U-TUBE
« RUN 11
1 «RUN 13
«RUN 14
B A R T L Ê T T ' S T E S T U S I N G ' X ' V A L U E S
T B E — C U M
SECTION 3
CORRECTED CHI SQUARE PROBABILITY L E S S T H A N P=» 0 . 0 5
F-TEST BETWEEN TO WITHIN SLOPES = 9.2767
CORRECTED CHI SQUARE » 1 7 . 9 4 8 8
DEGREES OF FREEDOM = 46"
SECTION 4
CORRECTED CHI SQUARE PROBABILITY L E S S T H A N P = 0 ,05
F-TEST BETWEEN ~n WITHIN SLOPES =0.205?
CORRECTED CHI SQUARE *? . 6 9 4 4
DEGREES OF FREEDOM - 46
SECTION 5
CORRECTED CHI SQUARE PROBABILITY G R E A T E R T H A N P — 0
F-TEST BETWEEN TO WITHIN SLOPES = 2.2503
CORRECTED CHI SQUARE - 1.829?
DEGREES OF FREEDOM • 7
SECTION 6
CORRECTED CHI SQUARE PROBABILITY L E S S T H A N P — 0 . 0 5
F-TEST BETWEEN TO WITHIN SLOPES «0.4520
CORRECTED CHI SQUARE - 1 8 . 7 0 7 9
DEGREES OF FREEDOM » 26
BARTLETT'S TEST USING 'X' VALUES
R U S K«a» — C L 1 M
SECTION 3
CORRECTED CHI SQUARE PROBABILITY L E S S T H A N P== 0 . 0 5-
F-TEST BETWEEN TO WITHIN SLOPES = 2 . 2 3 1 6
CORRECTED CHI SQUARE - 1 1 . 5 9 6 3
DEGREES OF FREEDOM = 46
SECTION 4
CORRECTED CHI SQUARE PROBABILITY L E S S T H A N P = 0 . 1 0
F-TEST BETWEEN TO WITHIN SLOPES = 1.2378
CORRECTED CHI SQUARE • 7.6899
DEGREES OF FREEDOM = 46
SECTION 5
CORRECTED CHI SQUARE PROBABILITY G R E A T E R T H A N P = 0 . 1 0
F-TEST BETWEEN TO WITHIN SLOPES '* 1 .8865
CORRECTED CHI SQUARE «= 8 . 2 4 8 8
DEGREES OF FREEDOM • 7
S E C T I OlvJ <&
CORRECTED CHI SQUARE PROBABILITY G R E A T E R T H A N P = 0 . 1 0
F-TEST BETWEEN TO WITHIN SLOPES = 2 3 . 3 9 3 5
C O R R E C T E D ' C H I SQUARE • 3 . 9 9 6 4
DEGREES OF FREEDOM = 26
B E T W E E N S L O P E S V A R I A N C E G R E A T E R T H A N W I T H I N S L O P E S V A R I A N C E W I T H P R O B A B I L I T Y L E S S T H A N P « 0 . 1 0
RITCEX 12 -B
Evaluation of the Calibration Data of RITCEX
D. Sellinschegg
Kernforschungszentrum Karlsruhe, Karlsruhe, Germany, F.R. of
In the framework of RITCEX (Reprocessing Input Tank Calibration Exercise)
four calibration runs, numbered as RUN 11 to RUN 14, were performed for the
annular input accountability tank of the EUROCHEMIC reprocessing facility,
Mol; Belgium, in January of this year. For that purpose the tank was filled
via a dedicated plastic tube by adding increments of demineralized water.
The additions were weighed by a Toledo scale with a demonstrated standard
deviation for the precision of about 5 g's.
The main purpose of these calibration runs was to compare the performance of
different instruments and techniques which can be used for tank calibration.
In this experiment the following instruments and techniques were investigated.
- RUSKA instrument
- U-tube manometer filled with TBE (Tetrabromidethan)
- SONAR acustic system
- TDR (Time Domain Refleetometer)
- Tracer technique
Unfortunately not all the instruments could be implemented in the tank before
the beginning of the calibration experiment. Table I shows which instrument
and technique was used in each run.
Table I: The instrument and technique used in each run is marked by an X
RUN 11
SUN 12
RUN 13
RUN 14
RUSKA
X
X
X
X
U-tube
X
X
X
X
SONAR
X
X
X
TDR
X
TRACER
X
X
The results of the tracer experiment were not included in this analysis
because the data were not available at the time of the evaluation.
- 2 -
1. Model Assumptions
The data set of one calibration run consists of the observations for the
liquid level and corresponding liquid volume. Let us denote the true value of
the i-th level observation 1. and that of the true volume observation v.. x l
These true values can usually not be observed because of measurement errors. Therefore, we observe the values of the random variables L. and V
l l
which are defined as L. - 1. • *.; i l l
V. - v. • V
for all i observations, i = 1, ..., n. The 4 and c are supposed to
be normally distributed random variables with zero mean.
It is assumed in this analysis that the standard deviation of c.
(d ) is much larger than that of 6, (o . ) , so that we can ci i 4i
write approximately o.. = 0 for all i. The errors e. are also il 1
supposed to be independent of i and uncorrelated amongst themselves. Then we
have
E (4 ) = E U ) = 0, for all;
Var (4 ) « 0, for all;
Var U.) - a2, for all;
Cov (c , c ) * 0, for all i, j » i.
It is further assumed that the true value of the volume can be expressed as a
k-th order polynomial of the true value of the level, so that we can write
vi " Bi + fla1i •" + ^ i 1 ! for all i, k « 1, 2
Then the observed values for the volume can be written as
V. « B + 8 1. + ... + 6. 1. + « for all i. i i a i k+i i
On the basis of the observed calibration data (V , 1.), i » 1, ..., n, we
wish to find estimates for the parameters S , ..., fl. The order k i k+i
of the polynominal can be determined, at least approximately, from the
- 3 -
geometrical form of t>e tank. Under these circumstances the estimation of the
parameters B in question is a classical regression problem.
Remark; One might argue that the assumption of o^ = 0 for all i, i.e. no error in measuring the level, is not a very realistical one because the error in measuring the volume should be very small due to the very small error in weighing the additions and due to the dedicated plastic tube through which the increments were poured into the tank. So the opposite assumption of oc± = 0 might seem to be more appropriate. But it was shown, e.g. for a linear relation between V | and lj *, that the estimates for B turn out to be almost the same in both c*ses.
In practice we wish to estimate the volume of liquid in a tank on the basis of
a measurement of the corresponding liquid level. This can be determined after
a calibration experiment was performed and the parameters B in question A A
were etimated (B ) . Then the estimate of the volume (V ) can be written as
V. = B + B L. + ... + Î. L* for all i, k = 1, 2,... l x a l k+i i
The uncertainty in the estimates B cause a systematic error in the estimate
V.. In the following the estimate of the standard deviation of B is
denoted as 9 and that of the systematic error of V. is denoted as fik i
vi
2. Comparison of the Performance of Different Instruments
In this analysis the performance of the different measurement instruments
considered in the experiment is compared for the linear part of the tank; i.e.
the part of the tank for which a linear relationship between the volume and
the level is to be expected according to the mechanical drawings. In the case
of the considered input accountability tank the linear part of the tank should
start at levels larger than 700 mm.
2.1 Results
The data set obtained with a specific measurement instrument was at first
evaluated separately for each calibration run in order to determine the
estimates for the parameters B. Then the data sets of the four calibration
runs were combined to one data set and the parameter 8 were estimated on the
basis of the combined data set. The results tor the different measurement
instruments are given in Table II to Table V.
- 4 -
Table II: Results for the linear region from 700 itm to 3455 ran obtained by using the RUSKA Measurements
RUN 11
RUN 12
RUN 13
RUN 14
RUN 11 c o 14
[J -293.41
-294.97
-259.46
-294.35
-294 . / 0
°9 ,
0.88
0.56
0.83
0.75
0.48
[l/mm]
0.9277
0.9274
0.9273
0.9276
0.9278
0 2 [1/mm]
0.00034
0.00035
0.00039
0.00029
0.00019
V
w 0.45
0.63
0.69
0.39
0.28
When we compare the estimates for the intersection (fl ) and for the slope
(fi ) obtained with the RUSKA measurements (Table II) and that obtained
with the U-tube measurements (Table III) then we find that these estimates are
rather close together. But the estimated standard deviation for these
estimates (5 and o„ ) is larger for the U-tube measurements Bl 02
than that for the RUSKA measurements. This was to be expected because the
RUSKA instrument is known to be the instrument with the highest precision.
The estimated standard deviations o- and «•• in the case of the SONAR -Bl B2
and the TDR measurements, however, are almost one order of magnitude larger
than that obtained with the RUSKA measurements. For that reason the SONAR and
the TDR instrument should not be used for safeguards purposes for the time
being. Further work is needed to increase the precision of these instrument?. An important question is whether the assumed error model does described the
observed data properly or not. The definition of the volume residual should
help in analysing this question. The volume residual (VR.) is defined as
VR. V, - T . i • 1, ..., a;
i.e. the volume residual is the difference between the observed volume (V^)
and that volume (V ) which is estimated according to the corresponding level
observation. The estimate of the standard deviation of the systematic error
in the volume residual is obviously 3 ., the estimate of the systematic
error in V,, because the volume measurement is assumed to have a random
error only. The value for $ is given in the Tables for a full tank or a
level of 3455 mm.
- 5 -
Table III: Results for the linear from 700 mm to 3455 ram obtained by using the U-tube Measurements
RUN 11
RUN 12
RUN 13
RUN 14
RUN 11 t o 1A.
A
[l]
-292.76
-292.61
-294.07
-293.16
-293.45
0 .99
1.12
1.05
0 .86
0 .56
h [l/mm]
0.9270
0.9253
0.9272
0.9270
0.9270
e 2 [1/mm]
0.00038
0.00052
0.00049
0.00033
0.00023
V
W
0.51
0.94
0.88
0.45
0 .33
Table IV: Results for the linear region (700 nm - 3455 mm) obtained by using the SONAR Measurements
RUN 11
RUN 12
RUN 13
RUN 14
RUN 11 t o 14
A
»1
-
-339.51
-326.36
-320.30
-328.57
li]
-
9 .19
4 .42
2 .72
3 .00
3 2
[l/mm]
-
0.9338
0.9328
0.9313
0.9335
A
[l/mm]
-
0,00446
0.00204
0.00106
0.00125
V
W
-
8.12
3 .62
1.43
1.93
Table V: Results for the linear region (700 ran - 3455 mm) obtained by using the TDR Measurements
RUN 11
RUN 12
RUN 13
RUN 14
RUN 11 t o 14
A
CiJ -
-
-
-201.46
-201.46
\ •
-
—
-
4 .30
4 .30
[l/mm]
-
~
-
0.8983
0.8983
[l/mm]
-
—
—
0.00191
0.00191
V
-
""
(—
3.03
3.03
- 6 -
In the following the volume residual is calculated with that volume estimate A
V. which is based on the combined data Sit of the four calibration runs, l
The obtained volume residuals as well as the one-o*—bound is plotted
versus the observed level in Fig.l to Fig.4.
• 5.0
4
3
Z 2
5ll
20, en
a. 1 ÜJ
.0
.0 ..
.0 ..
.0
0
0 ..
0
.0 |
.0
0
cane a- bound v
i i 1 i i •
0 350 700 1050 1400 1750 2100 2450 2800 3150 3500
HEIGHT mm
SYMBOL/RUN: a l l ; • 12 ; o 13 ;x 14 s
Fig. 1: Results obtained with the KUSKA Measurements
^seyj 0 350 700 1050 1400 1750 2100 2450 2800
HEIGHT (MM)
SYMBOL/RUNs o 11 •• 12 $o 13 jx u ,
500
Fig. 2: Results obtained with the U-tube Measurements
- 7 -
+ 25.0L
20.a.
is.a.
Z ia.a.
-J 5 . 0
2 0 -0 «n tu K
UJ
3 _! O >
5.0
ia.a.
is.a.
20.a .
- 2 5 . a 0
H 1 1 1—t——I 1-
350 700 1050 fteg^jVso
HEIGHT (MM)
SYMBOL/RUN: a 12 ;o 13 ?o14 ;
+ 25.0,
1050 1400 1750 2108 2450 2800 3150 3500
SYMBOL/RUN.' a 14 ;
HEIGHT IMMJ
- 8 -
In Fig.l and Fig.2 the volume residuals are shown foi the RUSKA and the U-tube
measurements. From these figures we find first of all that there is a
significant deviation from the expected linear relationship between the volume
and the level between a level of about 3070 mm and 3165 nan. In this section
of the tank a volume contraction of about 6 liters is indicated. A detailed
analysis of the mechanical drawings of the tank showed that the internal
decontamination line is installed in this section of the tank. This
decontamination line ccasists of a horizontal ring-tube which has a number of
small nozzles which arc pointing toward the top of the tank. The ring-tube is
fed by a vertical tube. The decontamination line is operated by a steam jet
which is located at the lowest point of the vertical tube. Obviously the
small nozzels were plugged up during the calibration runs, so that the
ring-tube was not filled with water.
The next observation from the volume residual plots is that the systematic run
to run difference of the volume residuals is significantly larger than would
be expected according to the one-o*-bound for the systematic error. This
is true for the RUSKA, the U-tube and the SONAR measurements. The TDR
instrument was only used in one calibration run, so no statement can be made
in this case. It should be noted that the significant systematic run to run
difference indicates that the assumed error model does not describe the
observed data adequately; I.e. there mutt be a systematic error contribution
in the measurements. This phenomenon can best be seen in the RUSKA
measurements, Fig.l because of the very small random measurement error.
In the case of the U-tube measurements, Fig.2, we find that the reading error
turns out to be so large that the systematic run to run difference becomes rr.t
that obvious. In any case there seems to be an error in the observations of
RUN 12.
For the SONAR measurements we find from Fig.3 that the random measurement
error is rather small. But there seems to be a significant systematic
measurement errcr. In the observations of RUN 12, also there» seeu.i to be en
error.
- 9 -
When we compare Fig.l, Fig.2 and Fig.3, then we find that the systematic run
to run shift observed with these measurement instruments goes into the same
direction. This is not true for RUN 12. but in this run there seems to be a
problem in the U-tube and the SONAR measurements. The same direction of the
systematic run to run shift indicates that there might be a systematic effect
which comes from the calibration procedure and whicu has nothing to do with a
systematic measurement error of the instruments.
2.2 Reasons for a Systematic Run to Run Shift
What caused the run to run shift is not known for the time being,
nevertheless, there are some reasons which might be responsible or do at l»ast
contribute. Some of these reasons are discussed in the following.
2.2.1 Addition of Tracers
In order to examine the performance of the tracer technique a tracer was added
to the water during the calibration procedure of RUN 12 and RUN 13. It should
also be noted that in these two runs a lower number of additions was forseen
than in RUN 11 and RUN 14. It is well known that the performance of the
tracer technique is strongly dependent on the homogenous distribution of the
tracer in the liquid. For that purpose air sparging was done before a sample
was taken. Overall there was a two hours air sparging period in each of those
two calibration runs. But air sparging causes evaporation. Thus evaporation
might be one reason why a significant difference is observed between the runs
with and without a tracer addition which can best be seen in the RUSKA
measurements, see Fig.l.
2.2.2 Change of Implemented Instruments
Unfortunately not all the different measurement instruments could be installed
in the tank before the beginning of the calibration runs. For that reason the
observed liquid volume and the corresponding level observation did not
represent the normal situation of the tank and a correction had to be made.
In practice the volume of the installed instruments was geometrically
determined and added to the observed volume of the water. These corrected
volume values were used in the evaluation.
- 10 -
At the end of the four calibration runs all the installed instruments were
removed from the full tank and the change in the level observed with the RUSKA
instrument was recorded. A change of about 2.2 mm which corresponds to about
2 liters was observed. The geometrically determined volume of the instruments
was about 1.63 liters. Thus the volume correction might have introduced a
systematic error.
2.2.3 Different Pressure Drop in the Probes
At the beginning of each calibration run the pressure in the level and the
reference probe was measured with the RUSKA instrument. It is to be noted
that the level probe dit not dip into the water at this time. The observed
values show that the pressure drop changed from run to run though it was tried
to keep it constant by a proper adjustment of the rotameters. Obviously the
setting mechanism of the rotameter is not sensitive enough to do a proper
adjustment. A reasonable correction for the different pressure drop at the
beginning of each run could not be made, because the pressure drop is changing
throughout the whole calibration process. For that reason the difference in
the pressure drop from run to run was simply neglected j.r. the evaluation which
caused a systematic error in the data.
2.2.4 Temperature Gradient in the W»*dr
The temperature of the cell in which the tank was locacted was rather constant o
over the time and measured to be about 19 C. The temperature of the room
in which the water increments were weighed was also rather constant and o
measured to be about 20 C. The weight of each increment of water was
determined by measuring the gross and tare weight of a weight tank with a
volume of about 230 liters. This weight tank was filled up with water which
had to be pumped up from a special tank in the plant. The température of the
vater in the weight tank was measured when the tank was full. This o o
temperature changed between about 25 C and 28 C. For that reason the
temperature of the water increment was in any case higher than that of the
tank. The build-up of a temperature gradient in the water of the tank to be
calibrated was to be expected.
In calibrating a tank we are interested in the relationship between the volume
and the level of the tank. Actually we are measuring the weight of the
increments and the pressure of the level and reference probe as far as the
- 11 -
RUSKA and the U-tube measurements are concerned. In order to determine the
volume and the corresponding level of the liquid in the tank we have to divide
the weight of the increments and the pressure difference between the level and
the reference probe by the density of the liquid. But this becomes a problem
when the liquid has a temperature gradient because in this case we would need
a number of density probes or thermocouples which are installed at different
levels in order to determine the density. However these were not available in
this experiment. The tank temperature was measured at the bottom of the tank
and this temperature was used to determine the density. For that reason we
know that we do have an error in the density which increases with an increase
in the level. Ve know further that the observed values for the volume and the
level are directly correlated. This is a point which is not taken into
account in the error model.
It should be noted that the temperature gradient was not the same in each run
because, firstly, the number of additions were different in the runs with and
without tracer addition and secondly the calibration procedure with the same
amount of additions did take different times due to various unforeseen
problems.
2.2.5 Systematic Shifts in the Pressure Measurement
Let us for a moment look at Fig.l again in which the volume residuals versus
the level of the tank are plotted for the RUSKA observations. Then we find in
the case of RUN 11 a positive shift of the voluae residuals of about ona liter
between the level of 1750 mm and 2800 mm. An attempt was made to find out
what the reason for that shift might be. For that purpose the observed
pressure increase in the level and in the density probe was examined for each
addition. The pressure increase in both probes should obviously be the same
when both probes dip into the water. The analysis showed that the observed
pressure increase is usually the same in both probes with an error of about o •
+ 0.05 mm H,0, 0 C. In RUN 11, however, a difference is recognized for
that observations which coincide with the beginning and the end of the
observed shift in the volume residuals. This indicates a change in the
pressure of a probe which might be caused by an irregularity of the
rotameter. In this case the pressure in the level probe was suddenly lass
than it should be and became normal after a while. It should be noted that
this problem coulc'. only be identified with the RUSXA instrument, because this
- 12 -
instrument allows to measure the absolute pressure in the probes and not the
pressure difference of two probes, the standard procedure by using U-tube
manometers.
2.3 Conclusion
The comparison of the results obtained with the different measurement
instruments made evident that the accuracy of the SONAR and the TDR instrument
needs further improvement before it can be used for safeguards purposes. On
the other hand it became clear that the use of the RUSKA instrument opens a
new dimension in tank calibration. The precision of this instrument seems to
be so high that almost the real relation between the volume and the level of a
tank can be determined. The evaluation of these calibration data showed,
however, that there are systematic shifts from run to run which cannot be
resolved at the moment. A number of reasons which might be responsible for
the systemic run to run shift were mentioned. It seems that some of the
reasons could have been eliminated by a proper design of the experiment, if
one would have known before that these reasons might play an important role.
In this sense RITCEX was a very valuable and interesting experiment in order
to show where we are and what problems should be attacked further.
3. Determination of the Calibration Curve of the Tank
It was mentioned before that the assumed error model does not adequately
describe the observed data points because of the significant systematic run to
run difference. But on the other hand we don't know where the systematic
errors come from. Thus an adequate error model cannot be defined at the
moment. For that reason the calibration curve of the tank is determined by
using the assumed error model, though it is known to be inadequate, just for
demonstration purposes.
In order to determine a somewhat realistic calibration curve the tank was
subdivided into 6 different sections which are given in Table VI.
- 13 -
Table VI: Subdivision of the input accountability tank
Section
NL-I
NL-II
L-I
L-II
L-III
L-IV
From Level
Qnm]
0
350
700
2000
3070
3165
To Level
[mm]
350
700
2000
3070
3165
3455
Relationship
Volume/Level
v. = B,+S2V*3Li
v. - «,*82L i+83Lj
V. - 81+ê2L.
V. - ^Î2L.
V. - 61+ê2L.
V. - 61+62L.
The annular tank should according to the mechanical drawings be divided into
two parts. The one which starts right at the botton of the tank should have a
non-lineur relationship between the volume and the level. And the other part
up to the top of the tank should have a linear relationship between the volume
and the level.
As can be seen from the table the non-linear part was divided into two
halves. In the first half the volume should be a aecond order polynomial In
the level. This should also be true for the second part, but In this case the
parameters B should be different.
According to Flg.l the linear part of the tank turns out to be not linear la
practice. Por that reason this part of the tank was subdivided Into four
linear sections.
- 14 -
For each section an estimate of the parameters B in question was determined on
the basis of the four calibration runs; i.e. the data set of each calibration
run was combined to give a combined data set and the latter was used for the
estimation of the parameters. The results are given in Table VII to Table IX.
Table VII: • Parameter Estimates for the calibration curve obtained for the MJSKA Measurements
Section
NL-I
NL-II
L-I
L-II
L-III
, x v
0.8279
-2.5962
-295.29
-300.27
-8.81
-307.59
0.0604
0.0773
0.9279
0.9307
0.8360
0.9310
h 0.00064
0.00062
-
-
-
Table VIII: Parameter Estamites for the calibration curve obtained for the U-tube Measurements
NL-I
NL-II
L-I
L-II
L-III
L-IV
>i
0.7098
-3.3683
-293.35
-299.86
37.21
-313.73
h 0.0641
0.0813
0.9265
0.9302
0.8210
0.9325
B3
0.00063
0.00061
-
-
-
-
- 15 -
Table IX: Parameter Estimates for the calibration curve obtained for the SONAR Measurements
Section
NL-I
NL-II
L-I
L-II
L-III
L-IV
8.
-
-185.44
-303.89
-356.30
76.23
-527.54
e2
-
( .6754
0.9131
0.9432
0.8041
0.9948
B3
-
0.0O012
-
-
-
-
For a more illustrative presentation of the results the volume residuals and
the corresponding estimates for the standard deviation of the systematic error
were determined for each section of the tank. The results with the
one-0«-bound were plotted in Fig.5 to Fig.7.
+ 5.0
4.0
3.0
Z 2.8
20.0 V)
S 1.9 1
| 2 . .
53.0 1
4.0
-5 .0
NL-I NL-II
j - * * > • * ; ; ;
L-I
sa s 4
L-II
- » » • »
L-IV
i i i i i i 1 i * 0 350 700 1050 1400 1750 2100 2450 2800 3150 3500
HEIGHT CMH)
SYHBOL/RUNi o i l >• 12 « 13 >* 14 j
Fig. 5: Volume residuals of the calibration curve obtained with the SDSKA Measurements
- 16 -
0 358 700 1050 1400 1750 2100 2450 2800 3150 3500
HEIGHT (MM)
SYriBOL/RUN: a H •• 12 ; o 13 jx H •
Fig. 6: Volume residual of the calibration curve obtained with the U-tube Measurements
0 350 700 1050 1400 1750 2100 2450 2800 3150 3508
HEIGHT inn)
SYMBOL/RUN: o 12 ;»13 jo U ;
Fig. 7: Volume residual of the calibration curve obtained with the SONAR Measurements
- 17 -
We see from these figures that the subdivision of the non-linear part is well
taken while that of the linear part could be improved. This is especially
true for the second linear section. We should keep in mind, however, that
these calibration runs were not performed in order to determine the best
calibration curve of that tank but to demonstrate the performance of different
instruments and to identify problems.
4. References
1. D. Sellinschegg, 6. Negele, Franssen, "Evaluation of Tank Calibration Data
in RITCEX, ESARDA Symposium 1984.
<RC ZZT> •* - '6
RITCEX 12 -C
1644H
TARA Evaluation of RITCEX Calibration Data
H. Shimo.iima
S. Suda
K. Charwal
I. Data Evaluation
The data analyses contained in this report are limited to RITCEX
calibration runs 11 and 14 since data from runs 12 and 13 were found to be
significantly different. The aeasured and derived data are shown in
Attachment 1. The small differences between the data normalization
algorithms suggested in RITCEX report, dated 28 nay 1984, and those used in
this report are summarized below.
A. Measurement data.
1. Ruska_read RITCEX data sets o
«Het pressure in mm H_0 at 4 C,
ASTM reference: E380-77
2. Mass RITCEX data sets
«Cumulative net weight corrected for
buoyancy of water at ambient conditions,
NBS reference: Report 10396, 1973
by R. Schoonover and J. Houser.
3. Temp RITCEX data sets
«Water temperature in tank based on
thermocouple readings.
* RUSKA calibration software
- 2 -
Density Recalculated off-line
'Density of water at tank temperature o
relative to 4 C, NES reference:
PTB-Mittoilungen 6-71,
by H. Wagenbreth and W. Blauke.
Volcor RITCBX Report BSPSI No. 4
15 April 1984, F. Franssen corrections for
volumes displaced by instrument probes
installed in the calibration
Normalized data.
1. True-lq-lv (HA> Suska read/Density * mm H.O at 4 C.
2. Volume 1 Mass/Density » liters H.O at 4 C.
3. Volume 2 Volume 1 + Volcor » net volume corrected
for instrument probes.
Data normalization of the measurement data invlove the following steps.
1. Bubble probe (pressure) readings are converted to the adjusted
height (true liquid level) based on the solution density at the tank
temperature. On-line determination of the density involves a
temperature correction for the probe separation. The result is o
corrected to the reference calibration temperature of 4 C.
Temperature correction factors for the volume are probe and height
dependent and must be determined by a term by term basis in the
measurement equation.
- 3 -
II. Data Analysis Procedures
The general procedure for the analysis of tank calibration data is
outlined in Figure 1 (Attachment 2). Step 1 for these data was preformed by
SCK-CBN MOL. The results of step 2 were summarized above.
Step 3 involved the examination of the runs for internal consistency
and/or between-run agreement (alignment) based on linear equation fits of the
runs. The partitoining of the tank into six regions is based on the break
points proposed by SCK-CBN MOL.
Data recombination shown in step 4 involves the joining of the respective
data sets into regional data sets which are then used to generate the
"average** calibration equations for each region as
III. Least Squares Fitting of RITCEX Data
The measurement equations for the RITCEX tank, based on the fitting of
the inverse model to the six regions, is shown in Attachment 3. Since the
classical and inverse models are algebraically equivalent, they give
identical numerical results. For polynomials of order higher than two,
volume approximations for the classical model using numerical techniques are
available. The inverse model has been chosen because of its ea«e of
application, in particular, with respect to making temperature corrections
when a polynomial equation is fitted.
Attachment 3 contains a listing of the normalized data for each region
(run 11 data points followed by run 14), the usual results of the regression
parameters, the plot and coefficients of the fitted curve, and a list and
plot of the volume residuals.
- 4 -
IT. Measurement Equation
The objective of fitting a curve to the calibration data is to produce a
measurement equation which, when given a liquid level reading, (adjusted
height » H ) calculates the volume of solution in the tank. The form of
the equation is
Vol(liters) » Fn (H )
The breakpoints and measurement equations are summarized in Attachment 4.
V. Analysis of Volume Differences at the Break Points.
Attachment S contains a listing of the differences in volume for liquid
level readings at the break points. Liquid level values for plus and minus 2
of the five break points, at 0.2 intervals, hava been calculated. The second
and third columns, respectively, are the calculated volumes based on the two
equations jioning at the break point. This analysis shows that the mismatch
of equations 1 and 2 is approximately 60 millilitres of liquid. The values
for the other break points are 0.13, 0.9S, 0.43, and 2.1 litres, respectively.
- 5 -
Techniques for Reducinn Systematic Deviations.
1. Determining a cell pressure (vapor head) reference for estimating
the effect of run-to-run pressure drop differences.
2. Use of remote reading and setting rotometers to monitor and control
the bubbler probe air flow.
3. Precalibration testing to estimate the effect of entrained air on
the preesure probe density.
4. Using super increments that span 10 to 15 normal size increments to
estimate the effect of cumulatve error
5. Using mass data storage for unattended collection of temperature
data Uuring the cool down cycle.
- 6 -
Techniques for Evaluating, Calibration Curves.
1. Preperation of seperate calibration curves for the level and density
probes (and high level alarm probe, when available).
2. Analysis of volume offsets at the breakpoints
3. Simulation studies to compare effects associated with the model's
temperature correction algorithms on the volume.
f - . -
Table 1. Call Pressure (vapor head) Measurements
Sun # Start Finish Bange
11
12
13
14
111.38
144.44
112.05
142.29
109.16
136.73
108.32
141.77
6.35
35.28
4.51
2.59
noL- I«« Attachment 1.1 2 * 1 * r i l * n u i : * U N « Î ; : F 3 , 8 HuabffP Of a D l t r v t t t o n » : 73 Nuaber of u « r i * b l * « : S
V*r4*bl«i ntmw%: 1. 2. 3. 4. 5.
Ru»*»_r»»d n«»» T*nlt_T««ip D«n»7t J
Vol corr
TB1LE OF OBSERVATIONS
ors» i 2
a 9 ia tt 12 13 14 13 IS 17 IS 19 28 21 22 23 24 23 26 27 28 29
:a :i 32
:s :4
:-s •6
27 29 Î9 40 41 42 43 44 45 46
Vvtabl* »1
6.073 7.373 17.417 31.339 199.387 151.381 186.177 217.499 248.038 271.772 293.379 317.313 347.9*8 493.711 430.693 494.769 334.658 371.679 688.303 631.336 684.273 716.863 743.726 797.213 952.298 «03.938 937.633 1014.234 1067.038 1279.966 1499.965 1712.346 1763.668 1313.382 1372.nee 1923.338 1978.388 2831.424
2888.213
2141.338 2336.317
2488.399
2462.132 2318.728
2372.215 2622.104
v». t*b1« »2
1.2308
1.3388 1.9378 3.6140
13.1828 24.3768 34.2010
44.2040
34.9660 64.3210 74.4'40
34.38*0 99.3130
129.3910 138.2890
187.4328 216.0820 244.4120
274.1960 310.6398
348.9430 370.2880 397.7878 443.4118 496.2718 343.6688 393.8390
646.2600 693.0038 392.8708
1893.9930 1293.3820 1343.7718
1392.6030 1442.9310
1492.1080 1340.9588 1398.2298 1643.4248 1692.9230 1893.4100
1942.3630
1991.8828 2044.2380 2C93.8198 2139.892C
nOL-IRER
V*ri*bl« »3 v i r i u l c «4 V
19.3900
19.4300 19.4400
19.1300
19.3000 19.C38S 19.7100
19.8588
20.0200 20.0200 20.2200 20.2000 20.2600 20.6888 28.6088
28.6888 20.6300 20.7100
20.7300 20.7900
20.7900 20.7400
20.7400
20.7300 20.7400
20.7700
20.9000
28.5288 20.«400
21.1100
21.2888 21.3388 21.5388 21.6488
21.6580 21.6788 21.6738
21.6988 21.7100
21.7100
21.6200 21.6600 21.6300 21.6400
21.6708
21.7280
1 >84
5 )84 5 )84 5 '84
5 >83 1 «83 5 >83 5)83
1'82 5 >82 1)82 5 >82 5 >82 5)81 5 )9I
1)81 5)81
i >ei 5 '81 5)81
1)81
1 >81 1 '81
1 >8t 1 '81
: «ai 5)81 5 )81
1 >Sl 1>b0
< '88 5 )79 1 )79 1 >79 5 >79 1)79 1 »79
1 >79 1 (79 1)79 1 >79 1 )79
1)79 1 >79 1 >79 5)79
triabl* «3
8.0080 0.0008 9.3008
0.8800 8.8000
0.0000 0.0000 0.9800
0.0000 0.8008 8. 0880
0.0000 8.0800
.0100
.3180
.0100
.0180
.8100
.0100
.3200
.8280
.8200
.0200
.3200
.3200
.3200
.3300
. 3300
.0300
.0400
.0400
.0300
.9300
.8600
.8680
.9600
.3600
.8600
.8680
.0700
.9700
.0808
.9888
.8888
.3888
.9888
47 40 49 30 31 32 S3 !4 Î3 36 37 33 39 60 «1 62 63 «4 <3 <6 67 68 69 78 71 72 73
2678.313 2733.714
2739.833 2036.332 2896.136 2932.390 2972.364
2996.904 3020.636
3040.918
3063.119 3003.944
3109.319
3132.361 3134.910 3176.439 3190.449 3220.726 3273.678 3323.717 3379.474
3339.328 3402.761
3414.309 3423.737 3434 732
3444.607
2192.1360 2243.3900 2294.6633 2337.9190 2293.3368 2446.0098 2464.3310 2407,1120
2309.0960
2320 0166 2346.7000 2369.0070
2343.3423 2607.6170 2627.4003
2647.4300
2667.9090 2603.7020 2738.1700
2796.7090
2836.6033 2343.0228 2933.3390 2063.0730
2877.0000
2000.1668 20*7.4390
21.7100
21.7200 21.7400
21.7300
21.7600 21.7300 2i. 7330 21. 7900 21.3000
21.3188
21.8180 21.0200 21.0180
21.0300 21.7900
21.0200 21.8480 21.0300
21.0660 21.0200 21.7800
21.7600 21.0200 21.7300
21.0000 21.7830
21.7900
5 >79 .3900
1)79 .0900 5)79 .0900 5)79 .8900 1)79 .8900
1)79 .0900 1)79 .1000 1)79 .1080 5)79 .1000 1)79 .1000 1)79 .1000 5)79 .1880 1)79 .1000 5)79 .1000
5)79 .1008 5)79 .1888 5)79 .1888
5)79 .1888 5)79 .1108 5)79 1188 5)79 .1188 5)79 .1188
5)79 .1180 5)79 .1100 5)79 .1180 1)79 .1100 5779 .1100
1 .2
ONBLYSIS of VESSEL CALIBRATION BRT*
rtOL-iBEA
D t i * r n « nam*: C R L l t : F 9 , i Nw«b«r of o O i t r v « t ! 4 / i f : 73 Nuabir of u t r ' A b ) * * : 2
v » r i 1. T>u« ïa Iv 2. Vo lu i l 2
T B I L E OF OBSERVATIONS
nOL-ISE*
v * r i *b 1 * «1 V v i t l t «2
1 6.883 2 7.3SS 3 '7.446 4 31.621 S lie.889 » 151.433 7 186.493 8 217.874 » 248.474 8 272.249 1 296.11* 2 318.887 3 348.39* 4 484.4C8 3 431.343 6 4*3.783 7 533.«38 8 372.764 » «89.Sua 8 «32.382 t 683.383 2 717.428 3 747.143 4 798.731 3 833.928 6 987.3*8 7 939.488 8 1818.223 9 1869.133 8 1282.381 1 1382.998 2 1716.891 3 1769.343 4 1822.189 S 1874.733 6 1944.382 7 1982.739 8 2833.699 » 2892.619 8 214S.834
1.234 1.342 1.963 3.638 13.223 24.647 34.388 44.333 33.129 «4.311 74.633 84.637 99.614 136.888 138.788 186.842 216.739 243.179 273.837 311.647 342.823 371.438 399.842 446.613 497.832 347.383 393.732 648.321 697.222 994.943 1999.338 1297.868 1348.219 1397.238 1447.788 1497.126 1346.143 1393.383 1646.963 1698.636
1 2361.248 2 2413.933 3 2467.312 4 2924.6*2 3 2377.617 6 2627.634 7 2684.162 9 2741.499 9 2793.737 9 2942.339 1 2993.299 2 2939.143 3 2979.979 4 3963.336 3 3927.9*9 * 3847.397 7 3869.64S 9 3992.326 9 3116.443 * 3139.249 1 3161.619 2 3193.214 1 3299.294 4 3227.692 3 3299.699 6 3332.919 7 339*.632 9 3396.394 • 3419.919 9 3421.394 I 3439.994 2 3442.949 3 1432.911
1899.738 1946.993 1999.3*9 2931.989 2169.691 2147.199 2199.342 2232.929 2392.499 2343.994 2491.613 2494.327 2472.99* 2499.799 2317.621 2336.83* 2337.692 2377.993 2397.97* 2*16.727 2636.642 2636.667 2677.38* 2*96.163 2747.732 2796.421 2*46.342 2*33.694 2666.289 2679.892 2**7.911 29*9.1*1 2997.391
1.3 CSLISffftTION RUN OF l . - ï î - T O H K t R I ^ C E X T»»-K Î 2 1 - 4
D a t a f i l » n u t : «UN» 14: F 8 , i Nuaber o f o b s e r v a t i o n s : 71 Nuaber o f v a r i a b l e s : 5
V v t a M t i n w t i : 1 . 2 . 3 . 4 .
» u » k » _ r » » d nass Tank_Te«c> D e n s i t y
3 . Vo l C o r r
TRBuE OF OBSERVATIONS
CALIBRATION «UN OF l ' 2 3 - T H N K ««[TCEX Tfi>K 2 2 1 - 4
OIS» l 2 3 4 S 6 7
a 9
ia i i 12 13 14 13 16 17 ia 19
:a 21 22 23 24 23 26 27 28 29
:a 31 22 33 54
:s 26 : 7 58 Î 9 49 41 42 43 44 43 4C 47 4a
V a r i a b l e »1
^rrrrr" 7 . 4 3 8
9 3 . 2 2 1 1 4 1 . 9 1 9 1 7 8 . 2 1 8 2 8 9 . 8 2 3 2 4 2 . Ó49 2 6 7 . 8 B S 2 9 2 . 9 9 2 3 1 3 . 6 9 1 3 3 4 . 3 3 3 3 3 3 . 3 3 9 4 8 9 . 3 6 9 4 3 3 . 2 9 8 4 9 8 . 6 7 9 3 3 6 . 2 8 3 3 8 3 . 4 8 2 6 1 8 . 8 1 9 6 3 2 . 7 8 8 6 8 6 . 3 8 2 7 1 7 . 4 2 9 7 4 9 , 9 6 1 9 8 2 . 3 6 7 3 3 9 . 8 8 6 9 1 3 . 3 2 9 9 6 6 . 9 2 4
1 9 2 8 . 6 9 3 1 9 7 3 . 6 3 6 1 2 9 1 . 7 1 3 1 3 8 8 . 8 2 8 1 7 2 3 . 3 9 4 1 7 7 7 . 7 9 8 1 8 3 4 . 3 1 7 1 8 8 8 . 1 7 4 1 9 4 2 . 2 1 6 1 9 9 7 . 8 7 6 2 8 3 1 . 2 8 ? 2 1 8 4 . 2 9 4 2 1 3 7 . 9 1 2 2 3 7 2 . 8 2 3 2 4 2 9 . 4 1 7 2 4 8 1 . 4 4 8 2 3 3 3 . 4 9 1 2 3 8 9 . 1 1 9 2 6 4 4 . 7 9 3 2 6 9 7 . 7 6 1 2 7 3 1 . 9 6 9 2 8 9 4 . 6 4 9
V a r i a b l e «2
*^**f fS~ . 7 8 9 9
1 1 . 4 9 9 9 2 1 . 3 2 9 9 3 1 . 3 9 9 9 4 9 . 9 7 9 9 3 2 . 6 3 9 9 6 2 . 3 8 8 9 7 2 . 9 3 9 9 8 2 . 2 2 8 9 9 2 . 2 3 9 9
1 8 1 . 7 1 9 9 1 3 2 . 3 9 9 9 1 6 9 . 8 3 9 9 1 8 9 . 7 4 9 9 2 1 6 . 7 3 9 9 2 3 3 . 1 3 9 9 2 8 2 . 2 9 9 9 3 1 1 . 4 9 9 9 3 4 2 . 1 3 9 9 3 7 9 . 7 6 9 9 4 8 9 . 8 3 9 9 4 4 9 . 3 4 9 8 3 9 1 . 7 9 9 9 3 3 1 . 7 4 9 9 6 9 1 . 7 3 9 9 6 3 1 . 4 7 9 9 7 9 2 . 2 9 9 9 9 9 2 . 6 3 9 9
1 1 9 3 . 1 8 9 9 1 3 9 4 . 9 6 9 9 1 3 3 3 . 4 6 9 9 1 4 9 3 . 8 6 8 9 1 4 3 3 . 3 2 8 6 1 3 8 3 . 3 6 9 8 1 3 3 6 . 3 4 8 8 1 6 9 6 . 9 7 9 9 1 6 3 6 . 3 3 9 9 1 7 9 6 . 3 3 9 9 1 9 9 6 . 9 9 9 8 1 9 3 9 . 7 7 8 6 2 9 9 9 . 9 6 9 9 2 9 3 8 . 8 6 9 9 2 1 9 7 . 6 4 9 9 2 1 9 9 . 2 4 9 9 2 2 9 9 . 4 9 9 9 2 2 3 9 . 8 9 9 9 2 3 9 7 . 9 2 9 9
V a r i a b l e »3 V a r i a b l e »4
-4-8T7Î89 1 6 . 3 8 8 8 1 8 . 3 6 8 8 1 8 . 9 4 0 8 1 8 . 8 1 8 8 1 8 . 8 8 8 8 1 8 . 9 8 8 8 1 8 . 9 3 8 8 1 8 . 9 9 8 8 1 9 . 8 9 8 a 1 9 . 9 1 8 9 1 9 . 1 1 8 8 1 9 . 1 8 8 8 1 9 . 2 3 8 8 1 9 . 2 6 8 8 1 9 . 3 2 8 8 1 9 . 4 3 8 8 1 9 . 4 9 8 8 1 9 . 3 9 8 9 1 9 . 2 6 9 9 1 9 . 2 2 8 9 1 9 . 2 2 8 9 1 9 . 2 4 8 8 1 9 . 2 3 8 8 1 9 . 3 8 8 8 1 9 . 3 1 8 8 1 9 . 3 3 8 8 1 9 . 4 1 8 8 1 9 . 3 9 8 8 1 9 . 7 9 8 8 2 8 . 1 3 8 8 2 8 . 4 6 8 8 2 8 . 6 2 8 8 2 8 . 8 8 8 8 2 8 . 8 3 8 8 2 8 . 9 8 8 8 2 1 . 8 9 8 8 2 1 . 9 3 8 8 2 1 . 9 8 8 6 2 1 . 1 3 8 8 2 1 . 1 3 9 8 2 1 . 1988 2 1 . 1888 2 1 . 2 3 9 9 2 1 . 2 9 8 9 2 1 . 2 9 9 9 2 1 . 3 9 8 9 2 1 . 3 3 8 9
^ » t K —
S ' 3 8 S »83 5 >83 S >83 5 >3S S )85 5 >85 5 >84 ï »84 <>84 5 ) 8 4 S )84 S )84
aa* Ç>84 5 >84 ; )84 ï > 8 3 ï )84 S»84 ; >94 ? )84 S »84 ï >84 i >84 S )84 ï » 8 4 S >83 ï > 8 3 5 >82 S >82 5 >3t ï » 8 1 i )81 î «81 5 ) 3 0 5 ) 9 9 5 >88 5 >89 5 ) 8 8 5 ) 8 9 i >99 5 )89 5 >99 5 ) 8 8 5 ) 8 9 5 ) 8 9
V a r i a O l t »3
-.i?re . 3 7 4 9 • 6 8 4 8 . 6 2 4 8 . 6 3 4 8 . 6 3 4 8 . 6 6 4 8 . 6 7 4 8 . 6 8 4 9 . 6 9 4 9 . 7 8 4 9 . 7 9 4 9 . 7 3 4 9 . 7 7 4 9 . 7 * 4 9 . 8 2 4 9 . 8 4 4 9 . 3 3 4 9 . 3 7 4 9 . 3 9 ) 9 . 9 9 4 9 . 9 2 4 9 . 9 4 4 9 . * 6 4 9 . 9849
1 . 9 2 4 9 1 . 9 4 4 9 1 . 9 7 4 9 1 . 1 3 4 9 1 . 2 7 4 9 1 . 3 8 4 9 1 . 4 2 4 9 1 . 4 3 4 9 1 . 4 7 4 8 1 . 4 9 4 9 ! . S 2 4 9 1 . 3 4 4 9 i . 3 7 4 9 1 . 3 9 4 9 1 . 6 9 4 9 1 . 7 3 4 9 1 . 7 6 4 9 1 . 7 9 4 9 1 . 3 9 4 9 1 . 8 3 4 9 1 . 3 6 4 9 1 . 3 8 4 9 1 . 9 9 4 9
49 39 !1 32 S3 «4 S3 Ï6 «7 39 39 69 61 «2 «3 64 «9 «6 «7 69 ( 9 79 71
2 9 3 8 . 7 1 7 2399 2 9 1 3 . 7 9 2 2499 2 9 6 6 . 1 9 7 2499 2 9 9 7 . 2 7 9 2479 3 9 9 9 . 2 1 9 2499 3 9 3 9 . 9 4 2 2319 3 9 3 3 . 9 6 9 2349 3 9 7 4 . 6 3 7 2939 3 9 9 9 . 2 2 2 2 9 7 9 3 1 2 3 . 1 9 9 2999 3 1 4 6 . 2 9 2 2 ( 1 ) 3 1 6 6 . 9 9 1 2639 3 1 3 6 . 9 9 3 2697 3 2 9 9 . 3 9 1 2677 3 2 3 9 . 3 9 7 2 6 9 9 3 2 8 2 . 4 3 9 2746 3 3 3 9 . 9 6 3 2799 3 3 9 2 . 3 9 6 2849 3 4 9 3 . 4 3 6 2 9 9 9 3 4 1 3 . 1 9 1 2969 3 4 2 4 . 9 2 9 2 9 7 9 3 4 3 3 . 9 2 9 2 9 9 9 3 4 4 9 , 2 9 9 2999
3199 2 1 . 3 9 9 9 6969 2 1 . 3 1 8 9 9699 2 1 . 2 7 9 9 2169 2 1 . 2 9 9 9 6469 2 1 . 2 7 9 9 3999 2 1 . 2 9 9 9 3999 2 1 . 2 3 9 9 7399 2 1 . 2 7 9 9 9499 2 1 . 2 9 9 9 6399 2 1 . 2 4 9 9 9499 2 1 . 2 9 9 9 3199 2 1 . 1 6 9 9 4399 2 1 . 1 3 9 9 7699 2 1 . 1 3 9 9 3499 2 1 . 1 3 9 9 9«99 2 1 . 1 4 9 9 3999 2 1 . 1 3 9 9 298k. 2 1 . 1 3 8 9 9999 2 1 . 9 9 9 9 6989 2 1 . 9 9 9 9 9299 2 1 . 9 9 9 9 1269 2 1 . 9 7 9 9 7999 2 1 . 1 1 9 9
5 ) 8 9 5 ) 9 9 5 ) 8 9 5 ) 9 9 « >99 S >99 5 ) 8 9 5 ) 8 9 i )89 5 )39 5 )89 5 ) 8 8 5 ) « 9 5 ) 8 9 5 ) 9 8 5 ) 9 8 5 )89 5 )89 5 ) 8 8 5 ) 8 9 5 ) 8 8 5 ) 8 9 5 ) 9 9
1 .9349 1 . 9 3 4 9 1 . 9 8 4 9 2 . 9 9 4 9 2 . 9 9 4 9 2 . 9 2 4 9 2 . 9 2 4 9 2 . 8 3 4 9 2 . 9 3 4 9 2 . 9 7 4 9 2 . 8 7 4 9 2 . 9 9 4 9 2 . 9 9 4 9 2 . 1 9 4 9 2 . 1 1 4 9 2 . 1449 2 . 1649 2 . 1949 2 . 1 9 4 9 2 . 2 8 4 9 2 . 2 9 4 9 2 . 2 0 4 9 2 . 2 9 4 9
ANALYSIS of VESSEL CALIBRATION D*T*
CALIBRATION «UN OF 1'iS-TAnK «RITCÎX TSM; i;i-4
Data <"11« n u t : CAL14:F8,8 Nu«b*r of observations: 71 Nu»b*r> of w v t i b l f t : 2
Var iab l ts n u t i : t . rru» 1q lu 2. Vo luM 2
TABLE OF OBSERVATIONS
CALIBRATION RUN OF 1'23-TKNK «RITCEX T«Hi £21-4
OIS» I 2 3 4 5 £ 7 8 9
18 11 12 13 14 IS 16 i r 18 19 28 21 22 23 24 23 26 27 23 29
:e 31 22 33 34
:s :s 37 38 39 48
Var iab l t 81
J - r+9^ 7.439
93.364 142.139 178.481 289.346 243.822 268.228 293.448 314.179 333.187 333.897 418.828 436.819 499.488 337.131 384.361 619.841 633.888 687.483 718.376 731.161 883.634 968.466 914.793 968.488
1822.262 1877.417 1293.873 1318.688 1728.671 1781.876 1837.763 1891.792 1943.937 2888.977 2833.224 2188.436 2162.173 2377.333
Var iab l t I
1.333 12.112 22.478 32.872 41.667 33.373 63.131 73.727 83.842 93.878
182.573 133.333 161.862 190.839 217.983 234.398 283.328 312.«73 343.374 378.237 482.413 431.883 383.478 333.613 683.727 633.373 784.313 983.323
1186.342 1388.(71 1337.382 1489.933 1439.783 1389.934 1361.189 itu.ua 1661.364 1711.493 1912.439
41 42 4 3 4 4 4 3 46 4 7 48 4 9 • 8 31 2 2 3 3 Ï 4 Ï 3 36 Ï 7 * 9 Ï 9 6 8 61 6 2 6 3 6 4 69 6 6 6 7 « 6 69 7» 71
2 4 3 4 . 2486 . 2348. 2394 . 2698 . 2783 . 273b. 2818 . 2 8 6 4 . 2919 . 2972 . 2 9 9 3 . 3813 . 3836. 3899. 3888. 3184. 3129. 3132 . 3172 . 3192 . 3214 . 3236. 3298, 3343 . 3399. 3416. 3419. 3436. 3446, 3492.
2 3 8 .489 4 6 1 3 2 4 6 4 2 2 8 7 6 2 3
.334 3 4 3 6 7 6
.163 2 8 4
.277
.682 ,967 .831 .416 .471 ,374 3 * g 9 2 2
,773 ,799 .932 3 9 0
,839 ,162 ,929 ,793 ,699 ,673
1969 .482 2 8 1 3 . 3 3 9 2863 .191 2 1 1 3 . ( 8 1 2 1 6 9 . 4 3 3 2 2 1 4 . ( 1 3 2 2 6 4 . 4 9 7 2 3 1 4 . 4 8 3 2 3 6 9 . « 9 9 2 4 1 6 . 4 7 9 2 4 6 9 . 4 9 7 2 4 9 9 . 1 9 6 2 3 8 9 . 6 7 8 2 3 2 9 . 6 1 8 2 3 4 7 . 4 2 8 2 3 M . 9 4 1 2 3 8 6 . 1 3 1 2606 923 2 6 2 7 . 2 3 3 2 6 4 3 . ( 4 8 2 6 6 4 . 1 1 8 2 6 * 9 . 1 9 8 2 7 8 3 . 1 1 8 2 7 3 4 . 3 4 2 2 8 * 7 . 3 * 1 2 6 3 7 . 6 4 9 2 8 6 7 . 4 2 * 2 6 7 6 . 3 3 4 2 8 * 6 . 7 9 * 2 * 9 6 . ( 2 * 2 9 * 6 . ( 9 *
1. Raw Data Processing
2. Data Normalization
3. Preliminary Analysis and Partitioning
4. • Data Recombination
5. Least Squares Curve Fitting
o
3 n> 3
FIGURE 1. DIAGRAM OF THE MAJOR STEPS IN THE ANALYSIS OF TANK CALIBRATION DATA.
Attachment 3.T
: Ana lys i s of RITCEX Cal i brat i on Dat*: 3 3"53mm
REGION No. 1
•lumber of v a r i a b l e * : 2 -lumber of observat ions: 24
/ a r i a b l e names: t. True_1q_lu 2. Volume 2
TABLE OF OBSERVflTIOKS
REGION No. 1
DBS* I 2 3 4 5 6 7 9 9 18 11 12 13 14 15 le 17 13 19 28 21 22 23 24
Variable #1
5.383 7.335 17.446 51.521 L13.389 151.535 186.493 217.374 248.474 272.249 296.118 318.387 348.596 7.459 93.364 142.139 178.481 289.346 243.822 268.228 293.443 314.179 335.107 353.897
Variable »2
1.254- -1.342 1.963 5.638 15.225 24.647 34.388 44.333 55.129 64.511 74.633 34.637 99.614 1.355
12. 112 22.479 32.872 41.687 53.375 63.151 73.727 83.842 93.078 102.575
V
3.2 •CL-«Û»t»L 'CCtCSSlCN ju 3«r» U T :
•ceta» »». i
JfCaCJSIOH •M*«CTCM
V»*M1L«
ce»iïL»naw
50u»Cl
•OT»LCKDJ)
«-2
H
2» 2*
coerrtc
K | M
I »4 .« |7 43.244
«••IKBCt
13724.4*3 1133.117
•SHt . l " ! 22*3333*
•so. is
2<321.i*3 23322. M *
l l * * . t t t
• « f l tn lMMY MOV
•«4.3*9 r««3* . * *«
JCVIA1ON
u r . «32 13.>3*
3»
1.-2) 11. .» t )
: M K terexr
i * . i * « -3.»3«
• - 2
.4347**2
<ciu(.r< fo» »0(.T»OXI»L or o*c»« 2
1225*123*334
JOU»Cl
'CT»l. )C«ESS:OH
» - i » - 2
•CSI3UKI
23 2 1 1
21
sun or soumet
3(321 .«»3 2 * 3 3 1 . 3 ? ' 33322 .***
114*.2*1 .313
i j 2 ( 4 . ^ a * Zi3iZ.il*
115 1.3*1 • 13
1*27*4.•( lé*J73*.7»
••>«3*.'4
•C3N*T»HT-» - l
scc«tiJiOH cotf»ic:tMT$ jrs. rawww i-*o*x»T
.*4««*47
. • « • 6 * 2 1
.•*•«•«* . i * * * * 4 7 ( - * * . • * * * 2 * M - « 1 . « • • *«7 tC - *3
>T»HO»»D c**oi •CC. COIF'ICÎEHT
. <<«22t 1 3 . 0 '3 .33
2*2.3*
•C3n»I*nT' » - l x-2
.*••(•$
. M***2 41
»S il C9M«tMNCC [HfC»v*t LOWII UIMT U ' » I » I.IFIIT
.71**21
. (3 *37*
. ) * ( « 3 *
. *773»»
. M 1 7 M
. «M«4«
RC5I0N NO.1
% 3 8 % S S 8 f
TABLE of X-INCREHENTS «nd Y-RESIOUAL'î
3.3
s»
t 2 3 4 1
« 7
a 9
10 i t 12 13 14 13 16 17 13 19 20 21 22 23 24
OBSERVES X
6 . 3 9 3 7 . 3 8 3
1 7 . 4 4 6 3 1 . 6 2 1
l i a . 8 8 9 1 3 1 . 6 3 3 1 8 6 . 4 9 3 2 1 7 . 8 7 4 2 4 8 . 4 7 4 2 7 2 . 2 4 9 2 9 6 . 1 1 0 3 1 8 . 6 8 7 3 4 8 . 3 9 6
7 . 4 3 9 9 3 . 3 6 4
1 4 2 . 1 3 9 1 7 8 . 4 8 1 2 8 9 . 3 4 6 2 4 3 . 9 2 2 2 6 8 . 2 2 0 2 9 3 . 4 4 8 3 1 4 . 1 7 9 3 3 3 . 1 8 7 3 3 3 . 8 9 7
OBSERVES Y
1 . 2 3 4 1 . 3 4 2 1 . 9 6 3 3 . 5 3 8
1 3 . 2 2 3 2 4 . 5 4 7 3 4 . 3 0 0 4 4 . 3 3 3 3 3 . 1 2 9 5 4 . 3 1 1 7 4 . 6 3 3 8 4 . 6 3 7 9 9 . 6 1 4
1 .33S 1 2 . 1 1 2 2 2 . 4 7 8 3 2 . 8 7 2 4 1 . 6 8 7 3 3 . 3 7 3 6 3 . 1 3 1 7 3 . 7 2 7 8 3 . 8 4 2 9 3 . 8 7 8
1 0 2 . 3 7 3
INCREMENT X
6 . 8 8 3 1 .382
1 8 . 8 6 1 3 4 . 1 7 3 3 8 . 4 6 8 4 1 . 3 4 6 3 4 . 8 3 7 3 1 . 3 8 1 3 8 . 6 8 8 2 3 . 7 7 6 2 3 . 8 6 1 2 1 . 9 7 7 3 8 . 3 8 9
- 3 4 1 . 1 3 8 3 3 . 9 8 3 4 8 . 773 3 6 . 3 4 3 3 8 . 0 6 » 3 3 . 6 7 6 2 3 . 1 9 0 2 3 . 2 2 8 2 8 . 7 3 2 2 8 . 9 2 8 18. 798
PBEDICTSI Y
1 .237 1 .327 2 . 4 9 1 3 . 6 3 7
1 3 . 2 3 8 2 4 . 5 9 : 3 4 . 3 4 ^ 4 4 . 3 6 1 3 3 . 3 4 -6 4 . ' S S 7 4 . 3 3 c 3 4 . 3 0 4 3 9 . 6 7 Î
1 .332 1 2 . 6 4 4 2 2 . 3 3 É 3 1 . 9 0 7 4 1 . 3 1 2 3 3 . 3 0 C 6 3 . 8 7 g 7 3 . 6 6 7 9 2 . 9 8 6 9 2 . 9 3 2
1 0 2 . 3 7 E
RESIDUAL Y
. 9 1 6
. 3 1 3 - . t t 9 - . 3 2 8 - . 3 0 4 - . 3 4 8 - . 3 4 3 - . 3 2 7 - . 2 1 6 - . 1 9 7 - . 2 0 e - . 1 6 7 - . 3 3 9
. 3 2 3
. 3 6 8
. 1 4 2
. 3 0 4
. 1 7 4
. 3 7 3
. 3 0 0
. 3 6 1
. 3 3 6
. 1 2 6
. 1 9 7
S I O N I F .
I O 3 3
.53
.40
.30
.20
.10
> 0 .00
- . 10
- . 2 0
- . 3 0
- . 4 0
- . 5 0
REGION No.1 Degree of Regression
<3 19 CD
9 a» «•
s to «
s s M
S T (M
a co fy
es M <n
S U3 m
Tru«_l q_1 v
3 4
: Analysis of RITCEX Calibration Data: 358— 798mm
REGION No.2
Number of u a r i a b l e s : 2 .90 Number of obseruat ions: 15.80
Vari a b l e names: 1. True_lq_Ju 2. Volume 2
TflB-E OF OBSERVATIONS
REGION No.2
OSS» 1 2 3 4
5 5 ?• 8 9 19 11 12 13 14 13 16
Variable *1
404.463 451.545 495.795 535.638 572.764 699.660 652.392 685.583 410.020 456.019 499.480 537.151 594.361 619.841 653.800 697.493
Var abl e »2
130.000 158.708 198.042 216.739 245.179 275.837 311.647 342.025 133.555 161.862 190.839 217.985 234.390 «83.520 312.873 343.374
»?LY»omJH. »(«csi tON CM j«r» i tT : •fC:0» »«.2
3.5
• : :• In
» w 4 r t « « 1 « • r#*u« Iq I v
V t r t : a lu « • l u l » Î
• t C X S t t O H • • • « o t T t M
3 3 1 . 4 * * 2 9 9 . 3 7 1
> H I M C I
• « • « . 1 4 7 3129.««9
>«. i a * 7 i . i t »
: 3 f F » i c t t N r * 'MIXTION
1 7 . 1 J ] 3« .417
: C » » t L » f I O » C O t F r t C I t N T • . « * 7 t S « 1 4 4 7 9 4
n f L I I H M M Y «O» iOUUCC
» - l »-2
• 0 1 . t t
7 ( t « 4 . « « | 7 ( 3 3 3 . M S
3 2 1 . 1 »
' - W H . U f
1297 . J U 2 4 4 4 7 . « 4 «
< t , 14» < [ . 1 3 ) . « » » W 7
?:«»i.r» ra* «OLTHOFIUH. ir S E O I I 2
* - ( 0 U « » M • . I « f * f 7 7 2 9 ( l « ST»NDN*D ««O* OF t t T I l N T t » . 1 ' 9 * 7 1 9 S T « 9 t
iO'jUCt iv<% ar IOUMI» nc*N :aiit«c
Term. • « M C 9 S I 0 N M M
«-2 « C l I I U f t k
V « » I M L (
•C3N9TKNT* 4 M » - 2
19 2 t 1
12
• ICtCSStON S T Ï . »0»"NT
• 2 . « 9 ( 7 « 3 3 . « 7 7 M 3 I . « • • i l » !
7 ( 9 9 3 . M S 1 3 * . ( 2 3
. 1 7 9
C0«7»1C:CNTI t - » 0 ' «<T
- . 2 « 3 « 7 9 9 t « « l . 7 7 * « S « 4 f - * l . < l « 3 3 2 « « > « 3
3 « 4 4 1 . 7 * 1 : ( j : i . « d
i : n . < 2 3 . « i l
j r * N 0 * « g i » i o « •te. :o«K«ic:iwr
t . l 7 » 3 J . K 4 2 9 , * « « M
2 I 9 S M 4 . 2 S 3 < « l « « 4 . 9 *
] 4 4 4 7 . » S
r-votu*
- 2 . 2 7 17.»»
I 3 « . 3 «
C0177TCHNT
• 2 . ( 9 « 7 t S . « 7 7 « « »
.mm
( 9 * C O N ' l t l N C l [ H T M V O I . LOU»« L : B I T i.e»f» L ; » I T
• 9 . ' . « 2 « » .«««997 . • • • ( 1 1
- . 127M7 .0*7373 .<«««2I
SEGION No .2
A l t
Î 5
f 7 U « . l « . l "
3.6
rflBLE of X-INCREMEHTS *nd V-RESIOUfll-î
S»
1 2 3 4 5 6 7
a 9
ie a u 13 14 15 16
OBSERVES X
404. 4SI. 495. 535. 572. 539. Ó52. 583. 419. 456. 499. 537. 584. 619. 653. 637.
468 549 7<?3 658 764 668 392 589 928 819 488 151 361 841 886 485
OBSERVES y
139. 158. 138. 216. 245. 275. 311. 342. 133. 161. 199. 217 254. 283 312. 343.
888 788 842 759 179 857 647 923 533 862 839 983 398 520 373 574
INCREMENT X
484. 47. 44. 39. 37 36. 42. 33.
-273. 43. 43. 37 47 33 33. 33.
468 978 139 953 186 896 642 283 564 990 461 671 210 480 939 686
P92DIC :TEI Y
138. 158. 138. 216. 245. 275. 311. 341. 133. 161. 199. 217. 254. 283. 313. 343.
îae 39* 131 732 142 93; 632
3se 414 6é€ 772 391 357 5SC
aie 61!
RESIDUAL Y
-. 181 -.997 -. 199 -.923 .936 .922
-. 836 . 175 . 141 . 193 .967 .814 .933
-.868 -. 135 -.841
S I G N I
I 0 S 3
0 >
REGION No.2 Degree o-f Regression • 2
.50
.40
.30
. 2 0
. 10
0 .00
- . 10
- . 2 0
- . 3 0
- . 4 0
- . 5 0 (S 10
S ai <s
ru m s m ifl
(S a m
es ~* CO
(S v tû
(S PS. to
§ (V.
True^lq^l
3.7
: Analysis of RITCEX Calibration D*ia: 7QQ 2983mm
REGION No.3
Number of v a r i a b l e s : 2 .98 Number of observat ions: 32.88
Variable names: 1. True— 1q_1v 2. Volume 2
TABLE OF OBSERVATIONS
REGION No.3
OSS* I 2 3 4 S 6 7 8 9-18 11 12 13 14 15 16 17 18 19 28 21 22 23 24 23 26 27 28 29 38 31 32
Variable #1
717-. 428 747-. 145 798.731 853.928 987.588 959.488 1816.223 1869.133 1282.581 1582.999 1716.891 1769.343 1822.189 1376.733 1929.582 1982.735 718.576 731.161 983.634-868.466 914.795 968.488 1822.262 1877.417 1293.873 1518.688 1728.671 1781.876 1837.763 1891.792 1945.957 2888.977
Variable §2
371.438 399.842 446.813 497.832 547.383 595.752 648.321 697.222 894.945 1899.538 1297.868 1348.219 1397.258 1447.788 1497.126 1346.145 372.23' 402.41.5 431.885 383.478 333.613 683.727 633*373 784.313 983.323 1186.342 1388.671 1337.382 1489.933 1439.783 1589.934 1561.183
3
•OlrNOIttM. ICCHSliOH JN 3»T» K T : tfCIJN »«,.]
-Hhtr t : 9«*4*««M « « r > t t ! 4 • v«lu*«M2 In4»*«wqtni v«r*asl« • T*w« 14 1*
I I C I C S I I O H m t n i r i H
rr*#_l4_ '« WOtuM 2 »
12
1314.333 H 1 9 U . 4 * *
STUMMM* 3CVIKTIQM
4 ] * .
;0€f»IC!lMT V V IMIATIOM
33. »M •7.221
cc»»lL»no» catr ' lc i iMT • m n i m i K
»OU«Ct
roT«i.(»BJ>
»-2
4 M . f t
; * t ! 4 M . i l 7 1.2*4
PfXIMWWY 40»
11*4*17*. K7
17
<!.>•> <1,^*>
• - 2
. M***7«
. * * * *«<•
»fiuLr> 'o» •tt.YNaniH. gr 9 t a c c 2
•-taumCD • .»4>4)4>M|,4*M
irtHÜMI C M M 'S»- ClTtrWTl • .<3«21**273*4
roTXi. 'CClt l I IOH
« - 1 » « 1
•ttisunc
31 2 l
2 *
vin ar saumtt
3*12417.14* 3*124*3.4*1 3*124*4.117
1.2(4 11.7J»
"t«H » l i t *C
11SUU. 7(1 3*I24|. | . ut
1.2*4 .4(3
-1*2*7* . 4* I44(3737.«3
3.12
>cc*cnio> cac7»iciiMT« »T3. rq«mr I - ' O M H T
•eOHST»»T' -2*2 . K 2 I C M *"• -»33J»2*
- .2*2l«22t>«3 . * 33»2 I I>M . I 3 * 7 ] « 4 f . * t
• f t . caiKrtcuNT
1.1*2*7 • 4*24*
r-»*tu«
-1*4,51 373.2*
1.77
'COWtTHMf' X-l x - I
:oir»iei«MT
- 2 » . I *2 I«* . » a j s * j
»3 * CON'tllMCC IHTMVIH, LOM* LIBIT lK»f* btn'T
-2*3.214**3 . •1*39*
• - '»* . 4**171 .»2*«27 . t « H l
«CCJON No .3
3 I I ! 2 ! 2 ! 3 31 ! f f l r t ^ H ^ l v
3.9
TflILE of X-INCREMENTS tnd Y-RESIDUrtlS
S»
t 2 3 4 3 6 7 9 9 19 11 12 13 14 13 IC 17 18 19 28 21 22 23 24 29 26 27 28 29 38 31 32
01SSKVED X
717 747 798 833 987 939 1816 1889 1282 1392 17K 17S9 1822 1876 1929 1982 718 731 •S3 369 914 969
1822. 1877 1293 1318. 1728. 1781. 1937 1891 1943 2889.
«29 143 731 929 398 «89 223 133 391 999 891 343 189 733 382 733 37S ICI «34 «CC 79S «89 2C2 • 17 875 «89 «7t 978 763 792 937 977
OBSERVES y
371 399 «46 497 34 7 393 «48. «97 894 1899 1297 1348 1397 1447 1«97 1346 372 482 «3i. 383 333. «83. «33. 784. 983. 1196. 1388. 1337 t«89. 1439 1389. 1361.
«38 842 813 832 383 732 321 222 943 339 869 219 239 798 126 143 237 413 •93 478 613 727 373 313 323 342 «71 382 999 783 994 189
INCREMENT X
717. 29. 31. 33. S3. 31. 36. 32.
213. 228. 213. 53. 32. 34. 32. S3.
-1264. 32. 32. 36. 34. 33. S3. S3.
216. 216. 218. 32. 36. 3». 34. 39.
428 717 383 189 £68 998 733 911 368 «69 181 232 347 344 849 133 168 386 493 812 338 693 774 133 438 723 871 483 687 828 1«3 928
PREDtCTEr Y
371 396. 446 497 347 393 ««9 697 394. 1899 1297 1346. 1296. 1«'«. l«93. 13*3. 372 «82 431. 383. 334 633. 533. 784. 983. 1136. 1389. 1337. 1418. 1468. 1311. 1362.
271 73« 33S «77 39* 494 a<: 19E 974 397 311 991 I3ï 381 93Î 33C 334 386 Ut 74t e?ï 323 «61 78« 32! '.*: 195 894 S7« 881 13C 321
»E3t3U«t. Y
.178
.234
.234
. 133 -.318 .268 .237 . 114
-.339 -.339 .349
1.229 t.147 . Ï97
1. 192 .797
-.377 -.391 -.114 -.271 -.«39 -.399 -.399 -.273 -.293 -.321 -.32» -.312 -.•23
-1.917 -1.294 -1.217
5 I C N I F .
REGION No.3 Üagrae of degression • 2
I
. 3
I e.
-ï
Tru» 1q lv
3.10
: A n a l y s i s o f RITCEX C a l i b r a t i o n D a t a : 2QÔ9 3373*1»
REGION No.4
Number of v a r i a b l e s : 2 . 0 0 Number of o b s e r v a t i o n s : 4 0 . 0 0
V a r i a b l e names: 1 . True_Jq_1w 2. Volume 2
TABLE OP OBSERVATIONS
REGION No.4
• oss#
1 2 3 4 3 6 7 9 9 10 11 12 13 14 13 1$ 17 13 19 20 21 22 23 24 23 26 27 28 29 30 31 32 33 34 35 36 -37 38 39-48
Variable ti
2035.699 2692.619 2143.854-2361.240 2413.933 2467.312 2324.802 2377.617 2627.639 2684.162 2741.489 2795.737 2842.338 2902.293 2939.143 2973.878 3003.336 3027.863 3047.397 3069.643 2833.224 2108.436 2162.173 2377.333 2434.238 2496.483 2348.461 2394.324 2638.842 2703.207 2736.623 2918.334 2864.343 2919.676 2972.163 2993.284 3013.277 3836.602 3039.987 3080.831
Variable »2
1595.383 1648.963 1698.636 1899.738 1948.893 1998.569 2831.083 2108.831 2147.108 2199.342 2232.923 2302.403 2345.904 2481,613 2434.327 2472.936 2493.798 2317.821 2336.830 2337.602 1611.668 1661.364 1711.493 1912.439 1963.482 2813.833 2863.891 2113.681 2163.433 2214.813 2264.497 2314.483 2363.038 2416.479 2463.497 2483.196 2383.678 2323.619 2347.428 2366.941
3.11
»d .T~ont» i . • I O I S S I Q N J H a a r * i t T : •ICIOM » . . 4
t t a i M i i i t M » « * * * a l t • v « i w e « v t t n 4 « a * * a * f t t va r f « • < • • f ^ u * ta I v
r**»a l a >w * * « a l K M t «a
a c c * f t s i O H a a a a a c r m
i « 7 1 . t ? t t « 3 3 3 7 . 7 « t i i » 7 . * 3 i a 1314. a »
sraaBFao s c v t a t < O H
: « . i « « >a i . i 33
- a t m c i t H T OF v a a i a r i O H
i a . i s * i i . i a a
coaatLar iOM C S I F F I C I I N T • . i » a » » 3 7 3 « s 7 »
M f k l m n a a r aov s c u a e i
raTai(»w> x - l
« 0 1 . t t '-•m.m ] 3 M t a a . 4 « * I 3 < a a 3 3 . m o a a s j i s . a n
«MULT» FOK F4LTN0HI4IC OF 1 I C I I I t
t-«ouaa«» • . )«aa74-3i««-traNBaas laao* OF IITIIMTI • t.*(133t933M
touact 3F
J» r e r a t U C » C U I O H
'tstsum. f
t u n O F isuaacs
3 3 H 1 M . 4 M 3 3 < U 9 S . M I 3 3 M * 9 9 . « a s
**.t1T
*C»M JOl. IFf
j j « a a : i . > a i
C. LTi
i a 3 3 4 4 3 . « 3 3 ( 3 3 4 4 9 . f 9
' C C » « Ï « I O H C O ( F ' I C : I H T « : r a H i F « g : * * o a ' « a i a i L I » T J . F o a m r c-aoaaaT a t e . : o i f » i c i « H T r . o a c u i
ÎON»T»«T'
»*l -a»7.»«373«7
.43aai»7 -.2»7*«37I««J
. »3aanrt»aa 1.43739
.»«*93 -aai7.27 1741.4»
'COHfTaxT-« • I
C O W » t C I « T
- 1 » 7 . » « 3 7 3 7 • a w a a i
«9 x C O N F I M H C * l u r f n v a t UOMCM L IB IT \.*»« I . IB IT
- 3 M . «743*1 . t a m *
• ; » 3 . i s a » » 3 . > 3 l H I
REGION NO.«
r ' u * « ' ( . 'v
r»lL£ af x-tNC*EH6Nrs *"« r-»ESl3u*l. i 3.12
SI
I
tl 11 13 ia 14 13 te 17 11 15
OBSERVES X
2833 29*2 2143 2361 2413 2467 2324 2377 2627 2604 2741 2 7 M 2842 2982 2999 2973 3883 3027 3847 3869 2833 2188 2162 2377 2434 2486 2348 2394 2C38. 2783 2736 2318 28S4 2919 2972 2993 3819. 383C. 3839 3888
»99 £19 934 248 933 312 882 «17 «39 162 489 737 338 293 143 878 33S •63 397 «43 224 43C 173 333 23* 403 461 324 842 287 «23 334 343 «78 163 2*4 277 «82 987 831
OBSERVED Y
1393 1444 1S90 1899 1946 1998 2831 2188 2147 2199 2232 2382 2343 2481 2434 2472 2493 2317 293C 2337 1611 1461 1711 1912 1963 2813 2663 2113 2169 2214 2264 2314 2363 2416 2463 2483 2383 2323. 2347 2366
383 »63 «36 ?38 693 369 463 931 188 942 923 463 884 • 13 327 936 796 821
asa 602 «68 364 493 439 «02 933 691 •81 433 813 497 463 936 479 497 196 676 «16 428 941
[NcaenENT
* 2833
36 33
213 32 S3 36 33 36 36 37 34 46 39 36 19 24 23 28 22
-1814 33 93
219 36 32 34 S3 33 33 33 33 34 33 32 21 21 21 23 28
«99 928 233 387 713 339 «89 «16 622 322 328 247 622 937 846 733 • 78 789 332 240 421 211 737 360 717 133 636 864 710 163 410 70» 209 133 406 121 993 323 304 644
3"»EDI> :TE: Y
1393 ts48 t«?7
1398. 1947
1996 2849 2899 2143
2198. 2231. 2382
2343 2481 2434.
2472. 2493 2317 2336. 2336 1613 1C62. 1712.
1913. 1963. 2814. 2864. 2114
21«6. 2216.
2269. 2313. 23»«. 2417 2466. 2403. 2386. 2326. 2347 2367
277 2i: 72: <93« 46c 48* **l 271 79* 36« • 7! 12(
«s: 22f 89€
«s: 21? 267 17* 467 43: 92Ï
m 133 937 44S 71! 38Î 42S 87Ï 73Ï 782 llf 395 28f 43C 384 13* 884 27«
'EiiDum. Y
.389
.738
.914 1.714 1.333 1.984 t. 478 1.388 1.387 1.182 t.236 .279 .318 .367 .438 .303 .382 .334 .«74 .736
-1.776 -1.339 -1.486 -.738 -.334 -.487 -.924
-1.128 -1.199 -1.266 -1.233 -1.388 -1.466 -.914 -.789 -.«34 -.«26 -.326 -.4*4 -.329
S I C M t F .
REGION N O . 4 Oegrsa o-f R e g r e s s i o n • l
IM
* <\l (M rti
9 en <n <u
8 V
v Al
S m « IV
8 (0 10 «1
a f» r* r«
a a CD iU
s J» n IV
3 m
T r u « _ l q _ l v
: fln*lysis o f RITCEX C a l i b r a t i o n Data: 3 3 7 9 - —3iS3mm
REGION No.S
Number of v a r i a b l e s : 2. Number of o b s e r v a t i o n s : 7
V a r i a b l e names: 1. True lq 1v 2 . Volume 2
TABLE OF OBSERVATIONS
REGION No.5
CCJk
i 2 3 4 5 6 7
Variable *•!
3892.326-3116.443 3139.249 3161.£13 3184.41a 3129.471 3132.374
Variable «2
2377.983 2597.876 2616.727 2636.642 2586.131 2686.925 2627.253
3.14
•OLvnOnlai »«C»C»»IOn On 3"'» « T i »tC:3n ««.3
«tCKStlON • • • » n | T M «
' • • IDM.I
Tr\i9 ta tv 3 1 2 t . « l 2 ( M . f « 3
'M imet
«3».r««
srnagrito 3fvmt tan
21 . ><2
;3trric:tHT v V««I»T:QH
::>*lL«r:an cotmcitxr • . »*«3*)««u
JCU«CI
•CtUllHIJ) x- t
• t l . IS
273*.3*7 2733.2*1
r-vULU*.
2C2t.««2
»•
< t . 1 >
•«uur» ra* rotrucnlAt. or jcc 'U i
JT»l«««»t t*»0» 3^ CtTtmtTt • .M3«J»»«t7t
30U»Cl
roTH •tcnssioN
»-i •CSIIUUL
tun or ssu'ftts
2 7 » . 3*7 27S3. ] ( • 2733.J««
3 . J37
•WW j a i l U I
27M.3C* 2 7 M . 2 M
i.447
Uit. 7€ 2<2t.7«
'C9H*T«nr' K-I
•COKsttOM cscrrtcUMrt JTt. ro«R*T e-»0»n«f
-31.•(••«11 .3 IM««*t>«Z . M M N M . M
trmsmi (itou MC. cairrtcttMT
11.13*72 .11 «31
• - « l u l
31.27
'COH»T»MT' » - l
cotrricUHT
- S I . • • • • « ! . <3tM4
«9 x eoHriDCHCt iMffuvm. UOÏt» U M T u>»«» U M T
- I M . 2 2 2 M T .»*737»
• ! .<3'«>S .J«2«3«
3ESICN Na.S
f î ! 5 ! 2 § s
f'u«_l«;,.l*
TABLE of X-INCREPtENTS and Y-RESIDUfll:>
3.15
0BS# #
1 2 3 4 5 6 7
OBSERVED X
3892 3116 3139 3151 3184 3129 3152.
526 443 249 618 418 471 574
OBSERVED Y
2577. 2597. 2616. 2636. 2596. 2686. 2627.
993 876 727 642 151 925 2S3
INCREMENT X
3892. 23. 22. 22.
-«7. 25. 23.
526 919 884 369 281 854 183
PREDIC 'i
2576. 2597. 2616. 2633. 2586. 2683. 2627.
:TEI f
77*. 18? 49g 584 384 171 317
RESIDUAL Y
1.287 -.831 .237 1. 137 -.732 -1.255 -.564
3 I G N I F
C\J I
1) S 3
O >
1.50
1.20
.90
.60
.30
0 ,00
- . 3 0
- . 6 0
- . 9 0
- 1 . 2 0
- 1 . 5 0
REGION No.5 Degree o-f Regression * 1
(S in is cn
in
IS cn
s CO IS CO
in cn S cn
in
cn cn T r u e _ l q _ l v
O
cn
n n * • « •
<n
(S IN. —• cn
in GO • •
cn
S s CM cn
3.16
: Rn»l»»ifr of RITCEX C a l i b r a t i o n D*t* : 3160-. 3*5öm»
REGION No.S
Number of v a r i a b l e s : 2 Number of observations: 24
Var iable names: 1. True_lq_1v 2. Volume 2
TABLE OF OBSERVATIONS
REGION No.6
OSS* 1 2 3 4 5 9
7 9 9 19 11 12 13 14 13 IS 17 ia 19 20 21 22 23 24
Variable »t
3133.214 3293.294 3227.682 3280.688 3332.918 3386.652 3396.584 3410.018 3421.304 3438.994 3442.048 3452. 0U 3172.395 3192.922 3214.773 3236.799 3288.972 3345.598 3399.039 3410.162 3419.928 3430.785 3440.698 3452.075
Variable *Z
2656.667 2677.386 2698.163 2747.752 2796.421 2846.542 2855.694 296S.289 2873.882 2887.311 2398.191 2907.501 2645.648 2664.810 2685.190 2705.810 2754.542 2887.301 2857.0*9 2867.426 2876.554-2886.708 2896.020 2906.696
3.17
•OLTNOnlKl. «IXKIStON 3M 3KT» SCT: •CCZON H * . (
—>.»•>••: 3«»>»«ai<t . a r ' « a l t • v . i u . . _ 2
•cc*itt:oi> »«»»»iTt»t
Tr-u» I» It» 24 » c l « « ? 24
)J««.392 l l t « . ] 3 1 2 M 3 . U 7 4 7 * 9 . • * •
ctvmi ION
14*. 121 n. ;JJ
:5tF*tc:t»T OF <«*IKTtON
).4«3
amiuiiio» cotF'iciiMr • .4***«t»*33i
•es. i t r-»m.uc
rCT*tl*DJ)
»-2
2*19*7.M7 2*19*1.34«
.M7 M 3 3 M . I * *
. 3 3 ? <l.J2> C | , - ! ! >
• » W M .>'«*73«
•fsukrs ro» FOUYHOIWH. ar gccact i
JTBNOMO ««O*
tcunct
rOT»L UCXCUION
»*l »-2
«HI3UPH.
<><|>|L|
-eoN«Ti>«T-x-t x»2
ar i
or
13 2 1 t
4l
»T8.
ÏTIBHTt • 9M*747139J2
sun ar taur in*
• ( O f t l ION rqRnnr
-4J«.34*1272
2 « i 9 * r . « r 2»!9»1.133 2119*1.J44
.117 9.434
c c i r r t c i t H M C-roRHHT
- .42(34* l l< . >Mt7<>(<
• Ï I I I I I H -
• 3 • 1 • 4
»««« fSLlMf
I M H 1 . 1 I 7 2415»'.94*
.«•7
.29»
ITHNOFKD MOK •cc. eotFrtcteHT
1*2. I»21* .1l<3« . 4 M I 3
*-v«LÜ«
) l * 9 4 t . l « " * f * 7 . M
.3»
*-»»W.Ut
-2 .21 • . * •
ï o i r r i e i w T «9 « cohriifNCt iMTfnvn.
LOuC» LIBIT l l '»t» LIBIT
'COMTHNT'
x-2
-«2*.14*127 1.2M7M -.*•••!•
••37.9««23« .79*47»
- . • • • • 4 7
•19.132I1* 1.242*17
SCG-ON NO.e
! § ? S
t>u«„l«. lv
TABLE of X-INCREMENTS t n d V-RE31 DUAL'S
3.18
- ..
1 2 3 4 3 S 7 3 9 ia u 12 13 1 t 13 16 17 18 19 20 21 22 23 24
OBSERVES X
3183. 3293. 3227. 3239. 3332. 3386. 3396. 3419 3421. 3438 3442 3*32 31 ?2 3192 321*. 3236. 3288. 3343 3399. 3418. 3419. 3438. 3448. 3432.
214 294 «82 688 819 692 384 019 384 994 049 911 39S 922 773 799 932 399 839 162 929 783 698 073
OBSERVES Y
2636. 2677 2698. 2747. 2796. 2846. 2833. 2969. 2879. 2887 2898. 2907 Î643. 2644 2683. 2 70S. 2734. 2897 2837. 2867 2876. 2886. 2896. 2986.
667 386 163 732 421 342 694 289 882 811 191 381 648 819 198 918 342 381 949 426 53* 70S 929 696
INCRSrtENT X
3183. 22 22. 33. 32. 33. 9 13 11. 9 11 9
-279 28 21. 22 32. 36 33 11 9 19 9 11
214 971 313 886 121 942 832 514 283 698 034 964 616 327 931 826 133 638 449 123 763 838 912 377
PREDICTS! Y
263Ô. 2676. 2697 27*7 2793. 29*6 2333. 2867 2878. 2887 2897 2906 26*1» 2663 2633 2706. 2754 2387 2837 2868 2877 2887 2396 2997
US 79« 0-3Î 262 91*
u: 292 43? 38? *11 »9Ç
r/\ aas 21* ô3€
zs: 975 33S 634 914 10C 216 *4J 03e
*S3isum. Y
.339
.526
.310
.499
.387
.428
.401
.410
.413
.408
.492
.339 -.334 -.494 -.463 -.442 -.437 -.334 -.604 -.398 -.334 -.398 -.422 -.334
3 I C N I F .
I (M
O 3 3
1.00
.80
.80
.40
.20
> 0 .00
- . 2 0
- . 4 0
- . 8 0
- . 8 0
- 1 . 0 0
REGION No.S Degree o-f Regression
m
s • «« m
s (S
<n
9 tu ru en
<S (0 (M m
S (n m
"33 V
m tn
Q (9 f» CT
S 04 V
<n
<S U3 T
m
3 m m
True_1q_lv
ld.0348C Attachment 4.1
1984-06-21
Calculation of RITCEX Tank Volume
Equation
V(L) a + bL • cl2 • dL3 •
where V = Volume of Tank, and L = True Liquid Level
L 1 * L
L 2 ± L
L 4 * L
L 5 ± L
<
<
<
<
<
1st Region
2nd Region
3rd Region
4th Region
5th Region
6th Region
Break Point
Recommended values for break points (Ln)
350
700
2000
3070
3160
-2-
Coeffldent and Standard Error:
1st Region
V(L) - a • bL • cL2
= Coef (1,0) • Coef (l.l)L • Coef (1,2)1*
Coef (1,0) - .848005 .06220
Coef (1,1) . .060082 .00082
Coef (1,2) . .000641
2nd Region
V(L) - a • bL • cL2
2 = Coef (2,0) • Coef (2,1)L • Coef (2,2)L£
Coef (2,0) - -2.656785 1.17053
Coef (2,1) - .077-565 .00435
Coef (2,2) - .000619
3rd Region
V(L) • a • bL * cL2
• Coef (3,0) • Coef (3,1)L • Coef (3,2)L2
Coef (3,0) - -292.162169 1.50207
Coef (3,1) . .923593 .00246
Coef (3,2) - .000002
4.3
-3-
4th Region
V . a • bL
« Coef (4,0) • Coef (4,1)L
Coef (4,0) - -297.963737 1.43755
Coef (4.1) * .930020 .00053
5th Region
V - 3 • bl
- Coef (5,0) • Coef (5,1)L
Coef (5,0) - - 51.884461
Coef (5,1) . .850004
6th Region
V - a • bL • cL
- Coef (6,0) • Coef (6.1)L 4 Coef (6,2)L2
Coef (6,0) - -426.349127 192.88219
Coef (6,1) » 1.000768 .11638
Coef (6,2) - - .000010 .00002
KGharwal/»s<1846)
Id.0328C
51.85972
.01658
Attachment 5.1
ANALYSIS OF VOLUME DIFFERENCES AT THE BREAK POINTS
TrueLi qLeu
348 348.2 348.4 348.6 34e.8 249 349.2 349.4 349.6 349.8 '<=.* 358.2 350.4 350.6 350.8 351 351.2 351.4 351.6 351.8 352
Volume Calculated VI
99.384265 99.48547424 99.58679476 99.68816656 99.78958964 99.691064 99.99258964 1O0.O9416656 100.19579476 160.29747424 100.399205 100.58098704 100.68282836 100.76470496 169.86664084 100.968628 161.01666644 101. 11275616 161.21489716 161.31768944 161.419333
V2 99.438411 99.54619356 99.64262564 99.74396724 99.84583836 99.947819 166.64984916 160.15192884 160.25465864 160.35623676 100.458465 100.56674276 160.66367664 166.76544684 160.86787316 160.976349 161.67287436 161.17544924 101.27867364 161.38874756 161.483471
Li.ff -.654206 -.65471932 -.65523088 -.05574668 -.05624872 -.056755 -.05725952 -.05776228 -.05826328 -.65876252 -.65926 -.65975572 -.66624968 -.06074188 -.66123232 -.061721 -.86226792 -.66269308 -.86317648 -.86365812 -.864138
TrueLiqLew
698 698.2 698.4 698.6 698.8 699 699.2 699.4 699.6 699.8 760 700.2 700.4 709.6 7O0.8 701 701.2 701.4 701.6 701.8 702
Volume Calculated VI 353.342061 353.53656356 353.71899564 353.96753724 354.09612836 354.284769 354.47345916 354.66219884 354.85098864 355.03982676 355.228715 355.41765276 355.66664684 355.79567684 355.98476316 356.173899 356.36308436 356.55231924 356.74160364 356.93093756 357.120321
V2 353.486153 353.66543668 353.85676732 354.03598472 354.22126228 354.46654 354.59181788 354.77769592 354.96237412 355.147*5248 355.332931 355.51826968 355.70348852 355.88876752 356.07464668 356.259326 356.44466548 356.62988512 356.81516492 357.00044486 357.165725
Diff -.138692 -.13492652 -.13171168 -. 12344748 -.12513392 -.121771 -.11835872 -.11489768 -.11138688 -.16782572 -.164216 -. 16655692 -.69684848 -.09369068 -.63928352 -.685427 -.08152112 -.07756588 -.07356128 -.66950732 -.865464
TrueLiqLeu
5.2
1998 1998.2 1998.4 1998.6 1998.8 1999 1999.2 1999.4 1999.6 1999.8 2668 2308.2 2088.4 2888.6 2608.8 2901 2661.2 2681.4 2861.6 2681.8 2682
VI 1561.168653 1561.34697888 1561.53328732 1561.71968472 1561.96592228 1562.69224 1562.27855788 1562.46487592 1562.65119412 1562.83751248 1563.623831 1563.21814968 1563.39646852 1563.58278752 1563.76910668 1563.955426 1564.14174548 1564.32886512 1564.51438492 1564.78878488 1564.887825
V2 1568.2:6223 1560.462227 1568.588231 1568.774235 1560.960239 1561.146243 1561.332247 1561.518251 1561.764255 1561.890259 1562.676263 1562.262267 1562.448271 1562.634275 1562.820279 1563.606283 1563.192287 1563.378291 1563.564295 1563.750299 1563.936303
Diff .94443 .94474368 .94565632 .94536972 .94558328 .945997 .94631088 .94662492 .94693912 .94725348 .947568 .94788268 .94819752 .94851252 .94382768 .949143 .94945348 .94977412 .95668992 .95840588 .950722
Tru*L1qLev
3068 3068.2 3868.4 3068.6 3068.8 3069 3069.2 3069.4 3669.6 3069.8 3078 3070.2 3878.4 3078.6 3070.8 3071 3071.2 3071.4 3071.6 3871.8 3072
Volume Calculated VI
2555.337623 2555.523627 2555.709631 2555.895635 2556.881639 2556.267643 2556.453647 2556.639651 2556.825655 2557.011659 2557.197663 2557.383667 2557.569671 2557.755675 2557.941679 2558.127683 2558.313687 2558.499691 2558.685695 2558.871699 2559.857703
V2 2555.927811 2556.0978118 2556.2678126 2556.4378134 2556.6078142 2556.777815 2556.9478158 2557.1178166 2557.2878174 2557.4578182 2557.627819 2557.7978198 2557.9678206 2558.1378214 2558.3078222 2558.477823 2558.6478238 2558.8178246 i'558. 9878254 2559.1578262 2559.327827
Diff -.598188 -.5741848 -.5581816 -.5421784 -.5261752 -.510172 -.4941688 -.4781656 -.4621624 -.4461592 -.430156 -.4141528 -.3981496 -.3821464 -.3661432 -.35014 -.3341368 -.3181336 -.3021304 -.2361272 -.270124
5.3
TrueLiqLev Volume C a l c u l a t e d V I V2 D i f f
31S8 3158.2 3158.4 3158.6 3158.8 3159 3159.2 3159.4 3159.6 3159.8 3160 3160.2 3160.4 3160.6 3160.8 3161 3161.2 3161.4 3161.6 3161.8 3162
2632.428171 2632.5981718 2632.7681726 2632.9381734 2633.1081742 2633.278175 2633.4481758 2633.6181766 2633.7881774 2633.9581782 2634.128179 2634.2981798 2634.4681806 2634.6381814 2634.8081822 2634.978183 2635.1481838 2635.3181846 2635.4881854 2635.6581862 2635.828187
2634.346577 2634.5240982 2634.7216166 2634.9091382 2635.896657 2635.284175 2635.4716922 2635.6592886 2635.8467242 2636.034239 2636.221753 2636.4092^-52 2636.5967786 2636.7842982 2636.971801 2637.159311 2637.3468282 2637.5343286 2637.7218362 2637.909343 2638.896849
-1.918406 -1.9359264 -1.953446 -1.9709648 -1.9884828 -2.806 -2.6235164 -2.641032 -2.0585468 -2.6766688 -2.093574 -2.1110864 -2.128598 -2.1461688 -2.1636188 -2.181128 -2.1986364 -2.216144 -2.2336588 -2.2511568 -2.268662
RITCEX 12 D
Evaluation of RITCEX Converted Data by PNC Analytical Method
RITCEX at CEN/SCK in Mol
T. Uchida
£. Murakami
Tokai Reprocessing Plant
Power Reactor and Nuclear Fuel Development Corporation
Tokai-mura, Ibaraki-ken, Japan
September, 1984
CONTENTS
Abstract 1
1. Introduction 2
2. Evaluation 3
2.1. Analysis 3
2.1.1. Evaluated Data Set 3
2.1.2. Graphical Representation 3
2.1.3. Inverse Model 3
2.1.4. Break Point 4
2.1.5. Overlapping of Break ?oint 4
2.1.6. F and T tests 4
2.1.7. Standard Deviation 4
2.2. Results 5
2.2.1. Standard Deviation 5
2.2.2. Systematic Run to Run Difference 5
2.2.3. Comparison of Volume calculated with each calibration
equation at the typical value 7
2.2.4. Comparison of Volume calculated with each calibration
equation at break point 7
3. Conclusion 9
4. Reference 11
(1)
CONTENTS OF TABLE
Table-1 Evaluated Data Set 3
Table-2 The Resultant Calibration Equations(single data set)
12
Table-3 The Resultant Calibration Equations(combined data set)
13
Table-4 Data Point, Degree, and Standard Deviation of each
calibration equation 14
Table-5 Comparison of Volume calculated with each calibration
equation at the typical value 15
Table-6 Comparison of Volume calculated with each calibration
equation at break point 16
CONTENTS OF FIGURE
Figure-1 Graphical Representation of Ruska data
(Run#llto#14, 195points) 17
Figure-2 Graphical Representation of U-tube data
(Run#llto#14, 195points) 17
Figure-3 Graphical Representation of Acoustic data
(Run#12to#14, 99points) 18
Figure-4 Graphical Representation of TDR data
(Run#14, 53points) 18
Figure-5 Volume Residuals versus Height 19
(2)
Abstract
This report describes the evaluation of RITCEX converted data
by PNC analytical method. The main purpose of our evaluation is to
compare the performance of the different measurement instruments
and to identify problems.
Prom our evaluation, it is concluded that the results on Ruska
are the best of all the instruments, and the systematic run to run
difference is significantly large. The main reason for the systematic
deviation is considered to be the temparature gradient, which was
existed in the liquid of the tank, and it needs to be studied further
in the future calibration.
It seems to demonstrate that on the whole, all runs give a very
good fit to the resultant calibration equations, and that RITCEX
has the important possibility to improve tank calibration.
1
1. Introduction
RITCEX calibration of 4 runs was carried out at Eurochemic
Reprocessing Plant in Mol last January, according to the
calibration procedure, which was discussed at The First General
Information Meeting held in Mol last October. The data measurements,
on the usual measurement instrument(U-tube) and the new measurement
instruments(Ruska, Acoustic, TDR), were performed in the
calibration.
The measurement data were evaluated by PNC analytical method,
and the results were presented at the Second General Information
Meeting held in Luxemburg last May. At the meeting, break points
of six regions were decided, and the converted data were
distributed among the participants.
The evaluation of the converted data by our analytical method
is presented in this report. The main purpose of our evaluation
is to compare the performance of the different measurement
instruments and to identify problems.
2
2. Evaluation
Our main evaluation concentrates on the analysis of Ruska data,
because Ruska is known to be the instrument with the highest
precision, and the results on Ruska are compared with those on the
other measurement instruments.
2.1. Analysis
2.1.1. Evaluated Data Set
In order to evaluate the converted data in detail, We have many
data sets, which are shown in Table-1.
Table-1 Evaluated Data Set
Data Set
- Run#ll
Run#14
Run#li and #14
Run#ll to #14
Note *: The number of Data Point is 56.
**: Data Set is Run#12 to #14. The number of.
Data Point is 99.
***: The number of Data Point is 53.
2.1.2. Graphical Representation
Graphical presentations of all data on each measurement
insrument are shown in Figure-1 to -4. From these figures, it is
concluded that all data are acceptable. And, all data are analyzed
with "AVCD" statistic analytical program of Ruska computer developed
by Hewllet- P-ckerd, LTDCU.S.A.).
2.1.3. Inverse Model
In our preparation of the calibration equation, our analysis
is based on the fitting of the inverse model to each data set.
The classical and inverse models are algebraically equivalent and
give identical numerical results. The inverse model has been rhosen
because of 'ts ease of application, in paticular, when the second
3
Data Point Ruska U-tube Acoustic TDR
73 o o
70 o o o* o***
143 o o
195 o o o**
or third degree polynomial regression is fitted.
2.1.4. Break Point
The decided break points are applied to our evaluation. We
choose the points nearest to the points mentioned bellow in each
data set.
Region-1 : Oiran - 350mm, Region-2 350rora - 700mm
Region-3 : 700mm - 2,000mm, Region-4 : 2,000mm - 3,070mm
Region-5 : 3,070mm - 3,160mm, Region-6 : 3,160mm - 3,500mm
2 .1 .5 . Overlapping of Break Point
Data including the upper break point of previous region are
analyzed. For example, the upper break point in Region-1 is the
lower break point in Region-2.
2.1.6. F and T tests
Polynominal regressions of the first to third degree are fitted
to each region, and the degree is determined by F and T tests. The
level of significance applied to both tests is 1%.
2.1.7. Standard Deviation
Finally for each region, the resulting smallest standard
deviation(S.D.) is accepted as a criterion to indicate the best
suited equation.
As the number of data point on Acoustic as well as that on TDR
is small, no equation is analyzed for Region-1 on Acoustic,
Region-5 and -6 on TDR, respectively.
4
2.2. Results
The data sets shown in Table-1 are evaluated. But, as the number
of data point on Run#12 as well as that on Run#13 is small, no
equation is analyzed for Run#12, Run#13, respectively. Also, some
combined data sets of all the calibration runs are analyzed.
The resultant calibration equations are shown in Table-2
(single data set) and -3(combined data set).
2,2.1. Standard Deviation
Data point, degree, and standard deviation of each calibration
equation are shown in Table-4.
The following results are concluded from this table.
- With regard to data point, the number in each region on Ruska
and that on U-tube is the same.
- With regard to degree, which is decided for each region ,
the second degree equation is obtain for Region-1 and -2,
the first to third degree equation for Region-3 and -4,
and the first degree equation for Region-5 and -6(except TDR),
respectively.
- With regard to standard deviation, generally, in each region,
Ruska has the smallest standard deviation of all the measuement
instruments. This value shows that Ruska has the highcit precisior
of all the instruments. Also, this shows that the value of the
combined data set is bigger than that of the single data set. That
is, the tendency shows that the systematic run to run difference
is sginificantly large.
2.2.2. Sytematic Run to Run Difference
In order to observe the systematic difference mere clearly,
we represent graphically "Volume Residuals versus Height", which
is snown in Figure-5. Volume residuals are calculated by the first
degree equation fitted to the data set(over 700mm) of Run#llto#14
on Ruska.
5
From this figure, the value of the systematic difference is
estimated as follows.
Runill - Run#14 about 2 lit.
Run#12 - Run#14 about -1 lit.
Run#13 - Run#14 about -2 lit.
The difference of Run#ll-Run#14 probably decreases to about
1 lit. if the correction can be applied to the positive shift of
about 1 lit. bitween level 1,750mm and level 2,800 mm in Run#ll
caused by a change of bubbling pressure to be feeded to dip tube.
The negative difference of Run*12-Run#14 and Run#13-Run#14 is
caused by the evaporation by air sparging performed in Run#12 and
Run#13. Also, the difference of Run#12-Run#13 is caused by no
homogenity of Tracer in the tank.
As mentioned bellow, the significant temparature difference
is existed bitween the feed tank and the tank to be calibrated.
Run No. TEMP.(FEED TANK) TEMP.(TANK) Min. Max. Min. Max.
Run#ll 20.9°C 28.7°C 19.4°C 21.8°C
Run#12 18.8°C 28.8°C 19.0°C 22.3°C
Run#13 13.7°C 28.8°C 18.1°C 21.7°C
Run#14 24.7°C 30.7°C 17.0°C 21.4°C
Therefore, the built-up of gradient in the water of the tank
to be calibrated is concidered. The temperature gradient is one
of the main cause to be studied further.
The observed value for the volume was corrected by the
geometrically determined volume of the installed instruments in
the tank. From our evaluation, it is not concluded that the
correction procedure is reasonable. But, this problem is considered
to be solved easily.
With regard to pressure drop in the case of the empity tank,
th3 effect is not the main cause because the systematic difference
is existed outstandingly at the high level(over 700mm).
6
Also, with regard to the systematic error in the Ruska instrument,
the effect is not the main cause because the precision of Ruska
is + 0.1mm, and + 0.1mm is equal to + 0.1 lit. in the case of the
tank to be calibrated at the high level. But, assuming that the
precision of Ruska is properly controled by piston-gauge st .ndard,
the precision mentioned above is assured. And, it is concluded
that no systematic effect comes from Toledo scale because the scale
has a high precision, as reported in RITCEX Status Report No.2.
2.2.3. Comparison of Volume calculated with each calibration equation
at the typical value
The typical values of Ha are chosen, and the volumes are calculated
with each calibration equation at the values, which are as follows.
Region-1 : Ha= 200mm Region-2 : Ha= 500mm
Region-3 : Ha=l,500mm Region-4 : Ha=2,500mm
Region-5 : Ha=3,100mm Region-6 : Ha=3,300mm
The calculated volumes are showen in Table-5, and the difference
among the equations on all data sets is observed.
From this table, the following results are concluded.
- The equation on Ruska and that on U-tube is approximately
the same.
- The value of the equation on TDR minus that en Ruska is positive,
and TDR could be considered to measure the larger data.
- Being contrary to TDR, the value of the equation on Acoustic
minus that on Ruska is negative, and Acoustic could be considère
to measure the smaller data.
2.2.4. Comparison of Volume calculated with each calibration equation
at break point
The volumes are calculated with each calibration equation at break
points, and the continuity of all equations on all data sets is
observed. The calculated volumes are shown in Table-6, and the
following results are concluded from this table.
7
- The continuity of all regions on Run#14 is the best, and it is
considered that the data measurement of Run#14 was carried out
in the best condition of all runs.
- The continuity of Region-2 to -4 on Run#ll is no good, and
this fact could be considered to be caused by the positive
shift between level 1,750mm and level 2,800mm.
- From the results of Run#ll to #14, it is confirmed again that
the solution was not adequately homogenized, and was evaporated
by air sparging, at the time of Run#12 and #13, when Tracer .
Technique was applied to.
8
3. Conclusion
In our evaluation, analyzing all data sets on different instruments,
the performance of those instruments are compared, and some problems
are identified.
The performance of those instruments is considered to be not
perfectly compared with only standard deviation, but it could be a
standard in the case of comparing the performance. From standard
deviation and some elements, it is concluded that the resultant
calibration equation on Ruska is the best, and is followed by that on
U-tube. Through the results on TDR and Acoustic are not as good as
those on Ruska, both instruments give more confidence to the whole
measurement system becausa they have the good characeristics such as
indipendance from the physical characteristics of liquids in the tank
(density, temperature), etc.
For the identified problem, the systematic run to run difference
is significantly large, and the following reasons might be responsible
for the systematic deviation.
- The temparature gradient is existed in the liquid of the tank.
- The pressure is differently dropped at the beginning of each run.
- The solution, which Tracer is added to, is not adequately
homogenized and is evapolated by air sparging.
- The instruments installed in the tank are changed every run.
- Ruska has a systematic error.
The problems except the temperature gradient are considered to be '•*
solved easily or to be not so significant. The temperature gradient
is considered to be the main reason for the systematic deviation, and
needs to be studied further in the future calibration.
In the framewark of RITCEX, the usual direct calibration was
carried out in Run#ll and Run#14, and the indirect calibration, which
9
Tracer Technique was applied to, was done in Run#12 and Run#13.
And, every run was not carried out with the same procedure including
the installation of new instruments in the tank. From PNC's
experimental point of view, the three direct calibration runs should
be carried out with the same procedure in order to determine the
calibration equation of a tank.
Though some problems remains to be solved, it seems to demonstrate
that on the whole, all runs give a very good fit to the resultant
calibration equations, and that RITCEX has the important possibility
to improve tank calibration.
•
J
4. References
(1) F. Franssen : "RITCEX Status Repor -. No.l" (November, 1983)
(2) F. Franssen : "RITCEX Status Report No.2" (BSPSI No.4, 1984)
(3) S. Suda, and B. Keisch(BNL), M. Hayashi, Y. Fukuari, and
T. Uchida(PNC), R. Augustson, and H. Shimojima(IAEA) :
"TASTEX Task-E Demonstration of the electromanometer for
measurement of solution volume in accountability vessels"
TECHNICAL REPORT SERIES No.213, IAEA, VIENNA, 1982
(4) 0. Yamamura, and T. Uchida : "PNC Calibration of Input
Accountability Vessel" (October, 1983)
(5) 0. Yamamura, T. uchida, and Y. Murakami : "Evaluation of
Historical Converted Data by PNC Analytical Method"
(January, 1984)
(6) 0. Yamamura, T. uchida, and Y. Murakami : "Evaluation of
Historical Raw Data by PNC Analytical Method" (January, 1984)
(7) T. üchida, and Y. Murakami : "Evaluation of RITCEX Calibration
Data by PNC Analytical Method" (May, 1984)
11
D a t a S e t
Ruska (Runl l l )
U-tube (Runl l l )
Ruska (Runll4)
U-tube (Runll4)
Vcoustic (Runil4)
I t » (Runll4)
.._ _ ..
Region-1
V=6.40859xlO-4xHa2
+5.96374xlo" 2xHa
+8.35467X10"1
V=6.23120x l0 - 4 xHa 2
+6.51506x10"2xHa
+7.01885X10"1
V=6.40476*10~*xHa^
+6.04210*10 - 2 xHa
+ 8 . 5 1 8 1 8 x l 0 - 1
V=6.27935*10 _ 4*Ha 2
+6.53887xl0~ 2xHa
+6.59970x10"
V=3 .95062x l0 - 5 xHa 2
+3.97839xl0 _ 1 xHa
•6 .98818X10" 1
T a b l e - 2 The R é s u l t a
Reqion-2
V=6.20331xlO"*xHa2
+7.75261xl0" 2 xHa
- 2 . 8 2 0 9 4
V=5.76148xl0~ 4xHa 2
+1.22576xl0" 1 xua
- 1 . 3 8 7 7 9 x 1 0
V=6.17408xl0"*xHa2
+7.91203xl0" 2 xna
- 2 . 7 6 1 9 8
V^6.07899xl0 - 4 xHa
+8.98732xl0~ 2 xHa
- 5 . 2 3 9 6 4
vas^oaesxio^xHa' +1.30410»10" 1x| la
- 1 . 1 1 5 6 6 x 1 0
V=4.56835xl0" 4 xua 2
+3.46206xlO~XxHa
- 2 . 2 0 4 4 2 x 1 0
n t C a l i b r a t i o n Eau
Reqion-3
V=2.94611xl0"6> a 2
+9 .20567x l0 - 1 xHa
-2 .90494X10 2
V=9.27198xlO"1xHa
-2 .93B03X10 2
V=-2 .27317x l0 _ 9 xHa 3
+ 9 . 6 8 8 2 2 x l 0 _ 6 x H a 2
+9.14140xl0 _ 1 xHa
-2 .88836X10 2
V=9.26432x l0 _ 1 xua
-2 .92988X10 2
v^LBseagxio'^xHa2
+8.64458xl0 _ 1 xHa
- 2 . 6 9 1 1 6 X 1 0 2
V=8.93072xl0"1xHa
-1 .96716X10 2
é t i o n s ( s i n g l e d a t a
Region-4
^ l i 1 3 8 7 6 x l o : 8 x l i a 3
-9 .08608x lo" 5 xHa 2
+ U 6 9 3 3 x H a _ ..
- 5 .02446X10 2
V^9,29344xl0 _ 1xHa
-2 .96556XJ0 2
V=1.06844xl0~ 8 x | la 3
_ -8-23641xlQ~ 5 xHa 2
+1.14030xHa
-4 .767B9X10 2
V=9.30100xl0 _ 1 x | ia
-2 .99537X10 2
V=9.37309xo"6xHa2
+8.89777*10 xHa
-2 .79B28X10 2
V=8.99084xl0 _ 1xHa
-2 .05203X10 2
—
s e t )
Region-5
V=8,53141xlQ"1xHa
-6_,1M95J<1Q-....
JfebUSlf iSaxKL 1 xHev
-5 .81888*10 ...
V=8.53553xl0 - 1 xHa
-6 .37943x10
V=B.56569xlO_ 1x|la
-7 .39303x10
V=8.62765xlÖ - 1«Ha
-1 .06791X1O 2
_._..
B e g i o n - 6
i f e2 .32633x io - lxHa
-3.123B4.xJL02
5fea.35552xlQ"1xüa
_ -3 .23759X10 2
V = 9 . 3 3 0 1 9 x l 0 - 1 x n a
- 3 . 1 4 2 6 0 x 1 0
W 9 . 3 1 8 2 5 x l 0 ~ 1 x l l a
r 3 . 1 1 4 1 0 x l p 2
V=-3 .13229xl0" 6 «l la 3
+ 3 . 1 1 7 1 1 x l 0 " 2 x n a 2
- 1 . 0 2 3 6 1 x l 0 2 x / | a
+ 1 . 1 3 6 5 6 x l 0 5
12
Table-3 The Resultant Calibration Equation (combined data set)
Data Set
Ruska (Run 111
andtl4)
U-tube (Run *11
andfl4>
Ruska (Run 111
to!14)
U-tube (Run 111
tot 14)
Acoustic
(Run H2toll4)
Region-1
V=6.39567xlO"*xHa2
+6.03621xlO~2xHa
+8.27041X10-1
V=6.25531xl0"4xHa2
+6.52410xlO-2xHa
+6.8B469X10"1
V=6.38736xlO~4xHa2
+6.04057xlO_2xHa . -1 +8.27952x10
VM>.27978xl0"4xHa2
+6.41296xl0" 2xHa
+7.09760X10"1
Region-2
V=6.18612xl0"4xHa2
+7.85931xlO~2xHa
-2.86106
V=5.91447xl0~4xHa2
+1.06924xlO-1xHa
-9.76048
V=6.14914xlo"*xHa2
+B.17005xlO_2xHa
-3.64001
V^6.21564xl0~4xHa2
+7.48497xl0-2xHa
-2.04270
V=4.79471xl0"4xHa2
41.82«3?xlQ "»Ha
-2.18323x10
Region-3 Region-4 Region-5
V=9.27818xlO_1xHa V=9.30251xl0_1xHa „-1-
-2.94708x10* -2.98804x10
V=3.52907xl0_6xHa2 V=9.29721xl0_1xHa
+9.17264x10 xxHa
-2.87705X102
-2.98040x10
V=8.48187x10 x|ia
-4.64057x10
V=8.43966x10 «Ha
-3.41885x10
V^2.50705xl0-6xHa2 V=9.30657xl0-1xHa
+9.21193xlO_1xHa -3.00272xl02
-2.91337X102
V=4.47747xl0_GxHa V=9.30223x10 1xHa
+9.14655xio_ïxHa
-2.86374X102 -2.99855x10
\^=3.99570xlO~SxHa2 V=9.43192xlO_1xHa
48.07482x10 xxHa 2
-2.41603x10
-3.56298x10
V=8.08314xlO axHa
+6.19039x10
Reg ion -6
V=9.32842x10 *x||a
-3 .13367X10 2
V=9.33661x10 *x|la
-3 .17484X10 2
V=8.37627x10 »Ha
-1.37912x10
V=8.2S124xl0"1»Ha
+1.16299x10
V=9.30882x10 xxHa
-3.07108X102
V=9.32261xl0_1xlla
-3.13025X102
V = - 2 . 9 6 9 9 1 x l 0 _ 6 x H a 3
+ 2 . 9 3 7 2 0 x l 0 - 2 x | l a 2
- 9 . 5 7 8 0 3 x l 0 x | l a
+1.05700X10 5
1 1
T a b l e - 4
Data Set
Ruska (Runlll)
U-tube (Runlll)
Ruska (Run#14)
U-tube (Runfll)
Acoustic. (Run|14
TOR iRun|14L
Ruska(Runlll and!14)
U-tube(Runt11 A«1I14)
Ruska(Runlll
tolU)
U-tube(Runlll
to l l4)
Data P o i n t ( D . P
O.P.
13
13
11
11
9
2 3
2 3
2 9
2 9
Acoustic(Runll2to|14)
Region-1
Deg. S.D.
2 0.08*
2 0 . 2 U
2 0.051
2 0.271
...
2 2.381
_ 2 „ Q,1Q« . . . .
2 . 0 . 2 9 1
2 0.131
2 0 . 3 U
— - • - - • • -
) , D e g r e e ( D e g . )
Region-2
D.P. Deg. S.D.
9 2 0.061
9 2 0.76t
9 2 0.061
9 2 0.48t
7 2 1,901
10 2 5.461
18 . 2 Q.10A
18. 2 0.681
31 2 0.301
31 2 1.171
• - - • • - - -
17 2 3.231
and Standard D e v i a t i o n
Region-3
D.P. Deg.
17 2
17 1
11 3
17 1
-17 2
15 1
. 3 3 1
33 2
50 2
50 2
35 2
. . ..
S.D.
0.251
0.721
0.191
1.10*
UHt.
7.751
Q.62i
0.821
0.841
1.331
—
9.411
• - - -
( S . D . ) o f each
Region-4
D.P. Deg. S.D.
21 3 0.221
21 1 1.031
^<L 3__jh31l
20_ 1 0 .8H
20 2. _ _ 0 t 7 « .
20 1 7.221
4Q 1 X U 2 1
4Q 1 - . 1 . 0 6 1
50 1 1.241
50 1 1.651
30 1 5.191
--
calibration
Region
D.P. Deq.
5 1
5 1
5 1
5 1
.5 .1
a i
. _ 2 1
i i i
i i i
5 1
- -
equation
- 5
S.D.
0.651
0.781
0.781
1,281
Q_-75t
0,751
Q.671
1.011
1.421
2.471
Region
D.P.
13
13
13
13
11
25
25
29
29
16
Dag.
1
1
1
1
3
X
1
1
1
1
-6
S.D.
0.061
1.031
0.071
0.381
0.331
0.321
0.791
0.801
1.371
2.071
14
Table-5 Comparison of Volume calculated with each ca l ibrat ion equation at the typica l value
i i t . > i i * ' ' i ' i i i i i i i . i i i *
Region-2 Region-3 Region-4 Region-S Region-6
Ha = SOOnm Ha = l.SOOMn Ha = 2,500nm Ha = 3,100mn Ha = 3,300nm
191.021(0.081) 1,096.991(0.901) 2,028.431(2.061) 2,583.291(0.441) 2,765.301(0.501)
191.451(0.511) 1,096.991(0.901) 2,026.B0K0.431) 2,582.051(-0.801) 2,763.5611-1.241)
191.151(0.211) 1,096.501(0.411) 2,026.131 (-0.241) 2,582.22K-0.63D 2,764.70l(-0.10t)
191.671(0.731) 1,096.661(0.571) 2,025.711(-0.661) 2,581.4311-1.421) 2,763.6111-1.191)
189.261(-1.681) 1,070.251(-25.841) 2,003.201(-23.171) 2,567.781(-15.071) 2,752.871(-11.93l)
265.271(74.331) 1,142.891(46.801) 2,042.511(16.141)
191.091J0.151) 1.097^021(0.931) 2,026.821(0.451) ^,582.971W.121) 2,765.011(0.211)
191.561(0.621) 1,096.131(0.041) 2,026.261 (-0.111) 2,582.Ill (-0.741) 2^763.601 (-1.201)
190.941 1,096.091 2,026.371 2,582.851 2,764.801
19C. 771 (-0.171) 1.095.68K-0.4U) 2.025.701 (-0.671) 2,581.91K-0.941) 2.t763,441(-1.361)
189.251 (-1.691) 1.059.52t(-36.57M 2,001,68t(-24.69t) 2,567_.68li=15.17li 2,756.44t(-§.361)
Data Set
Ruska(Runlll)
U-tube(Runlll)
Ruska(Runtl4)
U-tube(Run#14)
Acoustic(Runtl4)
TDR(Runtl4)
Ruska(Runlllandll4)
»-tube(Runlllandf14)
Region-1
Ha = 200mn
38.401 (-0.061)
3B.66t(0.20t)
38.561(0.101)
38.861(0.401)
81.85K43.39t)
38.481(0^21)
38.761(0.301)
Ruska(Run»ltoll4) 38.461
U-tube LRunllltoll4 ) 38.151ifi. 1?»X_
AOQ«sUci(R«all2toll4).._
Note ( ) : The difference bitween the volume of each calibration equation and_that of Ruska(Runtlltoil4)
15
Table-6 Comparison of Volume calculated with each calibration equation at break point
Data Set Region-1 Region-2 Region-3 Region-4 Region-5
Ruska (Runlll)
U-tifce(Runlll)
—-
Ruska (Runli4)
U-tube(Runjl4)
—
Acoustic(Runtl4)
TOR (Runll4)
Ruska(Runlllandll4)
Uhtube (Runlllandll4)
Ruska(Run|lltpll4)
U-tubeIRuniil t o ! 1 4 )
- -
Acoustic(Runf12 t o 114 )
lia - 35unro Ha = 700mn
100.21» 100.301 355.411 356.291__ ( 0.091) ( (KBBt)
99.841 99.601 354.241 355.241
(-0.241) < A^9*J
100.461 100.561 355.151 355.031
( 0.101) (-0.121)
100.471 100.681 355.541 355.511
< 0.211) (-0.031)
345.151 345.301 ( 0.151)
144.781 155.091 444.151 428.431
(10.311) (15.721)
100,301 100.431 355.27» 354.761
( 0.131) (-0.511)
100.151 100.121 354.891. 356.111 (-0.031) ( 1.221)
100.221 100.2B1 354.861 354.731
( 0.061) (-0.131)
100.081, J.00,301 354.921 356.081 _
- ( 0 , 2 2 1 ) 11.161)
340.811 343.211 ( 3.60£)
Ha = 2,000nm Ha = 3,070mn
1,562.421 1,561.17». 2,557.471 2,557.691
(-0.551' ( 0.221)
1,560.591 1,562.131 2,556.531 2,556.501
(-1.541) (-0.031)
1,560.011 1,559.831 2,556.811 2,556.611
(-0.181) (-0.201)
1.559.881 1,560.661 2.555.871 2.555.741
( 0.781) (-0.131)
1.535.681 1,537.221 2.540.131 2.541.901
( 1.541) ( 1.771)
1.589.431 1,592.971
( 3.541)
1.560.834 1*561.101 2 ,55i .Q2i ._j , 552,524
( 0.771) ( 0.461)
1.560.941 _ JU56-U4Q1 2+55&*2Ql^2*55&*12l ( 0.561) ( 0.59i)
1,561.081 1,561.041 2.556.841 2,577.721
(-0.041) ( 0.881)
1.560.851 1,560.591 2,555.931 2,557.041
(-0,264) L - 1 L 1 M ) . _ .
l ,533.19t 1,530.091 2 ,539 .30^ 2,543.43»
, _ 1-3:12^ , r__ f „( 4.13d ,
Region-6
Ha = 3,160nm
2,634.481 2 634.741
( _0.26l.)
2,633.151 2.632.4B1
(-0.671)
1,633.431 2,634-OJi ( 0.651)
2,632.831 2,633.161
( 0.331)
_L619.55t 2,619.531 (-0.021)
„2,633.&Z4-2,634.4U .
1_0^5.44)
2.632.744 2,632.884 ( 0.144)
2,633.111 2,634.481
_1.1.37.i]
2^31^661 2,632,921
( 1.261)
2,616.1B£ 3,617.28»
( 1.101)
Note ( ) : The difference bitween the volume of upper Region and that of lower Region. ].6
t'igure-j. ^rapnicai RHpieseui.ai.iuji ux. n.iur>.»* i*wv-(Run#llto#14, 195 points)
3wae r
2530
aoae
150Ü
ï sas
53Q
^
r r ^
> * ^
u*«2
a '3 a i n
ö 'S o —
a •a in —
G Q O Cl
O Q u-i OJ
G G Q '."•"
G G 1/7 01
Height (inn)
Figure-2 Graphical Representation of U-tube data
(Run#llto#14, 195 points)
0Q0
;ao
2039
H ISÛÛ
r
§ 1033
5 3 9
G
: ' * >
y
s*
,.aae 1 ^
G G G m
G G O —
0 0 m —
G G G <••!
O G m AJ
G G O o?
G G ITJ
<n Height (jim)
Figure-3 Graphical Representation of Acoustic data (Run#12to#14, 99 points)
£530
CÖUÖ
5 ISÛÛ
2
1 ötfö
>ÜkJ
S a
, • > < * '
^ . # • '
O 'D in
"3 El S
•3 O tn
O ü o •M
Heiaht (ran)
lui
a
Ll
'il S i 3 in
Figure -4 Graphical Represen ta t ion of TDR da ta (Run#14, 53 po in t s ]
2530
: 2000 -- * ? •P • H
•g 1500 >
1 000
i0S
a G Ci m
'3 o 'S —
G G i n —
G Q O <>j
G Q tn '.•>j
'D Ö •S •n
Height (irai) 18
Figure-5 Volume Residuals versus Height
(Ruska, Run#llto#14, over 700mm, Degree of Reg. = 1)
3 c j Q r-.
a o 01
—
o «2 r-—
iS Q cvi OJ
a Q P->.">j
*b iS OJ
ro
Hèiaht (rati)
RITCEX 12 • E
ITREC EVALUATION OF RITCEX CALIBRATION DATA.
Giovanni ARCURI
ENEA - ITREC CRE - TRISAIA
ITREC EVALUATION OF RITCEX CALIBRATION DATA.
Giovanni ARCURI
ENEA - ITREC CRE - TRISAIA
Introduction
The evaluation of tank calibration data of RITCEX has been done using
the converted data set of the all calibration runs, distributed at
the meeting held in Luxemburg on May 22-23, 1984.
The tank has been subdivided in six regions as agreed during the above
mentioned meeting.
Data Evaluation
The evaluation of the converted data set has performed by using the
following models :
Region Model Relationships
0 - 350
350 - 700
700 - 2000
2000 - 3070
3070 - 3160
3160 - Top
2 , * Polynomial Regression (PRM) V. = aO + al • Xi + a2 • Xi + t L
Cumulative Regression (CUM)
and
V = a0 + al • Xi + 2- £ T J-i J
Least-Square Regression (LSM) V. = a0+ al 'Xi + £(
L. th C = the i random error
C th Cj = the j random error
2*T = th
the i random error
The Cumulative Regression model has been used as it is the conventional
method, applied at the ITREC Plant, for the evaluation of the calibration
of the accountability tanks.
The Last-Square Regression model (1-2), has been used as an alternative
evaluation of the data and to compare the results with those obtained with
the CUM-model.
As the main purpose of the RITCEX is to compare the performances of different
measurement techniques and instruments currently applied or under development
for accountability tank calibration and not to determine the best calibration
curve of the EUROCHEMIC facility, the evaluation of the converted data set
have been performed on all the calibration runs and increments.
The results are reported in the hereinafter enclosed tables and plot of
residuals.
References
1- C.G. Hough-Statistical Analysis-Accuracy Of Volume Measurements in A
Large Process Vessel. HW-62177, October 1959
2- U.V. Nalimov-The Application Of Mathematical Statistics To Chemical
Analysis - 1963.
RITCEX-SUMMARY QF EVALUATION OF THE CONCERTED DATA SET
TBE - L S M
THIRD SECTION
RUN! LEVEL X ( 9 )
(mm) )<<n)
ALPHA ! BETA ! R E S I D . ( L T . ) ! LT/mm! VAR.
BETA ! ALPHA-BETA!ALPHA !SVmax VARIANCE ÎCOVARIANCE! VAR. ! L T .
11 ! 12! 13! 14!
717, 792, 711 , 716.
29! 36! 45!
AVERAGE
1933, 1839. 1343,
36Î2091
33 43 25 16
-293.656!0.9271 ! 9.5305!1.5553E-97!-J.9002037!9 -294.296 ! 0.9257! 2.7101 ! 2.9523E-06!-0.0923233 ! 2 -293.71119.9267!1.2943!9.7657E-07!-8.0011142! 1 -293.1?7! 0.9265! 1.2743 ! 3.6729E-07!-4.844E-94! 9
,2999! ,9425! ,4152! ,7136!
30 91 39 23
!-293.535 !0. 9263 ! 1.. 235 ! 1 .7431E-07!-2.953E-04 ! 8 .2725! 1.19!
11 ! 2036.75 1212956.31!2924.6o 1312864.3212931.00 14Î2991.9613961.96
AVERAGE
FOURTH SECTiON
- 2 9 5 . 9 9 ? ! 0 . 9 2 9 1 ! 1 . 0 3 0 3 ! 5 . 2 2 4 6 E - 9 7 ! - 0 . 0 0 1 3 9 2 9 ! 3 . 7 6 7 5 ! 1 . 1 0 ! - 2 9 3 . 1 0 0 1 0 . 9 2 8 0 ! 0 . 4 1 7 3 ! 3 . 3 6 0 3 E - 9 7 ! - 0 . 0 0 2 2 0 5 7 ! 5 . 5 7 4 4 ! 9 . 3 2 ! - 3 9 0 . 9 1 7 ! 0 . 9 3 0 6 1 9 . 5 7 2 5 ! 1 . 2 1 9 6 E - 9 6 ! - 0 . 9 9 3 9 4 7 2 ! 7 . 7 2 3 3 ! 0 . 9 6 ! - 2 9 9 . 5 3 7 1 0 . 9 3 0 1 1 9 . 6 4 3 6 ! 2 . 8 2 7 7 E - 0 7 ! - 7 . 4 2 9 E - 0 4 ! 1 . 9 8 4 5 ! 9 . 3 6 !
Î - 2 9 8 . 5 7 0 Î 0 . 9 2 9 6 1 9 . 3 9 9 4 ! 1 . 2 3 9 2 E - 9 7 ! - 3 . 3 4 7 E - 9 4 ! 0 . 8 3 3 1 ! 0 . 9 2 !
1 1 1 3 0 7 1 . 6 1 1 3 1 6 3 . 4 1 12!' - ! 13! - ! 1 4 1 3 0 3 1 . 2 7 1 3 1 5 3 . 8 3
AVERAGE
FIFTH SECTION
- 5 8 . 1 9 3 1 0 . 3 5 1 7 1 9 . 6 1 0 3 ! 1 . 1 4 3 2 E - 9 4 * . • _ I — ' _
I I I
_ ' — ' ' _- » _ 9 . 2 0 1 1 0 . 8 3 0 0 1 9 . 1 7 1 4 Î 5 . 8 9 0 2 E - 9 5
-0.3563843
-0.1303239
1111.1
563.3
0.9?
0.54
-13.43410.337310.422214.5091E-051-9.1485721 ! 433.3! 0.74!
SIXTH SECTION
1113134.09!3453.96!-327.33110.936611.1215!1.0631E-95!-0.0356068!11 9.35 121 3145.5313455.291-305.61910.928910.0559!1.0334E-06!-0.0036144 ! 12.02 1 3 ! 3157.93 ! 3452.90 !-352.534 ! 8.9442! 9.2575 ! 5.5353E-961-9.0135333 ! 61.91 14! 3173.1213453.331-310.55919.931619.1600!1.2367E-06!-0.0042911 ! 14.32
1 .15! 0.31 ! &.66\ 0.44!
AVERAGE 1-312.354!0.931710.5662!1.3333E-061-0.0046463! 15.56! 9.77!
RITCEX-SUMMARY OF EVALUATION OF THE CONVERTED DATA SET
TBE - C U M
THIRD SECTION
RUN! LEVEL (mm) ! ALPHA ! BETA ! R E S I D . ! BETA ! X<0> ! X<n ) ! < L T . ) ! LT/mm! VAR. ! VARIANCE
ALPHA-BETA ! ALPHA !SVmax COVARIANCE! VAR. ! L T .
11 ! 12! 13! 14!
717. 702. 711 ,
2 9 ! 1 9 3 3 3 6 ! 1 8 3 9
, 3 3 ! - 2 9 4 . , 4 8 ! - 2 9 0 .
4 5 ! 1 3 4 3 . 2 5 ! - 2 9 2
05210 10410 , 440 ! 0
' 1 6 . 3 6 ! 2 9 0 1 . 0 6 ! - 2 9 1 . 4 6 1 ! 0
9 2 7 7 ! 8 . 0 1 5 9 ! 1 9 2 3 6 ! 0 . 1 3 9 9 ! 1 9 2 6 0 ! 0 , 9 2 5 8 ! 0 .
031217 0206!1
2 6 0 0 E - 0 5 2 3 0 7 E - 0 4 1 4 3 4 E - 0 5 6 8 4 9 E - 0 5
7 . 9 6 - 0 . 0 3 6 5 0 3 6 ! 1 5 9 . 1 2 1 2 2 . 6 3 -0 . -0503228! 9 3 . 9 3 ! 1 7 . 3 3 - 0 . 0 1 1 5 0 5 0 ! 2 3 . 0 2 ! 4 . 1 6
AVERAGE ! - 2 9 2 . 7 2 1 ! 0 . 9 2 6 6 ! 0 . 8 5 0 3 ! 1 . 0 7 9 2 E - 0 5 ! - 9 . 8 0 7 6 4 5 0 ! 1 4 . 3 4 ! 1 8 . 6 4 !
FOURTH SECTION
11!2036 .7513871, 12 !2856 .31!2924 . 13 !2064 .82 !2931 , 1412001.0613061,
AVERAGE
61 ! - 2 9 7 . 7 4 4 1 0 . 0 6 ! - 2 9 9 . 3 5 3 Î 0 . 0 9 1 - 3 0 1 . 9 3 2 1 0 . 9 3 1 2 1 0 96\-299.41210.929710
9 2 9 5 ! 8 . 8 3 6 3 ! 3 . 5 0 4 7 E - 0 5 ! - 0 . 0 7 1 3 8 2 7 ! 2 1 9 . 2 6 ! 1 4 . 9 3 ! 9 2 8 3 ! ^ . 0 0 3 3 1 3 . 3 3 1 7 E - 0 6 1 - 0 . 0 0 7 3 7 9 8 ! 2 3 . 0 4 ! 4 . 3 8 !
, 8 8 3 6 1 4 . 2 2 4 3 E - 0 6 1 - 0 . 0 9 3 7 2 2 0 ! 2 5 . 5 6 ! 4 . 6 3 ! 0 2 7 3 1 2 . 5 7 5 6 E - 0 5 ! - 0 . 0 5 1 5 3 9 0 ! 1 5 7 . 8 1 ! 1 2 , 9 4 !
! - 3 0 0 . 3 5 3 ! 8 . 9 2 9 8 ! 8 . 0 2 6 9 ! 6 . 4 5 3 7 E - 0 6 ! - 0 . 0 1 3 0 5 3 0 ! 3 9 . 9 9 ! 1 0 . 1 4 !
1113071.6113163.41 12! - ! 13! 1413081.2713153.38
FIFTH SECTION
- 8 7 . 3 2 3 1 0 . 3 6 1 8 1 8 . 8 5 1 1 1 5 . 5 6 3 5 E - 0 4
6 . 7 9 3 1 8 . 3 3 8 9 1 0 1 9 3 ! 1 . 2 7 4 9 E - 0 4
- 1 . 7 0 3 9 0 3 0 1 5 4 0 5 . 9
- 0 . 3 9 2 3 3 4 8 ! 1 2 3 3 . 9
1 7 . 9 7
7 .64
AVERAGE • 1 0 . 7 5 7 1 0 . 3 3 6 5 ! 0 . 0 3 3 2 ! 1 . 3 6 2 8 E - Ö 4 ! - 0 . 5 7 2 4 3 3 8 ! 1 3 1 0 . 1 ! 1 2 . 5 3 !
SIXTH SECTION
11 12 13 14
3184. 3145, 3157, 3173.
09! 35! 93!
3453 3455 3452
1213453
, 961-302, ,291-306, ,00 1-359, ,331-311.
383 244 317 150
929410, 9291!8, 943610, 931810,
169716 0905!1 0033!1 027119
.2331E-04!
.7793E-06!
.1383E-05!
.6786E-05!
-2, -0, -0, -0,
0822000! 0855938! 0356958! 30635301
6915, 19. 123,
1059.
34 1 , 4 13,
24! 95! 79! 63!
AVERAGE -312.25218.931 I ! 8.8036!7.6939E-05!-0.2459800! 846.3!13.98!
RITCEX-SUMMARY OF EVALUATION OF THE CONVERTED DATA SET
RUSKA - L S M
THIRD SECTION
RUN! I 1
11 ! 12 ! 13 ! 14i
LEVEL X < 0 ) !
7 1 7 . 4 4 7 0 4 . 9 9 7 1 3 . 2 7 , 7 1 3 . 5 8
•', mm > X < n >
1 9 3 2 . 3 0 1 3 3 8 . 1 0 1 3 4 9 . 3 1 2 0 0 1 . 0 4
ALPHA < L T . )
- 2 9 5 . 2 1 0 - 2 9 4 . 6 3 3 - 2 9 5 . 3 5 0 - 2 9 4 . 3 4 7
BETA LT/mm
0 . 9 2 3 5 0 . 9 2 6 3 0 . 9 2 6 9 0 . 9 2 7 2
RESID . VAR.
0 . 2 1 5 9 0 . 0 7 1 4 0 . 1 4 3 3 -0 . 0 2 5 9
BETA VARIANCE
6 . 3 5 0 3 E - 0 S 5 . 4 1 6 8 E - 0 3 1 . 0 S 5 5 E - 0 7 7 . 4 7 5 3 E - 0 9
ALPHA-BETA COVARIANCE
- 8 . 3 1 6 E - 0 5 - 6 . 1 4 9 E - 0 5 - 1 . 2 4 0 E - 0 4 - 9 . 3 6 3 E - 0 6
ALPHA ! VAR. !
1
0 . 1 2 2 4 ! 0 . 0 7 7 5 ! 0 . 1 5 7 7 ! 0 . 0 1 4 6 !
SVmax ! L T . !
0 . 5 0 ! 0 . 3 2 ! 0 . 4 6 ! 0 . 1 3 !
AVERAGE - 2 9 4 . 5 2 6 ! 0 . 9 2 7 3 ! 0 . 1 1 6 3 ! 1 . 2 8 6 1 E - 0 3 ! - l . 5 6 4 F - 0 5 ! 0 . 0 2 1 4 !
FOURTH SECTION
11 ! 2 0 3 5 . 7 7 ! 3 0 6 9 . 7 6 ! - 2 9 5 . 2 3 0 ! 0 .9292!0 . 1 2 ! 2 0 5 3 . 3 7 1 2 9 1 9 . 4 9 ! - 2 9 9 . 2 0 4 ! 0 .9297! 0 , 13 ! 2066 .63 ! 2933 .37 ! - 3 0 1 . 2 4 4 ! 0 .9303 ! 0 , 1 4 ! 2 0 0 1 . 0 4 1 3 0 6 0 . 0 8 ! - 3 0 1 . 3 3 4 ! 0 .9309! 0
2 7 7 0 ! 1 . 3 3 9 4 E - 0 7 ! - 3 . 5 7 0 E - 0 4 ! 0 . 9 6 5 1 ! 1 9 6 3 ! 4 . 1 9 4 5 E - 0 7 : - 0 . 0 0 1 0 4 2 7 ! 2 . 6 3 1 6 : 2630 ! 5 .5982E-07! -0 .0013994 ! 3 .5509 ! 1030 ! 4 .5001E-08! - .132E-04! 0.1030 !
AVERAGE - 2 9 9 ,
s j . D6 ; 0 . 5 6 ! 0 .65 ! 0 . 3 4 !
,9304 ! 0 . 1 9 6 9 ! 3 . 9 7 6 6 E - 0 8 1 - 1 . 0 2 2 E - 0 4 ! 0 . 2 4 4 7 ! 0 .44 !
1113069 .76!3161 .73 12! - ! 13! - ! 14!3030 .9313152 .66
AVERAGE
FIFTH SECTION
- 6 1 . 4 4 2 ! 0 . 8 5 3 1 ! 0 . 4 2 4 8 ! 7 . 9 3 3 1 E - 0 5 t i t ~
! I t "
-20.36010.339710.3165!1.0965E-04
-9.2437539
-0.3417763
i.2
1065.4
0 .32!
_ I i
0 .73!
-44.139!9.3475!0.3734!4.6305E-05!-0.1443104! 449.3! 0.711
SIXTH SECTION
11 13183 .3313452 .14! -312 .570 ! 0 .9327!0 .0010 ! 3 . 9 9 9 4 E - 0 9 ! - 3 . 0 1 3 E - 0 5 ! 0 . 1 0 0 9 ! 0 . 0 3 ! 1 2 ! 3 1 4 1 . 4 3 1 3 4 5 1 . 2 6 ! - 3 0 4 . 2 5 7 ! 0 . 9 2 6 9 ! 0 . 0 3 6 7 ! 7 . 2 3 0 6 E - 0 7 ! - 2 . 4 1 5 E - 0 3 ! 3 . 0 2 1 9 ! 0 . 2 5 ! 13 ! 3156 .33 ! 3454.50 ! -313 .652 ! 0 .9322 ! 0 .0263 ! 5 .5720E-07! -0 .0013544 ! 6 .1304 ! 0 . 2 1 ! 1 4 ! 3 1 7 2 . 4 9 1 3 4 5 2 . 1 7 ! - 3 1 4 . 5 0 5 ! 0 . 9 3 3 1 1 0 . 0 1 7 7 ! 1 . 4 2 4 9 E - 0 7 ! - 4 . 7 5 1 E - 0 4 ! 1 . 5 3 5 2 ! 0 . 1 4 !
AVERAGE - 3 1 2 . 6 0 3 ! 0 .9327 ! 0 .0127i 4 . 0 7 4 0 E - 0 3 ! - 1 . 3 5 5 E - 0 4 1 0 . 4 5 1 5 ! 0 . 1 2 !
- 4 -
R.TCEX-SUMMARY QF EVALUATION QF THE CONVERTED DATA SET
RUSKA - C U M
THIRD SECTION
RUN
11 12 13 14
LEVEL XC0) '
7 1 7 . 4 4 ! 7 0 4 . 9 9 7 1 3 . 2 7 ! 7 1 3 . 5 3
(mm) X<n )
1 9 3 2 . 8 0 1 8 3 3 . 1 0 1 3 4 9 . 3 1 2 0 0 1 . 0 4
ALPHA (. L T . )
- 2 9 4 . 5 7 5 - 2 9 4 . 0 3 3 - 2 9 4 . 5 6 7 - 2 9 3 . 9 5 6
BETA LT/mm
0 . 9 2 3 3 0 . 9 2 6 4 0 . 9 2 6 7 0 . 9 2 7 0
RESID. VAR. !
0 . 0 0 1 7 ! 0 .0010 0 . 0 0 3 2 ! 0 . 0 0 0 4
BETA VARIANCE
1 . 3 3 5 3 E - 0 6 8 . 6 7 1 9 E - 0 7 2 . 3 6 2 7 E - 0 6 3 . 2 9 4 3 E - 0 7
ALPHA-BETA COVARIANCE
- 9 . 5 3 4 E - 0 4 - Ó . 1 1 4 E - 0 4 - 0 . 0 0 2 0 4 1 S - 2 . 3 6 7 E - 0 4
ALPHA VAR. !
1 . 9 0 0 3 ! 1 . 1 2 3 7 3 . 7 7 6 1 ! 9 . 4 7 3 7
SVmax L T .
2 . 5 9 1 .90 3 . 4 6 1 .30
AVERAGE ! - 2 9 4 . 1 1 5 ! 0 . y 2 / 1 1 0 . 0 0 1 4 ! 2 . 9 7 9 2 E - 0 7 ! - 2 . 1 2 3 E - 0 4 ! 8 .4065! 1.39!
11 12 13 14
2035. 2053. 2066. 2001 ,
7713069 37Î2919 63 ! 2933.37 0413060.03
FOURT SECTION
76 ! -298 .425 ! 0 .9303! 0 .0015! 49! -300 .211 ! 0 .9300!0 .0013!
-302.53110.930710.0016! -302.66110.931410.0004!
1.4324E-061-0 1.5361E-061-0 1.3973E-06!-0 3.9542E-071-7
0030170! ,0631540! 0039220! .913E-04!
9. 9, 11 .
264! 2031 506! 421!
3. 07 79
3.10 1 .60
AVERAGE -301.636 ! 0.930910.0011 ! 2.6855E-07!-5.472E-04! 1.1571 1.39!
11 ! 12 13 14
3969.76', _ _
3 0 8 0 . 9 3
AVERAGE
3161 . 7 5
• -3152.66
FIFTH SECTION
-80.844 ! 0.8594! 9.0338! 3.6742E-04 I I I I I • I l i ™
-24 .32910.841110.013812.6165E-04
-1 .127330813566.1 ! 14.60
-0 .306127012541.4110 .36
-47 .84710 .3437!0 .0273!1 .6104E-04 ! -0 .494990011563 .5 !11 .33 !
SIXTH SECTION
11 1 3138 .3313452 .14! -313 .76310 .9330!1 .1936E-04!4 .459E-07! -0 .00142 ! 4.90 10.91 ! 12! 3141 .4313451.20 ! -304 .722 !0 .9298!2 .9356E-04 !9 .640E-07 ! -0 .00303 ! 1 0 . 4 5 ! 1 . 4 3 ! 13 ! 3156.8313454.50 ! -313 .745 ! 0 .9322!9 .0928E-06! 3 .055E-03! -9 .64E-05 ! 0 . 3 3 i 0 . 2 4 ! 14! 3 1 7 2 . 4 9 1 3 4 5 2 . 1 7 ! - 3 1 6 . 1 6 5 ! 0 . 9 3 3 6 ! 1 . 5 0 3 4 E - 0 6 ! 5 . 3 9 3 E - 0 7 ! - I . 7 1 E - 0 3 ! 5.91 ! 1.02!
AVERAGE 1-313 .616!0 .9323!2 .9031E-05 ;1 .233E-07! -3 .91E-04! 1 .3510.47!
-5-
RITCEX-SUMMARY OF EVALUATION QF THE CONCERTED DATA SET
SONAR - L S M
THIRD SECTION
!RUN LEVEL x-:0)
(ram) X<n)
ALPHA ! BETA 1RESID.! BETA <LT.) ! LT/mmi VAR. ! VARIANCE
! ALPHA-BETA!ALPHA ICOVARIANCE! VAR.
SVma; LT.
12 13 14
728.77!1393.11 733.42!1830.68 731.63!1972.37
-297.649 ! 8.3967 ! 91.546 ! 6.5095E-05!-0.07647501100.02 -305.399!0.9146! 9.944!7.3086E-06!-0.0035427! 11.09 -300.51610.9165! 3.716!2.4572E-06!-0.0032960 ! 4.97
11 .63 ! 3 .84!
AVERAGE -301 .36310 .9155131 .132!6 .3131E-06! -0 .00806981 19 .65! 5.981
FOURTH SECTION
12! 2107.9912943.491-402.323! 0.9584 ! 52.227 ! 1312097.08 ! 2951.37 !-357.232 ! 0.9439 ! 1.7761 ! 14!2025.96!3977.27!-347.83110.9393197.754!
1.1333E-04!-0.2981747 ! 3.3926E-06!-0.0098210! 2.1474E-05!-0.0609940 !
761.75! 9.16! 25.13! 1.69! 176.51 ! 10.39!
AVERAGE •357.37310.9437176.790!1.1973E-95!-9.0295260 ! 30.26! 92!
FIFTH SECTION
12! 13! 14!3097.93 3163 .93 - 6 1 . 1 6 6 0 .348310 .2318 3.1980E-05 -9 .25630001304 .74! 0 .63
12! - ! 1313175.4213454.49 1413133.9613452.17
SIXTH SECTION
-438.72210, -536.73710,
9825172. 99751 1,
95710.00177600 908 il.7344E-05
-5.9236000!19772 -0.0596700!199.76
11.19! i .51
AVERAGE !-439.380 ! 0.9852 ! 14.320 ! 1.6833E-04!-0.5629220 ! 1 379.2 ! 4.39 !
RITCEX-SUMMARY OF EVALUATION OP THE CONCERTED DATA SET
SONAR - C U M
THIRD SECTION
RUN LEVEL x>:0)
< mm ) X ( n >
ALPHA < L T . )
BETA ÎRE3 ID , LT/mm! VAR.
BETA ! ALPHA-BETA ! ALPHA ! 3Vma;< VARIANCE 1C0VARIANCE! VAR. ! L T .
12 13 14
7 2 0 . 7 7 ! 1 8 9 3 . 1 1 ! - 2 3 6 . 3 6 2 ! 0 . 3 9 5 4 ! 0 . 5 3 9 6 ! 4 . 6 9 2 3 E - 0 4 ! - 0 . 3 3 1 7 2 6 ! 6 2 3 ! 4 5 . 2 7 3 3 . 4 2 ! 1 3 8 0 . 6 8 1 - 3 0 6 . 5 9 2 ! 0 . 9 1 7 6 ! 3 . 1 0 3 7 1 2 . 7 8 9 7 E - 0 3 ! - 1 . 9 3 7 3 5 0 ! 3 7 3 3 ! 1 0 5 . 1 731 . 6 8 ! 1 9 7 2 . 3 7 ! - 2 9 9 . 9 0 5 ! 0 . 9 1 3 6 ! 0 . 0 5 3 0 ! 4 . 0 9 5 4 E - 0 5 ! - 0 . 0 2 9 9 6 9 ! 6 1 ! 1 4 . 7
AVERAGE ! - 2 9 8 . 3 2 6 ! 0 . 9 1 6 6 ! 0 . 9 9 7 6 ! 2 . 8 8 1 4 E - 0 4 ! - 0 . 2 1 0 3 0 1 ! 3 9 3 ! 5 1 . 9 !
FOURT SECTION
1 2 ! 2107.99 ! 2943.49 !-422.359 ! 0.9641 ! 0.3714 ! 4.444SE-04 ! 13! 2097.00! 2951 .37!-358.391 ! 0.9441 ,'0.0106! 1 .2374E-05! 1 4 ! 2025.96 ! 3077.27 !-339.745 ! 0.9332 ! 4.6529 ! 4.4253E-03 !
-0.936961! 2753! 46.3! -0.025943! 77! 7.9! -3.966600! 27592!169.2!
AVERAGE -360.563!0.9446!3.3303!1.0607E-03! -2.150300! 66121116.5!
FIFTH SECTION
12! 13! 14!3097, 98 3163.93 -67.315!0.350310.0141 ! 1.9300E-04 -0.614100 1946 9.4
SIXTH SECTION
12! 13!3175. 14!313S,
42!3454.49 9613452.17
-459.525! 0.9727! 0.93791 0.00354009 -517.337 ! 0.9929 ! 9.1820 ! 3.3739E-94
-11 .241090 -1.235399
33332 4265
32.6 26.5
AVERAGE !-512.066!0.9901!0.2630!4.3929E-04! -1.527309! 5275! 36.91
RITCEX-SUMMARY OF EVALUATION OF THE CONVERTED DATA SET
T D R - C U M
THIRD SECTION
RUN! LEVEL (mm) X < 9 !» ! X < n >
ALPHA <LT.)
BETA ÎRESID. LT/mm! VAR.
BETA VARIANCE
ALPHA-BETA I ALPHA COVARIANCE! VAR. L T .
14! 636 1970 - 1 9 4 . 6 2 2 0 .3912 I3 .3363 0 . 0 0 2 9 -1 .3299 1 360: 1 22 .9
14! 1970 !
FOURTH SECTION
3857! -226 .500!0 .9074131 .607! 0.00151 - 2 . 9 1 2 4 1 3 9 0 3 1 9 9 . 1 2 !
1 4 ! 636',
T D R - L S M
THIRD SECTION
1970! - 1 9 0 . 5 5 ! 0 . 3 8 9 1 ! 7 9 . 1 7 9 : 2 . 1 0 0 E-05! -0.02641 33.261 9.73!
FOURTH SECTION
141 19701 30571-203.620!0.3981 ! 44.672!1.3100E-05! -0.0475:126.38: 7.10
RITCEX-SUMMARY OF EVALUATION OF THE CONVERTED DATA SE1
COMPARISON BETIJEN DIFFERENT SYSTEMS
L S M
THIRD SECTION
SYSTEM
TBE RUSKA SONAR TDR
ALPHA ! BETA 1RESID. ! BETA (LT.) ! LT/mm! VAR. I VARIANCE
-T*3.584!0.9263! 1.2351 ! 1.7431E-07 -294.526!0.9273! 0.1163!1.2361E-98 -301.363!0.9155!31.1315!6.8981E-06 -190.55a,0.3991!79.1737!2.18E-05
ALPHA-BETA COVARIANCE
-2.0577E-04 -1.5644E-05 -3.1Ó93E-03 -0.0264
ALPHA VAR.
0.2725 0.0214 10.64S6 38.2600
SVmax LT.
1.19 0.35 9.16 9.73
iTBE !RUSKA ! SONAR !TDR
FOURTH SECTION
-293.570!0.9296! 0.3004!1.2892E-07 -299.863 ! 0.9304 ! 0.1969 ! 3.9766E-0S -357.373!0.9437!76.7901 ! 1.1073E-05 -20 3.620!0.8931 ! 44.6717!1.31E-05
-3.3474E-04 -1 .0215E-04 -0.029516 -0.0475
0.3331! 0.92! 0.2447! 0.44! 30.2611! 3.92! 126.3300! 7.10!
FIFTH SECTION
!TBE !RUSKA ! SONAR
-13.434! 0.8373! 0, -44.139!0.3475! 0 -61.16610.3433! 0,
4222Î4.509E-05 378414.6305E-05 2313Î3.19E-05
-0.140572 -0.1443 -0.2563
! 433.2790! 1 449.7300! 1 304.7400!
0 0 0
74! 71 ! 63!
ITBE !RUSKA !S3NAR
SIXTH SECTION
-312.354!0.9317! 0.5662!1.333SE-06!-8.004646 -312.603!0.9327! 0.9127!4.0740E-08!-1.3553E-04 -439.38 10.9352!14.8195!1.6833E-04!-8.56292
15, 0,
1379,
5603! 4515! 1700!
0, 0 , 4,
77! 12! 39!
RITCEX-SUMMARY OF EVALUATION OF THE CONVERTED DATA SET
COMPARISON BETWEN DIFFERENT SYSTEMS
CUM
THIRD SECTION
'. SYSTEM
!TBE !RUSKA ! SONAR !TDR
!TBE !RUSKA ! SONAR !TDR
ALPHA (. LT. >
-292.721 -294.115 -298.326 -194.622
-300.358 -301.636 -298.326 -226.5
BETA LT/mm
0.9266 0.9271 0.9166 0.3912
RESID. VAR.
0.0503 0.9014 0.9976
BETA VARIANCE
1.0792E-05 2.9792E-07 2.3814E-94 0.0029
FOURTH SECTION
0.9293 0.9309 0.9166 0.9074
0.0269 0.0011 0.9976 1.6078
6.4537E-06 2.6859E-67 2.3814E-04 0.0015
ALPHA-BETA COVARIANCE
-0.00 7645 -2.1273E-04 -0.210301 -1.32900
-0.013053 -5.4715E-04 -0.210301 -2.9124
ALPHA VAR.
1 4.34 0.41
397.49 3603.08
39. ?? 1 .16
397.49 3903.09
SVmax ! LT.
10 1
51 122
10 1
51 ??
64! 3?'< 93! 94!
14! 39! 93! 12!
ITBE !RUSKA ! SONAR
! -10 ! -47 ! -67
757 .847 .315
0 0 0
FIFTH SECTION
, 3365 !8 .0332 !1 .3623E-04 .3487 !0 .0273 !1 .6104E-04 ,8503 !0 .0141 ! 1.93E-04
- 0 . 5 7 2 4 4 - 0 . 4 9 4 9 9 -0 .61410
1810.05 1563.47 f 4 6 . 2 9
12 .53! 11.38! 9 . 4 4 !
TBE RUSKA SONAR
SIXTH SECTION
• 3 1 2 . 2 5 2 ! 0 . 9 3 1 1 ! 0 . 0 8 3 6 ! 7 . 6 9 3 9 E - « 5 ! - 0 . 2 4 5 9 - 3 1 3 . 6 1 6 ! 0 . 9 3 2 3 ! 3 E - 0 5 ! 1 . 2 3 3 3 E - 0 7 ! - 3 . 9 1 1 4 E - 0 4 - 5 1 2 . 0 6 6 ! 0 . 9 9 0 1 ! 0 . 2 6 3 8 ! 4 . 3 0 2 9 E - 0 4 ! - 1 . 5 2 7 3
346.27 1 .35
274.14
! 1S.98 ! 8.47 ! 33.83
- 1 9 -
RITCEX-SUMMARY OF EVALUATION OF THE CQNUERTED DATA SET
T B E - P R M
FIRST SECTION
! RUN ! LEVEL X0 ! Xn
a0 al S (at f (a l )
7 .411349.751 23.71 ! 381 .12!
13! 1 7 . 7 3 ! 3 9 1 . 3 9 ! 14! 7 .411354 .25 !
11 1 12!
0.7019! 0 .0652! 6 .2312E-04! 0.37121 0 .0537! 6 .4155E-04! 0 .7722! 0 .0595! 6 .3771e -94! 0 .6620! 0 .0653! 6 .2311E-04!
0 .12505! 0.21501 ! 0 .38590! 0.266971
0.00137 0.00261 0.90461 0 .90293
5 . 4 3 9 3 E - 0 6 ! 6 . 4 5 0 0 E - 0 6 1 1.1260E-051 7.5638E-06!
AVERAGE 0.7355! 0 .0632! 6.3033E-041 0 .1073 ! 0 .09129 3 . 3 3 9 6 E - 0 6 I
SECOND SECTION
11 1404.61 i 636 .231-16 .373 . ' 0 .1333! 5.666SE-04! 11 . 37733! 0.04239 121381.121702.36! 2 9 . 1 2 1 1 - 0 . 0 4 3 1 ! 7 .3425E-04!14 .19132! 0.05370 131391.301711.45! - 3 . 5 6 3 ! 0 .0959! 6 .0520E-04! 4 .95909! 0.01349 141354.251716.36! -3 .6031 9 .0320! 6 .1537E-94! 3 .69850! 0.01379
3 . 3 6 3 7 E - 0 5 1 4 . 2 2 S S E - 0 5 ! 1 . 6 5 3 6 E - 0 5 ! ! . 2 7 3 2 E - 0 5 !
AVERAGE ! - 4 . 6 9 6 ! 0 . 0 8 4 7 ! 6 . 1 5 3 7 E - 0 4 ! 4 . 5 3 0 9 0 ! 0 . 0 1 7 0 3 ! 1 . 4 5 1 3 E - 0 5 !
- 1 1 -
!RUN!
RITCEX-SUMMARY OF EVALUATION OF THE CONVERTED DATA SET
RUSKA - P R M
FIRST SECTION
LEVEL X0 ! Xn
a9 al S (as S < a 1 ) K a l '.
11 ! 12! 13! 141
6 22 17 7
.08
.49
. 23
.46
343.6 ! 381.16! 399.19! 353.9 !
9.7374 9.3712 9.3569 9.3518
0 0 0 0
.0597! 0587! .9594! .0684!
6.4199E-04! 6.4155E-04! 6.4058E-041 6.4048E-94!
0 . 0 0 4 0 1 ! 9 . 1 6 E - 9 7 0 . 2 1 5 9 1 1 9 . 0 0 2 6 1 0 9 . 1 3 5 9 5 ! 9 . 9 9 1 6 3 1 0 . 9 5 1 6 5 1 0 . 0 0 0 5 7 3
AVERAGE ! 9 . 3 2 9 9 1 0 . 0 6 0 1 ! 6 . 4 0 6 4 E - 0 4 ! 0 . 0 4 0 3 9 1 0 . 0 0 9 5 2 5
SECOND SECTION
11 1 4 0 4 . 4 8 1 6 3 5 . 6 1 ! - 3 . 2 3 9 1 1 0 . 0 7 9 2 ! Ó . 1 3 3 5 E - 0 4 ! 9 . 3 5 3 2 3 ! 9 . 9 0 3 2 0 1
12 ! 3 8 1 . 1 6 Î 7 9 4 . 9 9 1 - 6 . 2 3 6 5 1 0 . 9 9 1 6 ! 6 . 0 5 2 E - 0 4 ! 1 . 1 4 3 9 6 1 0 . 0 0 4 3 1 9 1 3 ! 3 9 0 . l 9 ! 6 6 3 . 7 5 ! - 3 . 7 9 3 7 1 0 . 0 8 1 9 ! 6 . 1 3 7 7 E - 0 4 ! 9 . 3 5 4 3 9 ! 9 . 9 0 3 2 9 9 14 ! 4 1 0 . 0 3 1 7 1 3 . 5 3 ! - 5 . 8 4 7 5 1 0 . 0 9 1 4 ! 6 . 9 5 4 5 E - 0 4 ! 2 . 4 0 3 8 3 ! 0 . 0 0 8 6 8 0
2 . 7 7 7 8 E - 0 6 ! 6 . 4 5 0 1 E - 9 6 ! 4 . 0 9 2 3 E - 0 6 ! 1 . 4 6 3 6 E - 0 6 1
1 . 4 9 4 0 E - 0 6 1
2 . 9 2 1 l E - 9 6 ! 3 . 9 5 7 5 E - 0 6 ! 3 . 1 0 2 6 E - 9 6 ! 7 . 6 4 6 0 E - 0 6 !
AVERAGE ! - 4 . 2 2 3 7 1 0 . 0 8 3 4 ! 6 . 1 3 7 2 E - 0 4 ! 0 . 7 9 7 4 1 ! 9 . 0 9 2 9 1 2 5 9 5 9 E - 0 6 !
- 1 2 -
RITCEX-SUNMARY OF EVALUATION OF THE CONVERTED DATA SET
T D R - P R M
FIRST SECTION
! RUN 1 LEVEL ! 1 X0 ! Xn
a9 a l > < a 9 ) ! S*!a l :•:*!)
! 141 30 .0 1254.9 i -1 .69041 ,45131-1 .7545E-04! 2 .73337 ! 9.04398 1 1.5233E-04!
SECOND SECTION
! 141320.0 1636.0 1-71.7391 9.57961 1.9384E-04127.46983 ! 0 .11756 1 1.2293E-94 1
SONAR - P R M
SECOND SECTION
1 2 ! 4 4 9 . 1 4 ! 6 7 9 . 1 2 1 - 1 6 . 6 9 0 ! 0.15751 5 .9964E-94! 16.274801 9.05895 131455 .381690 .641 -26 .581 ! 9 .2233! 4 .1474E-94! 17.32234 ! 0 .96393 141456 .921699 .791-11 .157! 9 .1304! 5 .4036E-04! 41.60730 ! 0 .14595
5.2537E-051 5.4337E-05! 1.2603E-04;
AVERAGE 1-19.670! 9.17911 4.7635E-94! 17.59060 ! 9.06194 1 5.3699E-051
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§ g s § § § HEIGHT ( MM )
![Decision 15 2006 by MOF 200306 [E]](https://img.dokumen.tips/doc/110x75/553d5c675503468c338b462d/decision-15-2006-by-mof-200306-e.jpg)
