INTERNATIONAL STANDARD ISO 12917-1 Second edition 2017-03 Petroleum and liquid petroleum products — Calibration of horizontal cylindrical tanks — Part 1: Manual methods Pétrole et produits pétroliers liquides — Jaugeage des réservoirs cylindriques horizontaux — Partie 1: Méthodes manuelles Reference number ISO 12917-1:2017(E) © ISO 2017 ISO 12917-1:2017(E) COPYRIGHT PROTECTED DOCUMENT © ISO 2017, Published in Switzerland All rights reserved Unless otherwise specified, no part o f this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission Permission can be requested from either ISO at the address below or ISO’s member body in the country o f the requester ISO copyright o ffice Ch de Blandonnet • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel +41 22 749 01 11 Fax +41 22 749 09 47 copyright@iso.org www.iso.org ii © ISO 2017 – All rights reserved ISO 12917-1:2017(E) Contents Page Foreword v Introduction vi Scope Normative references Terms and definitions Precautions 4.1 4.2 4.3 General Internal method External method 5.1 5.2 5.3 5.4 Equipment as used in ISO 7507-1 Telescopic rod Distance meter Leveller 7.1 7.2 General Measurement of circumferences — External 7.2.1 Introduction 7.2.2 General 7.2.3 Repetition of measurements Measurement of circumferences — Internal 7.3.1 Overview 7.3.2 General Measurements of lengths 7.4.1 Method 7.4.2 Length o f horizontal cylinder 7.4.3 Lengths of segments 7.4.4 Lengths of heads 7.4.5 Gauge lengths 7.4.6 Measurement/calculations of radii of the heads Tank tilt Plate thickness Reference height Deadwood Measurements of temperature and pressure Equipment General requirements Calibration procedures 7.3 7.4 10 7.5 7.6 7.7 7.8 7.9 Re-calibration Descriptive data Computation of tank capacity table 10 10.1 General rules 10 10.2 Accuracy o f volume 10 10.2.1 General 10 10.2.2 Calculation parameters 10 10.2.3 Volume calculation 13 10.3 Corrections of volume of tank table 22 10.3.1 General 22 10.3.2 Working pressure 22 10.3.3 Tank-shell temperature 24 10.4 Deadwood 24 10.5 Calibration table at gauged levels 24 © ISO 2017 – All rights reserved iii ISO 12917-1:2017(E) (informative) Annex A Computation of tank capacity tables based on individual segment dimensions 26 (informative) Calculation examples 29 Annex C (informative) Calibration uncertainties 39 Annex B Bibliography 46 iv © ISO 2017 – All rights reserved ISO 12917-1:2017(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work o f preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters o f electrotechnical standardization The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part In particular the different approval criteria needed for the di fferent types o f ISO documents should be noted This document was dra fted in accordance with the editorial rules of the ISO/IEC Directives, Part (see www.iso org/directives) Attention is drawn to the possibility that some o f the elements o f this document may be the subject o f patent rights ISO shall not be held responsible for identi fying any or all such patent rights Details o f any patent rights identified during the development o f the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso org/patents) Any trade name used in this document is in formation given for the convenience o f users and does not constitute an endorsement For an explanation on the voluntary nature o f standards, the meaning o f ISO specific terms and expressions related to formity assessment, as well as in formation about ISO’s adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso org/iso/foreword html This document was prepared by Technical Committee ISO/TC 28, Petroleum products and lubricants, Subcommittee SC 2, Measurement of petroleum and related products This second edition cancels and replaces the first edition (ISO 12917-1:2002), which has been technically revised with the following changes — The total length o f the tanks has been limited and also only the calibration via ISO 7507-1 is described in order to improve precision — Most o f the figures have been improved in order to further clari fy the measurement procedures These, in turn, have been described more logically and in a more use ful order For instance, tank shell measurements are no longer described separately and the former Annex on “tilt” has been incorporated in the text — A new annex on calibration uncertainties has been added — Correction for tank tilt is now calculated rather than read from a figure It also incorporates the Technical Corrigendum ISO 12917-1:2002/Cor 1:2009 A list of parts in the ISO 12917 series can be found on the ISO website © ISO 2017 – All rights reserved v ISO 12 917-1:2 017(E) Introduction This document forms part of a series on tank calibration methods In some countries, some or all of the the fact that it is possible that differences exist between this document and those regulations item s covere d b y th i s c u ment are s ubj e c t to lo c a l re gu lation s T he attention o f the u s er i s d rawn to vi © ISO 2017 – All rights reserved INTERNATIONAL STANDARD ISO 12917-1:2017(E) Petroleum and liquid petroleum products — Calibration of horizontal cylindrical tanks — Part 1: Manual methods Scope This document specifies manual methods for the calibration o f nominally horizontal cylindrical tanks, installed at fixed locations The methods in this document are applicable to insulated and non-insulated tanks, either when they are above-ground or underground The methods are applicable to pressurized tanks and to both knuckledish-end and flat-end cylindrical tanks as well as elliptical and spherical head tanks This document is applicable to tanks inclined from the horizontal, provided a correction is applied for the measured tilt Although this document does not impose any limits on the maximum tank diameter and maximum tank tilt to which this document is applicable, the practical limits would be about m in diameter and 10° in tilt Normative references The following documents are re ferred to in the text in such a way that some or all o f their content constitutes requirements o f this document For dated re ferences, only the edition cited applies For undated re ferences, the latest edition o f the re ferenced document (including any amendments) applies ISO 7507-1:2001, Petroleum and liquid petroleum products — Calibration of vertical cylindrical tanks — Part 1: Strapping method Terms and definitions No terms and definitions are listed in this document ISO and IEC maintain terminological databases for use in standardization at the following addresses: — IEC Electropedia: available at http://www.electropedia org/ — ISO Online browsing platform: available at http://www.iso org/obp Precautions 4.1 General The general and sa fety precautions specified in ISO 7507-1 shall be applied © ISO 2017 – All rights reserved ISO 12917-1:2017(E) 4.2 Internal method Be fore a tank which is to be calibrated is entered, a sa fe-entry certificate shall be obtained All lines entering the tank shall be disconnected and blanked NOTE The attention of the user is drawn to the possible existence of local regulations regarding the safe- entry certificate and entry into tanks, which have contained leaded fuels 4.3 External method NOTE tank area The attention o f the user is drawn to the possible existence o f local regulations regarding entry to the Equipment 5.1 Equipment as used in ISO 7507-1 Equipment used in the calibration o f horizontal tanks shall form to the specifications laid down in ISO 7507-1 All equipment shall be traceable to a reference standard NOTE The equipment required to carry out the calibration is dependent on the method to be employed This document uses techniques and equipment described in ISO 7507-1 5.2 Telescopic rod For the internal method, in addition to the equipment mentioned in 5.1 , a telescopic rod may be used This telescopic rod shall have a scale capable of being read to mm, and shall be calibrated with an uncertainty o f less than mm 5.3 Distance meter For the internal method, as an alternative to a telescopic rod, a laser-based distance meter may be used The distance meter may also be used in measurement o f tank tilt This distance meter shall have a scale capable o f being read to mm, and shall be calibrated with an uncertainty o f less than mm 5.4 Leveller Level-measuring instrument used to determine vertical distances between pairs of points It can be based on either mechanical or optical measurements Example Rotating optical/laser instrument that establishes horizontal reference line/plane, with a mechanical height-measuring device General requirements The tank shall be filled to its normal working capacity and working pressure at least once and allowed to stand while full for at least 24 h prior to emptying and preparing it for calibration 6.1 NOTE The hydrostatic test applied to new or repaired tanks will satis fy this requirement when additional pressure tests have been carried out The following parameters shall be determined: — tilt; — deadwood; 6.2 © ISO 2017 – All rights reserved ISO 12917-1:2017(E) — temperature; — pressure; — position of gauge point, reference height and height of the dip plate, if there is one Calibration procedures 7.1 General T he c a l ibration pro ce du re s for c a l ibration o f hori z onta l c yl i nd ric a l tan ks sha l l be p er forme d as 7.2 (external measurements) and 7.3 (internal measurements) The remainder of Clause applies to both external and internal measurements For both methods, measurements shall be taken at around 1/4 and 3/4 of the length of each segment in accordance with Figure s p e ci fie d i n 7.2 Measurement of circumferences — External 7.2.1 Introduction E x terna l me as u rements may b e exe c ute d with a ny dep th o f l iquid a nd l iqu id pre s s u re i n the tan k T he temperature and pressure of the liquid at the time of calibration shall be recorded 7.2.2 General For the me as u rement pro ce du re s , a c i rc u m ferentia l tap e o f s u ffic ient leng th to comple tely enc i rcle the tank should be used and measurements of the total circumference shall be taken a) I n a l l c a s e s , the tap e to b e u s e d s hou ld b e appl ie d to the ta n k s u r face at the pre s c rib e d lo c ation s b y the wraparound procedure; i.e the required length of tape should be applied in a slack condition, p o s itione d , and tightene d b y the appl ic ation o f the prop er ten s ion As indicated in Figure 1, strapping should be undertaken around 1/4 and 3/4 of the segment length b) In the case in which the circumferential measuring tape is in contact with the tank surface at all points along its path, circumferential measurements should be made and checked in accordance with the relevant procedure given in ISO 7507-1 c) If the circumferential measuring tape is not in contact with the tank surface, corrections should be made for i nd i vidua l ob s tr uc tion s a s s p e c i fie d i n I S O 75 7-1 © ISO 2017 – All rights reserved ISO 12917-1:2017(E) W W c W i W 1/4 (W ) /4 ( i ) H i H δ Weld line g W W et D g W ?b ft W eb Circumference strapping Key D δHg Hg Wc Wi Wft W Wet Web W fb tank diameter dip plate height reference (gauge) height cylinder length segment length s traight flange length (to p o f tank) s traight flange length (b o tto m o f tank) head length (top of tank) head length (bottom of tank) total tank length Figure — Measurements of the diameters/circumferences 7.2.3 Repetition of measurements After the circumference has been measured, the tension shall be released and the tape brought again to the required level and tension The readings shall then be repeated and recorded Ta ke mu ltiple me as u rements o f the c i rc u m ference I nve s tigate a nd, i f ne ce s s a r y, remove the p erceive d outl iers I f the fi rs t th re e s e c utive me a s urements agre e with i n ± m m, ta ke thei r average a s the ci rc u m ference a nd thei r s tandard devi ation as the s tandard u ncer ta i nty I f they no t agre e with i n this tolerance, repeat the measurements until two standard deviations of the mean of all measurements is less than the half of this tolerance Use the average as the measured circumference and the standard devi ation a s the s tanda rd u ncer tai nty © ISO 2017 – All rights reserved ISO 12917-1:2017(E) t0 Kp = 0,01 [m]; = ,7 E − [1 /Pa] ; = (nominal) pressure [Pa] Parameters: R = D/2 = 1,689 * [m] Wc = 15,882 [m] E = 2E + 11 [Pa] σ = 0,30 [1] Volume of full tank: V = 14,468 [m ] P Variables and calculation result: p NOTE t R + dR Wc + dWc dV kPa m %full 10 0,010 1,689 79 15,882 0,002 50 0,011 1,689 84 15,882 0,007 100 0,012 1,689 89 15,882 0,014 200 0,013 1,689 96 15,882 0,024 500 0,018 1,690 11 15,882 0,044 1000 0,027 1,690 23 15,883 0,060 2000 0,044 1,690 34 15,883 0,074 p = P r - P = difference between pressures at reference and at calibration B.3.2 Correction for temperature Parameters: Cs = ,1 E − exp a n s ion co e fficient o f the ta n k s hel l [1/° C ] Tref = 20 temperature at reference [°C] Ts = tank shell temperature at calibration [°C] Variables and calculation results: Ts °C −80 − 40 −2 0 20 50 34 Ctv 9,9E-01 1,0E+00 1,0E+00 1,0E+00 1,0E+00 1,0E+00 dV %full -0,63 -0,38 -0,25 -0,13 0,00 0,19 © ISO 2017 – All rights reserved ISO 12917-1:2017(E) Ts °C 100 200 400 Ctv 1,0E+00 1,0E+00 1,0E+00 dV %full 0,50 1,13 2,39 B.4 Volumes of tank ends B.4.1 Knuckle-dish end Measured: R k = 0,422 [m] = knuckle radius R2 = 1,367 [m] = radius of weld between knuckle and dish X1 = 0,606 [m] = length of the end Numerical solution for β: a) make two estimates of β ( β0 , β1); b) calculate errors Er = (X1 - Rk × cos β) × sin β - R2 × (1-cos β) for each of these: Er0 , Er1 ; c) calculate the next estimate (i = 2, 3, 4, …) of βi = (D i-2 × b i-1 - D i-1 × b i-2 ) / (D i-2 - D i-1) and error (Eri) for it; i until error (Eri Table of calculations: i = = estim1 = estim 10 11 0,11 0,50 0,1979 0,2662 0,3541 0,3121 0,3171 0,3176 0,3176 0,3176 0,3176 0,3176 Error = 1E-02 1E-02 7E-03 9E-04 8E-05 2E-09 4E-14 0E+00 0E+00 result: β = 0,317 [rad] Calculated: X2 = 0,401 [m] Xd = 3,483 [m] dX = 0,030 [m] (length of slice X for volume integration) Volume calculations: d) c a rr y on with i ncrementi ng ) = (approxi mately) β [rad] = − 4E - 02 index X 0,000 0,030 0,061 h-index: h: Xh: Vh: Rx 1,689 1,688 1,684 −7 E - 3 0,000 0,338 0,675 1,013 1,351 1,689 0,017 0,414 0,478 0,549 0,592 0,605 0,000 0,137 0,452 0,888 1,409 1,973 Area (Xh): 0,000 0,466 1,275 2,260 3,346 4,479 0,000 0,463 1,272 2,256 3,341 4,473 0,000 0,456 1,261 2,243 3,326 4,456 © ISO 2017 – All rights reserved −1 E - 6 2,026 0,592 2,537 2,364 0,549 3,059 2,702 0,478 3,494 3,039 0,414 3,810 10 3,377 0,017 3,947 S y m me tr i c a l w i th b o t to m h a l f 35 ISO 12917-1:2017(E) 10 11 12 13 14 15 16 17 18 19 20 0,091 0,121 0,151 0,182 0,212 0,242 0,272 0,303 0,333 0,363 0,394 0,424 0,454 0,484 0,515 0,545 0,575 0,606 1,679 1,671 1,661 1,648 1,632 1,612 1,589 1,561 1,526 1,482 1,419 1,205 1,102 0,988 0,857 0,701 0,497 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,444 0,428 0,406 0,380 0,348 0,312 0,269 0,221 0,167 0,106 0,039 0,000 0,000 0,000 0,000 0,000 0,000 0,000 1,244 1,220 1,188 1,149 1,102 1,046 0,980 0,902 0,810 0,699 0,555 0,169 0,051 0,000 0,000 0,000 0,000 0,000 2,221 2,191 2,151 2,102 2,042 1,970 1,885 1,785 1,665 1,518 1,321 0,742 0,518 0,310 0,130 0,006 0,000 0,000 3,300 3,264 3,217 3,159 3,087 3,002 2,900 2,780 2,635 2,455 2,214 1,477 1,175 0,878 0,589 0,317 0,079 0,000 4,427 4,385 4,331 4,264 4,181 4,083 3,966 3,826 3,657 3,447 3,164 2,280 1,907 1,5320 1,1533 0,7717 0,3872 0,0000 B.4.2 Spherical end Same as knuckle-dish end with Knuckle radius Rk = Measured: R = , [m] = rad iu s o f tan k b o dy = 3,000 [m] = radius of the sphere result: β = 0,292 [rad] Calculated: X2 = [m] Xd = 2,494 [m] dX = 0,026 [m] (length of slice X for volume integration) Volume calculations: Rd index 36 X 0,000 0,026 0,052 0,079 0,105 0,131 0,157 h-index: h: Xh: Vh: Rx 1,689 1,660 1,619 1,577 1,534 1,489 1,441 0,000 0,338 0,007 0,204 0,000 0,048 Area (Xh): 0,000 0,466 0,000 0,404 0,000 0,324 0,000 0,249 0,000 0,179 0,000 0,115 0,000 0,060 0,675 0,348 0,215 1,013 0,447 0,498 1,351 0,505 0,867 1,689 0,524 1,282 1,275 1,185 1,065 0,947 0,830 0,716 0,605 2,260 2,147 1,995 1,843 1,692 1,540 1,389 3,346 3,213 3,032 2,850 2,667 2,483 2,298 4,479 4,326 4,118 3,907 3,694 3,480 3,263 2,026 0,505 1,697 2,364 0,447 2,066 2,702 0,348 2,349 3,039 0,204 2,516 10 3,377 0,007 2,564 S ym me tr ic a l w i th b o t to m h a l f © ISO 2017 – All rights reserved ISO 12917-1:2017(E) 10 11 12 13 14 15 16 17 18 19 20 0,183 0,209 0,236 0,262 0,288 0,314 0,340 0,366 0,393 0,419 0,445 0,471 0,497 0,524 1,392 1,341 1,286 1,229 1,169 1,105 1,036 0,961 0,879 0,788 0,684 0,560 0,397 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,018 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,497 0,393 0,295 0,204 0,122 0,054 0,006 0,000 0,000 0,000 0,000 0,000 0,000 0,000 1,240 1,091 0,945 0,800 0,659 0,523 0,392 0,268 0,156 0,061 0,001 0,000 0,000 0,000 2,113 1,926 1,740 1,554 1,367 1,181 0,997 0,814 0,634 0,459 0,292 0,138 0,016 0,000 3,044 2,822 2,599 2,373 2,146 1,916 1,684 1,450 1,213 0,975 0,734 0,491 0,247 0,000 B.4.3 Elliptical end Measured: X1 = 0,606 [m] (length of the end = horizontal half-axis of the ellipsoid) R = , [m] (rad iu s o f ta n k b o dy = ver tic a l h a l f- a xi s o f the el l ip s oid) Volume calculations: h m 0,000 0,338 0,675 1,013 1,351 1,689 2,026 2,364 2,702 3,039 3,377 Volume m3 0,000 0,101 0,376 0,781 1,273 1,808 2,343 2,835 3,240 3,515 3,617 B.5 Calibration table with gauged levels Gauged levels are calculated from vertical level with no dip plate, on which the calculations are based, while the corresponding volumes are maintained The following example illustrates changes from the original vertical level Table B.4 shows an example of a calibration table © ISO 2017 – All rights reserved 37 ISO 12917-1:2017(E) Table B.4 — Calibration table example Gauged level = Calibration result Vertical innage dLg = 0,29 Vertical ullage dD = Lg = 38 Level Volume 0,000 10,178 0,289 16,403 Level Volume Level 0,30 Aligned innage cos y = 3,720 Volume Level Aligned ullage 0,985 Volume Lg / cos y= 3,777 Level Volume 0,385 18,846 0,095 18,846 3,625 18,846 0,097 18,846 3,681 18,846 0,578 24,285 0,288 24,285 3,432 24,285 0,292 24,285 3,485 24,285 0,771 30,466 0,481 30,466 3,239 30,466 0,488 30,466 3,289 30,466 0,963 37,359 0,673 37,359 3,047 37,359 0,684 37,359 3,094 37,359 1,156 44,926 0,866 44,926 2,854 44,926 0,879 44,926 2,898 44,926 1,349 53,118 1,059 53,118 2,661 53,118 1,075 53,118 2,702 53,118 1,541 61,876 1,251 61,876 2,469 61,876 1,271 61,876 2,507 61,876 1,734 70,946 1,444 70,946 2,276 70,946 1,466 70,946 2,311 70,946 1,927 80,025 1,637 80,025 2,083 80,025 1,662 80,025 2,116 80,025 2,119 88,811 1,829 88,811 1,891 88,811 1,857 88,811 1,920 88,811 2,312 97,040 2,022 97,040 1,698 97,040 2,053 97,040 1,724 97,040 2,505 104,646 2,215 104,646 1,506 104,646 2,249 104,646 1,529 104,646 2,697 111,581 2,407 111,581 1,313 111,581 2,444 111,581 1,333 111,581 2,890 117,807 2,600 117,807 1,120 117,807 2,640 117,807 1,137 117,807 3,082 123,291 2,792 123,291 0,928 123,291 2,836 123,291 0,942 123,291 3,275 128,034 2,985 128,034 0,735 128,034 3,031 128,034 0,746 128,034 3,468 132,046 3,178 132,046 0,542 132,046 3,227 132,046 0,551 132,046 3,660 135,354 3,370 135,354 0,350 135,354 3,422 135,354 0,355 135,354 3,853 137,974 3,563 137,974 0,157 137,974 3,618 137,974 0,159 137,974 4,046 139,939 3,756 139,939 -0,036 139,939 3,814 139,939 -0,036 139,939 4,238 141,279 3,948 141,279 -0,228 141,279 4,009 141,279 -0,232 141,279 4,431 142,066 4,141 142,066 -0,421 142,066 4,205 142,066 -0,428 142,066 4,624 142,398 4,334 142,398 -0,614 142,398 4,401 142,398 -0,623 142,398 4,816 142,444 4,526 142,444 -0,806 142,444 4,596 142,444 -0,819 142,444 © ISO 2017 – All rights reserved ISO 12917-1:2017(E) Annex C (informative) Calibration uncertainties C.1 Uncertainties of tank body C.1.1 Diameter — External method Uncer tai ntie s o f the c i rc u m ference s me a s ure d b y the e xterna l me tho d (s trappi ng tap e) are the s a me as described in ISO 7507-1:2001, F.3 Result = uD f temperature or pressure = uncer ta i nty o the (average d) d iame ter o f the b o dy o f the tan k with no corre c tion s for C.1.2 Diameter — Internal method Uncertainties of the measured diameter shall be estimated as follows: — uDir f uncertainties of read-out; — uDip f f f = u ncer tai nty o tele s copic ro d or the d i s tance me ter [m] , i nclude s the ro d pre ci s ion and = p o s ition u ncer tai nty o the ro d [m] rom ol lowi ng table: Tank internal diameter up to m above m Uncer tai nty o f averagi ng , a s s um i ng the e quation deviation: uD av = abs [MAX (D ir) - AVG (D ir)] / sqrt (n) [m] Uncer ta i nty ±1 m m (0 , 01 m) ± m m (0 , 0 m) b elow yield s (ver y approxi mately) the s tandard (C.1) where n is the number of diameters measured in one location in one segment Uncer tai nty (s tand ard devi ation) o f average d d ia me ter i n one lo c ation i n one s e gment: uD im = (uDir2 + uDip2 +uDav2 ) 1/2 [m] Uncer tai nty (s tand ard devi ation) o f average d d ia me ter uD (C.2) for the tan k b o dy: = uDim / sqrt (m) [m] (C.3) where m is the number of locations in all segment of the tank C.1.3 Lengths C.1.3.1 General uncertainties Uncertainties of the tank length measured strapping tape are similar to those described in ISO 7507-1:2001, D.4 © ISO 2017 – All rights reserved 39 ISO 12917-1:2017(E) The following are figures for worst cases: — tape calibration certificate = 0,5 mm; — tape resolution = mm; — tape tension and position = mm (in case of horizontal tanks) Further uncertainties are due to — deformation of tank heads = 10 mm C.1.3.2 Tank body As the length is measured as sum o f two measurements, both subject to the above uncertainties, the resulting standard uncertainty uW = [sqrt (2) × sqrt (0,5 ^2 + 1^2 + 3^2 + 10^2) ] C.1.3.3 / [2 × sqrt (3)] = 4,4 mm = 0,004 m Gauge location Location o f tank gauge (length along the top o f the tank body away from its lowest point) is measured only once Its standard uncertainty is: uWg = sqrt (0,5 ^2 + 1^2 + 3^2 + 10^2) / [2 × sqrt (3)] = 3,1 [mm] = 0,003 [m] C.1.4 Angle of tilt The tilt is measured by repeated measurements o f distance X and Y (see 10.2.2.3 above) Uncertainty o f tilt is derived from that o f slope o f line fitted to pairs o f X and Y points uX and uY are identical for all points Uncertainty o f slope is derived from its equation (see 10.2.2.3) as: us2 = uX2 × SUM (ds / dXi ) + uY2 × SUM (ds / dYi ) where ds / dXi = [n × Yi - - s × (2 × n × Xi - × SUM (Xi)] / {n × SUM (Xi ) - [SUM (Xi)] }; ds / dYi = {n × Xi - 1} / {n * SUM (Xi ) - [SUM (Xi )] } Assuming that the uncertainties of measured X and Y are as above, i.e 0,003 m each, the uncertainties us can be estimated a) Uncertainty o f tilt is derived as: uγ = us × cos γ for one fitted line uγ = us / sqrt (2) × cos2 γ for two fitted lines b) Uncertainty o f calculated slope (typical figure, based on the above uncertainties, for tank with nine segments): us = 0,000 [1] for one fitted line us = 0,000 [1] for two fitted lines 40 © ISO 2017 – All rights reserved ISO 12917-1:2017(E) c) Uncer tai nty o f angle o f ti lt derive d from the s lop e: uγ = , 0 [rad] = , 02 [deg] for one fitte d l i ne uγ = , 0 [rad] = , 017 [deg] for two fitte d l i ne s C.1.5 Volume Uncertainties are estimated for the numerical method outlined in Clause 10 (using averaged diameter of the tank), for heights (levels) not exceeding low (0) or high (D) limits for the entire lengths of the tank T he tan k i s a s s u me d to b e an ide a l c yl i nder, with cro s s - s e c tion s o f a l l s egments b ei ng co - a xi a l ci rcle s Po tenti a l de formation s i n the tan k and any m i s a l ignments o f ta n k s e gments a re ne gle c te d Volu me o f the ta n k b o dy i s a length) and Wg V = f (R , W, Wg , γ) fu nc tion o f: h (gauged height), R (tank radius), γ (angle of tilt), W (tank ( leng th b e twe en the lowe s t p oi nt o f the tan k b o dy a nd the gauge p o s ition) uV2 = (uR × δV / δR) + (uW × δV / δW) + (uWg × δV / δWg) + (uγ × δV / δγ) Derivatives of volume: δV / δR = × V / R + [R × (Zb × h b - Zt × h t)] / tan γ (C.4) (C.5) δV / δW = (V × H ) / (W2 × sin γ × cos γ) - R2 × Zt (C.6) δV / δWg = R2 × (Zb - Zt) (C.7) δV / δγ = R2 × (Zb - Zt) / sin γ (C.8) where intermediate variables are: Zb = αb - sin αb × cos αb = αt - sin αt × cos αt Zt αb = arccos [(R - h b) / R] αt = arccos [(R - h t) / R] hb = (h + Wg × sin γ) / cos γ = height (level) at the lowest point of the tank [m] ht = [h + (Wg - W) × sin γ ] / cos γ = height (level) at the highest point of the tank [m] γ = angle of tilt of the tank [rad] R =D / = i nterna l rad iu s o f the tan k b o dy [m] © ISO 2017 – All rights reserved 41 ISO 12917-1:2017(E) C.1.6 Correction for temperature Assuming zero uncertainties o f the re ference temperature, the additional uncertainty o f the volume o f the tank body is: uCtv = {[3 × (Ts - Tr) × uC1] + [2 × C1 × uTs] }1/2 (C.9) C.1.7 Correction for pressure Assuming that all components of the equation in B.3.1 formula applies: uC pve ? = ? { [3 × (1 − σ ) (2tE ) are subject to uncertainties, the following × [( R × uP ) + ( P × uR ) + ( Pr × ut / t ) + 2 ( P × uE / E ) + P × uσ / ( tE ) ] } r r where / ] / (C.10) P = internal pressure o f the tank at calibration conditions, with uncertainty uP [Pa]; = pressure at reference conditions; = D / = radius of the tank body, with uncertainty ur = uD / [m]; = thickness o f the tank shell, with uncertainty ut [m]; Pr R t E = Young’s modulus o f the tank shell material, with uncertainty uE [Pa]; = Poisson’s ratio o f the tank shell material, with uncertainty σ u σ [1] Uncertainty o f pressure at calibration may be di fficult to establish It is recommended that i f in doubt, this particular uncertainty should be neglected C.1.8 Corrected volume Assuming that the total volume in the tank is calculated as: Vtotal = (Cpvc × Vc + Cpve × Ve) × Ctv its uncertainty is uV to tal ? ( = ? {[ C ) + (V × uC ) + (C × uV ) ) × C + (V × C + V × C ) × uV (V × uC 2 c c p vc p ve e + × uC Uncertainties o f tank ends may normally be neglected, i.e uCtv = e NOTE p vc p ve ] tv c p vc e p ve tv } 1/2 (C.11) C.1.9 Numerical examples C.1.9.1 Basics Calculated for approximate calibration table, based on assumption that all segments have the same diameters Uncertainties of corrections for temperature and pressure are neglected 42 © ISO 2017 – All rights reserved ISO 12917-1:2017(E) C.1.9.2 Tank diameter Based on the same calibration data (see above) with the following uncertainties of source data Strap tape: Uncertainties: a-st = 2,00E-05 [1/°C] Tstc = 20,0 [°C] Ta n k b o dy: straps/segment = number of straps = STD of straps = a-tk = Temperature reference: Tref = length = Read-out = position = T tape/tank = T-exp, = thick-m+ P = 36 0,047 5,77E-07 [1/°C] 15 ent,value 0,001 0,001 0,009 2,0E-06 0,000 typ e max max max max max max 0,000 43 0,000 29 0,002 60 1,443 5,8E-07 0,000 14 [m] [m] [m], from table [°C] [1/°C] [m] [°C] Values and uncertainties of measured circumferences and diameter at calibration conditions, corrected to reference temperature: Outputs: values std uncert’s [m] [m] Average: Avg Cem = Cet = Ci = Di = C.1.9.3 10,678 10,677 10,608 3,3776 0,047 0,047 0,047 0,0150 Tank body volume Source parameters: avg int diameter D irc: tilt angle y: W: gauge length Wg: thick metal + paint: b o dy leng th value s td u ncer ta i nty 3,378 0,003 [m] 0,175 15,882 8,100 0,011 0,000 0,004 0,003 0,000 [rad] [m] [m] [m] uL = [m] - level u ncer tai nty i s norma l ly i nclude d i n gaugi ng gge height [m] 0,433 0,578 0,722 0,866 1,011 1,155 1,300 Zb 0,436 0,577 0,727 0,884 1,047 1,213 1,383 © ISO 2017 – All rights reserved Zt 0,079 0,173 0,286 0,413 0,553 0,701 0,857 dV/dy 35,40 40,09 43,76 46,68 48,99 50,77 52,08 dV/dR dV/dW dV/dWg uVolume [m3 ] 20,92 1,02 0,035 31,13 1,15 0,050 42,35 1,26 0,067 54,31 1,34 0,085 66,80 1,41 0,104 79,64 1,46 0,124 92,66 1,50 0,144 −0,20 − ,4 − ,7 −1 ,1 −1 , 51 −1 ,9 −2 , [%full] 0,02 % 0,04 % 0,05 % 0,06 % 0,07 % 0,09 % 0,10 % 43 ISO 12917-1:2017(E) 1,444 1,588 1,733 1,877 2,022 2,166 2,310 2,455 2,599 2,743 2,888 3,032 3,177 3,321 NOTE 1,553 1,724 1,894 2,061 2,225 2,383 2,535 2,678 2,810 2,929 3,030 3,108 3,142 3,142 1,019 1,185 1,354 1,525 1,696 1,866 2,033 2,198 2,357 2,510 2,655 2,789 2,910 3,015 52,97 53,44 53,51 53,19 52,46 51,31 49,71 47,60 44,92 41,55 37,28 31,68 22,95 12,56 105,69 118,59 131,21 143,38 154,92 165,66 175,38 183,81 190,64 195,42 197,51 195,69 189,84 193,87 −2,82 −3,28 −3,76 −4,24 −4,72 −5,19 −5,66 −6,12 −6,57 −6,99 −7,40 −7,77 −8,11 −8,40 1,53 1,54 1,54 1,53 1,51 1,48 1,43 1,37 1,29 1,20 1,07 0,91 0,66 0,36 0,163 0,183 0,202 0,221 0,239 0,255 0,270 0,283 0,294 0,301 0,304 0,301 0,293 0,299 0,12 % 0,13 % 0,14 % 0,16 % 0,17 % 0,18 % 0,19 % 0,20 % 0,21 % 0,21 % 0,21 % 0,21 % 0,21 % 0,21 % I f one o f the simplifications mentioned above is used in measurements and/or calculations, additional error will result that has to be added to these uncertainties As shown above, i f the tank tilt is only measured at two points (lowest points at the lowest and upper- most segments, the added error could be of the order of 0,1 % If the tank volume is calculated from the averaged diameter, the added error could be as much as % or even more The size of the errors depends on the variations in elevations of individual segments and in their diameters C.2 Uncertainties of tank ends Uncertainties o f volumes o f tank ends are normally neglected C.3 Errors in calculation of tank body volume Errors in calculations o f volume o f tank body may result i f the method based on average diameter and total tank length is applied to a tank where the segment diameters vary Worst-case errors in calculations, estimated in 10.2, should be added to the estimated uncertainties to yield: uVtotalC = {(uVtotal) + [Verr / sqrt (3)] }1/2 (C.12) where uVtotal Verr NOTE = total uncertainty o f volume o f tank body calculated in C.1.9; = worst-case error due to simplified calculations o f tank body volume estimated in 10.2 Distribution o f worst case errors is normally either fully positive or fully negative Hence only sqrt (3) rather than [2 * sqrt (3)] is used in the above equation Numerical example: uVtotal = 0,21 % of full volume (see C.1.9.2) uVerr = 0,64 % of full volume (see B.2) for tilt angle γd = 1,65 deg 44 © ISO 2017 – All rights reserved ISO 91 7-1 : 01 7(E) = 3,38 m D var = 0,029 m uVtotalC = 0,43 % of full volume Davg © ISO 2017 – All rights reserved 45 ISO 12917-1:2017(E) Bibliography [1] 46 ISO 1998 (all parts), Petroleum industry — Terminology © ISO 2017 – All rights reserved ISO 91 7-1 : 01 7(E) ICS 75.180.30 Price based on 46 pages © ISO 2017 – All rights reserved