EURAMET.M.FF-K5a. Bilateral inter comparison FORCE PTB

Transcription

1 Blateral nter comparson FORCE EURAMET.M.FF-K5a EURAMET-Project E1111 Follow up to CCM.FF-KC5a Volume flow rate for Natural Gas un Hgh Pressure - Plot laboratory: contact: B. Mckan, H. Toebben, (-pgsar TM ), Boo.Mckan@ptb.e, - Partcpatng Laboratory: FORCE Technology Navervej Vejen, Denmark. contact: Jesper Busk. jrb@force.k 1 INTRODUCTION 2 THE PRINCIPLES OF THIS INTERCOMPARISON 2.1 The stuaton of the traceablty chans 2.2 The evaluaton of key comparson ata of facltes wth common source of traceablty 2.3 The basc prncples for the lnkng of the results of CCM.FF-K5a wth ths nter comparson 3 THE TRANSFER PACKAGE 3.1 The meters (techncal escrpton) 3.2 The measurement program an the calbraton of transfer package wth the BIPM Reference Value 3.3 Reproucblty of the transfer package an the plot faclty as well as lnk to the KCRV of CCM.FF-KC5a 4 THE TEST RESULTS 5 SUMMARY, FINAL REMARKS 6 REFERENCES BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 1 of 15

2 1 INTRODUCTION 2 THE PRINCIPLES OF THIS INTERCOMPARISON 2.1 The stuaton of the traceablty chans The operates at the test faclty PIGSAR an Hgh Pressure Pston Prover as a prmary reference evce to trace back the gas measurement own to the SI-Unts. FORCE Technology s the Natonal Metrology Insttute n Denmark for gas flow measurement, an operates the low pressure an hgh pressure calbraton test faclty for calbraton purpose n Denmark. It has been ece by the staff of FORCE to get ther traceablty from the (Germany). Hence, the test faclty of FORCE traces back rectly to the KCRV of CCM.KC-FF 5a. Wthout an nepenent traceablty at FORCE, the actual nter comparson (EURAMET.M.FF-K5a) wll not establsh a new KCRV but wll proof the consstency of FORCE calbratons wth the exstng KCRV of KC-FF 5a. For the evaluaton of the nter-comparson results t s necessary to conser the epenence (correlaton or covarance rsp.) of both partcpant -PIGSAR an FORCE ue to ther common reference (the KCRV of CCM.FF-KC5a). Ths s explane n the followng chapter 2.2. Fg. 1 explans the relatons of the partners to the KCRV. LNE France (PIGSAR) Germany BIPM Key Comparson Reference Value of CCM.FF-KC 5a (entcal to EHRV of year 2005) NM Netherlans Ths comparson FORCE Denmark Fg. 1: The traceablty of the partcpants n relaton to the BIPM Reference Value of CCM.FF-KC5a an the poston of ths blateral nter comparson 2.2 The evaluaton of key comparson ata of facltes wth common source of traceablty BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 2 of 15

3 In any key comparson, the fferences between the partcpatng laboratores an the key comparson reference value KCRV have to be calculate accorng to x x (1) KCRV Base on these fferences, the Degree of Equvalence (DoE) shall be calculate accorng to: E (2) U ) ( were U() s the expane uncertanty (k = 2) of the fference. The DoE s a measure for the equvalence of the results of any laboratory wth the KCRV: - The results of a laboratory are equvalent (passe) f 1 < E. - The laboratory was etermne as not equvalent (fale) f E or Ej > For values of DoE n the range 1 < E or Ej 1.2 we efne warnng level were actons to check s recommene to the laboratory. The reason for such warnng level s that we have to conser the confence n the etermnaton of the uncertantes (for the results of labs as well the KCRV). Conventonally we work at a 95% confence level. Therefore n some nter comparsons a range up to E < 1.5 s use for these warnngs [2] [3]. Ths s a reasonable value f stochastc nfluences omnate the uncertanty bugets. In the case of nter comparsons for gas flow, the smaller value 1.2 was chosen whch reflects the omnance of non-stochastc parts of uncertanty compare to the stochastc parts (the reproucblty s usually much better than the total uncertanty of a laboratory) [1]. The calculaton of the DoE nees the nformaton about the uncertanty of the fferences acc. to eq. (2). To make statements about ths, let us conser frst the general problem of the fference of two values x1 an x2. If we look to the pure propagaton of (stanar) uncertanty we fn: x1 x2 2 2 x1 x2 x1 x2 u1 cov x u x 1 2 2cov 1 2 x 2 cov u u (3) x x 2 u2 x x x 2 In the case of ths nter comparson, the results of the partcpants are correlate uo to the common traceablty. The correlaton leas to a sgnfcant covarance cov between the measurement results whch has to be consere n the eq. (3). The worst case estmaton for the covarance whch can occur ue to the common traceablty s the square uncertanty of ths common reference. In our case t s the uncertanty of the key comparson reference value of CCM.FF-K5a (see also Fg. 1). The value for the expane uncertanty of the KCRV was etermne between 0.12% an 0.138% epenng on flow rate an pressure. We assume an upper value of 0.14% an make wth ths sure that no unerestmaton of the egree of equvalence has been one. BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 3 of 15

4 2.3 The basc prncples for the lnkng of the results of CCM.FF-K5a wth ths nter comparson The key comparsons for hgh pressure gas organze up to now have all the same common concept for the measuran. Even the basc mathematcal relatons are smple, we lke to explan here somethng n etal to avo any confuson or msunerstanng, especally where we have to lnk fferent nter comparson roun by fferent meters uner test. The central expresson use to quantfy the meter uner test n relaton to the flu quantty s the relatve evaton of the ncate quantty 1 MuT to the reference quantty Lab# prove by the Lab # for the measurement (meter evaton f). f MuT Lab# 1 Base on all results for the meter evaton at the fferent laboratores the key comparsons reference value fkcrv was calculate as a weghte mean (w s the weght for Lab #). f KCRV w f MuT KCRV 1 The key reference value for the meter evaton can also be formally expresse as a relatve evaton of the meter ncaton to the key reference quantty. To express the egree of equvalence the fference (an ts accompane uncertanty) between the measure value f at Lab # an the key reference value fkcrv s calculate: f f KCRV The nterest s fnally the relatve evaton #,rel of the quantty Lab# to the key reference quantty KCRV: Lab# #, rel 1. (4) KCRV The relaton shp of ths to the usually use fference (3) shall be shown here. Even ths was the common unerstanng among the flow experts t was never expresse n etal n the CCM.FF-protocols up to now. The relaton s easly shown f we expan the expresson (4) by an unty MuT/MuT. Furthermore we make use of (1) an (2) as well as some small approxmaton ue to the fact that f as well as fkcrv are much smaller than 1. 2 The fnal outcome s that the usual use value s the negatve value of the orgnal nterest #,rel. (1) (2) (3) 1 Please note the here the quantty can be volume, mass, volume flow rate or mass flow rate accorng to the ncaton of the meter uner test. The meter uner tests n the CCM.FF-KC5 are turbne meters. 2 E.g. f the evatons f are n the orer of 0.5%, the fnal error of the approxmatons use n (5) can reach ±0.005% n maxmum. Ths s of course an atonal uncertanty whch has to be consere but n the fel of hgh pressure gas measurement efntely nsgnfcant compare to the CMC uncertantes. BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 4 of 15

5 1 f # 1 fkcrv f fkcrv f (5) Lab# MuT KCRV, rel MuT KCRV 1 f The expanson by MuT/MuT n (5) s mae on the backgroun that the epenency of the meter evaton f on the flu quantty s normally neglgble small at least for small changes of quantty. 3. It has to emphasze here that the expanson s nepenent to a specal value of MuT an therefore also nepenent to the meter uner test. Ths means the nepenence of the #,rel to the meter uner test use for comparson whch was utlze n the past CCM.FF-KCs (1 to 6 except 4) by slent agreement of the flow experts. Wthn the comparson rouns the results comng from at least two fferent meters uner test were combne (n case of CCM.FF-KC6 even results of 4 meters uner test were summarze). The next step are conseratons about the fferences,j between to laboratores Lab # an Lab #j etermne n a comparson. We make use of the same approach as above to transform the relatve evaton of the quanttes to the fference of the meter evatons etermne n the comparson: 1 f Lab# Lab# j MuT, j f f j (6) Lab# j MuT Lab# j 1 f j Ths comparson ocumente n ths protocol s an subsequent comparson (SC) to the CCM.FF-KC5a. Hence, we have to look careful to the tme orer of values whch we put nto our calculatons when we want to etermne fnally the fference (egree of equvalence) FORCE of the Lab # to the KCRV of the prevous key comparson [1] nrect va the Lab # usng the fference,force. The brackets wth the nces KC an SC ncates values etermne n the key comparson an the subsequent comparson: FORCE, fforce f SC SC f SC FORCE f SC KC (7) wth f SC f KC Wth ths we get our fnal expresson (8) for the fference of the Lab #FORCE to the KCRV of the prevous KC: lab# FORCE 1 NIST fforce fkcrv SC KC FORCE, (8) SC KCRV s ocumente n the protocol of the prevous KC [1] an s summarze n KC chapter The value s assume normally as zero wth an uncertanty whch s the reproucblty of the Lab # (stablty versus tme). In the specal case of ths subsequent comparson t s known that s fferent from zero ue to the complete new recalbraton of the test faclty pgsar [4] n 2007 an the new cycle wthn the European Harmonzaton Group startng 2008 (were also all other partners [LNE, VSL] recalbrate ther facltes before). Therefore t s etermne an estmator 3 Ths assumpton s of course not exactly fulflle an leas agan to atonal uncertantes. If these uncertantes are not acceptable, the next level can be the expresson the epenency of f to by an approprate analytcal functon to apply an small correcton (as t was one e.g. n the CCM.FF-KC6) to reuce these atonal uncertantes. BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 5 of 15

6 n chapter for ths base on the measurements of four measurement seres at pgsar n years 2004 an 2005 (harmonzaton cycle ) an n the year 2009 (harmonzaton cycle ). All components n equaton (8) have contrbutons to the total uncertanty of the fnal value NIST. They are etermne an ocumente n chapter 3.3 an 4 n ths protocol. 3 THE TRANSFER PACKAGE AND TEST PROGRAM 3.1 The meters (techncal escrpton) The transfer package s entcal to the package whch was use n the CCM.KC5a.1 - Two turbne meters n seres - Sze of meter: DN150 (6 ), max = 1000 m 3 /h - Each turbne meter s equppe wth nlet ppe of 1,5 m (10D) length, flow contoner at the entrance of ppng an outlet ppe of 0,45m (3D) length. - Manufacturer: Meter #1 by Elster-Instromet; Meter #2 by RMG - Both meters are Reynols balance n a we range 3.2 The measurement program an the calbraton of transfer package wth the BIPM Reference Value (Equvalence between KCRV-KC5a an Ref.Val.KC5a.1) Tab. 2: Flow rates an pressures use wthn the key comparson CCM.FF-KC5a.1 Flow rate Force [m 3 /h] (actual contons) pressure pressure [MPa] [MPa] X X X X 100 X X X X 160 X X X X 250 X X X X 400 X X X X 650 X X X X 1000 X X X X 1250 X X X X BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 6 of 15

7 Tab. 3: Dates of measurements an pressures use wthn the key comparson CCM.FF-KC.5a KC5a.2 - #1 March 2009 March 2009 KC5a.2 - FORCE August 2009 August 2009 KC5a.2 - #5 September 2009 September Reproucblty of the transfer package an the plot faclty as well as lnk to the KCRV of CCM.FF-KC5a Here the results of nvestgaton about stablty of the transfer package as well as the plot lab wll be place. The nvestgaton wll be base on the measurement results gathere wthn ths nter comparson as well as on the calbratons results of artefacts of CCM.FF-KC5a.1 [5]. The evaluaton wll be performe n smlar way as for all the CCM.FF-KC5. The nformaton about reproucblty wll also be use for the lnkng to the KCRV of CCM.FF-KC5a an to etermne a egree of equvalence n relaton to ths KCRV Reproucblty The protocol of the CCM.FF-KC5a [1] escrbe an apply a metho to etermne the reproucblty of the transfer meters as well as the test facltes base on the measurements urng the pero of the KC. Ths proceure was also successfully apple n the CCM.FF-KC5b for compresse ar an ntrogen [6]. Here agan we make use of ths metho to emonstrate the stablty of the transfer package an the plot faclty. Usng the correlaton plot of the fferences of sngle measurement results wth respect to the least square ft of all test results (.e. the resuals) for both meters n the transfer package one obtan to the vsualzaton of Fg. 5. The scatter of the resuals ncates the reproucblty of the measurements an can be splt by analyss nto the components of both meters an the reference stanar. BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 7 of 15

8 resual meter #2 0,15 0,10 0,05 0,00-0,05-0,10-0,15-0,15-0,10-0,05 0,00 0,05 0,10 0,15 resual meter #1 Fg. 3.1: The correlaton plot of two meters wthn EURAMET.M.FF-K5a etermne at the plot laboratory usng the fference (resuals) between the sngle measurement results fmeter# an the average value fave# (least square ft of test result measure at 1600 kpa an 5000 kpa n March an September 2009). The values n the Fg. 5 have been evaluate n the same ways as ocumente n [1]. We refran from showng the complete set of equatons here agan (please see [1]) an gve only the results n Tab Tab. 3.4: Tabulate results for reproucblty Urepro (k = 2) of the transfer meters an the plot lab n all comparson loops relate to CCM.FF-K5 Reproucblty Package ppe sze 150 mm 300 mm Test pero Meter # Meter # Meter # Meter # Plot lab pgsar CCM.FF-K5a 0, 009 0, , 013 0,007 0,0700,010 CCM.FF-K5a.1 0, 007 0,038 0,005 0,058 0,077 0, , 015 0,008 0,011 CCM.FF-K5a , 010 EURAMET.M.FF-K5.a 0, 021 0,064 0,013 0,015 0,009 0,031 0,006 0,014 0,044 0,008 0,062 0,019 0,012 0, , 023 0,071 0,014 BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 8 of 15

9 shft ,009 Please rea e.g 0,050 0,007 as 0,050 for the estmate value an 0,050-0,007 = 0,043 for the lower confence level as well as 0,050+0,009 = 0,059 for the upper confence level (k = 2). Tab. 3.4 presents n aton the results out of the CCM.FF-K5a, K5a.1-Meter an EURAMET.M.FF-K5.a to emonstrate the equvalence of the results n all KC loops Shft n the calbraton value at pgsar The complete new recalbraton of the test faclty pgsar [4] n 2007 an the new cycle wthn the European Harmonzaton Group startng 2008 (were also all other partners [LNE, VSL] recalbrate ther facltes before) efne a new calbraton value at the test faclty -pgsar compare to the stuaton n 2005 (when the actual KCRV of CCM.FF-k5a was etermne). For the lnkage between the test result of NIST an the KCRV we nee nformaton about the shft f f (see also chapter 2.2) between 2009 an For the etermnaton of ths value we mae use of followng sets of ata measure at pgsar before an after recalbraton: - of both meters use n CCM.FF-K5a.2 - of both meters use n EURAMET.M.FF-K5a - all meters use nse harmonsaton between, LNE an VSL - all workng stanars of -pgsar The shfts for the fferent sets of meters you can fn n Fg. 3.2 below. SC KC 0,4 % 0,3 CCM.FF-K5a.2 Meter1 Meter2 EURAMET.M.FF-K5.a Meter1 Meter2 harmon. /LNE/VSL nternal control avarage shft = (0.082±0.075)% 0,2 0,1 0,0-0, kg/h mass flow rate m BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 9 of 15

10 Fg. 3.2: Shft n the calbraton values for meters uner test at -pgsar ue to recalbraton 2007 for fferent sets of meters. The shft s plotte versus the mass flow rate m because the Reynols number not comparable ue to fferent ppe szes of the meters (100 mm to 400 mm) Fnally we foun an average shft of = ±0.075 % were the uncertanty of 0.075% for ths value s n goo agreement wth the reproucblty ocumente n table 3.4 above Value of fference The values for KC of the KCRV n CCM.FF-K5a KC n CCM.FF-K5a were etermne n a range of mass flow rate between 1040 an kg/h as shown n Fg The uncertanty of ranges from 0.08% to 0.10%. KC 0,2 p = bar % Meter #1 Meter #2 Mean 0,1 0,0-0,1-0, kg/h m Fg. 3.3: Results for the fference of to the KCRV n the CCM.FF-K5a. KC 4 THE TEST RESULTS BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 10 of 15

11 meter evaton meter evaton Meter #1 (Elster) 0,3 0,2 0,1 0,0-0,1-0,2-0,3-0,4-0,5-0,6 protocol CCM.FF-K5a.1 FORCE -0, E7 Reynolsnumber Re Meter #2 (RMG) 0,5 0,4 0,3 0,2 0,1 0,0-0,1-0,2-0,3-0,4-0,5 protocol CCM.FF-K5a.1 FORCE E7 Reynolsnumber Re The fference for the blateral comparson of FORCE- s calculate acc.: FORCE- = fforce f what leas consequently for the expane uncertanty U(FORCE-) = [U 2 (fforce)+u 2 (f)] 0.5 ; BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 11 of 15

12 The fference of FORCE to the KCRV of CCM.FF-K5a s calculate acc. eq. (8): FORCE fforce f SC KCRV KC FORCE, (8) wth U(FORCE) = [U 2 (,CCM.FF-K5a)+U 2 () +U 2 (FORCE-)-2*cov] 0.5 ; were cov s the square uncertanty of the common source of traceablty estmate wth (0.14%)^2 as mentone above n chapter 2.2. SC 0,4 % 0,2 0,0 FORCE- -0,2-0,4-0,6 p = MPa meter #1 meter # E7 Renols number Re Fg. 4.3: Plot of blateral fferences NIST- versus Reynols number Re both meters; BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 12 of 15

13 0,4 % 0,2 FORCE-CCM.FF-K5a 0,0-0,2-0,4-0,6 p = MPa meter #1 meter # E7 Reynols number Re Fg. 4.4: Plot of fferences FORCE-KCRVCCM.FF-K5a versus Reynols number Re both meters (turbne an USM); 5 SUMMARY, FINAL REMARKS The fferences for the meter evatons as gven n Fg. 4.2 an 4.3 are evaluate n comparson wth ther expane uncertanty by means of the (unsgne) egree of equvalence efne as: En U The Fg. 5.1 shows the overall result for the comparson (average for both meter) utlzng the ata out of Fg. 4.3 an 4.4. The fnal outcome of ths nter comparson s the full equvalence of the measurements performe by FORCE for hgh pressure natural gas wth the actual key comparsons reference value of CCM.FF-K5a. BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 13 of 15

14 En FORCE 1,2 1,0 0,8 0,6 p = 1.6 to CCM.FF-K5a blateral 5.0 MPa 0,4 0,2 0, E7 Reynols number Re Fg. 5.1: Plot of egree of equvalence (En) versus Reynols number Re (average of both meters); 6 REFERENCES [1] D. Dophee, B. Mckan, R. Kramer, H.-J. Hotze (-pgsartm), M.van er Beek, G. Blom (NM-VSL), J.- P. Vallet, O. Goreu, (LNE-LADG), CIPM Key Comparsons for Natural Gas at Hgh-Pressure Conucte n November / December 2004 CCM.FF-5.a - Fnal report [2] C. Ullner et al., Specal features n profcency tests of mechancal testng laboratores, In: D. Rchter, W. Wöger, W. Hässelbarth (e.) Data analyss of key comparsons, Semnar/Internatonal Workshop, ISBN [3] P. Robouch et al., The Naj Plot, a smple graphcal tool for the evaluaton of nter-laboratory comparsons, In: D. Rchter, W. Wöger, W. Hässelbarth (e.) Data analyss of key comparsons, Semnar/Internatonal Workshop, ISBN [4] Mckan., B, Kramer R., Veth D., Hnze H.-M., The Actual Results of Recalbraton an Improvements of the Traceablty Chan as well as the Uncertanty for Measurement n Hgh Pressure Natural Gas n Germany, Proceeng of the 14 th Flomeko 2007, Johannesburg, South Afrca, Sept. 19th 21st BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 14 of 15

15 [5] B. Mckan, D. Dophee, R. Kramer, D. Veth, James McLaren, W. Haner, G. Gruuesk, Fnal report on the blateral CIPM Key Comparson for natural gas at hgh pressure; conucte n October 2006; CCM.FF-K5.a.1. K5.a.1.pf [6] Detrch Dophee, Fnal report on the CIPM key comparsons for compresse ar an ntrogen conucte n November 2004/June 2005: CCM.FF-5.b; 2006 Metrologa BIPM/CIPM Key Comparsons for hgh-pressure gases, CCM-FF-KC5a.2-Draft Techncal Protocol; Page 15 of 15