Simplified indirect estimation of pump flow discharge: An example from Serbia

wa e Technical No e Simpli ied Indi ec Es ima ion o Pump Flow Discha ge: An Example om Se bia Milica Raši´c Amon 1,2 , Milan Radi´c 1, Zo an S aji´c 1,2, Dejan B ki´c 1,2,3,* and Pa el P aks 3   Ci a ion: Raši´c Amon, M.; Radi´c, M.; S aji´c, Z.; B ki´c, D.; P aks, P. Simpli ied Indi ec Es ima ion o Pump Flow Discha ge: An Example om Se bia. Wa e 2021,13, 796. h ps://doi.o g/10.3390/w13060796 Academic Edi o s: S e ano Al isi and Helena M. Ramos Recei ed: 17 Decembe 2020 Accep ed: 10 Ma ch 2021 Published: 14 Ma ch 2021 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2021 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). 1Facul y o Elec onic Enginee ing, Uni e si y o Niš, 18000 Niš, Se bia; [email p o ec ed] (M.R.A.); [email p o ec ed] (M.R.); [email p o ec ed] (Z.S.) 2Resea ch and De elopmen Cen e “IRC Al a ec”, 18000 Niš, Se bia 3 IT4Inno a ions, VSB—Technical Uni e si y o Os a a, 708 00 Os a a, Czech Republic; [email p o ec ed] *Co espondence: [email p o ec ed] o [email p o ec ed] Abs ac : In he absence o a lowme e o due o i s inaccu acy, he low a e a he discha ge sec ion o he pipeline ollowing he obse ed pump can be oughly es ima ed i he p essu e can be measu ed ins ead. To use he p oposed p ocedu e wo main condi ions should be achie ed: (1) a manome e should be ins alled a he discha ge pipeline be ween he pump and he low egula ion al e, and (2) he ac ual cu e ha ela es p essu e and low o he obse ed pump uni should be known in ad ance. The desc ibed example is om Se bia, bu i is o in e es o any wa e pumping s a ion wi h a subme sible pump (ins alled in wells o anks) whe e a limi ed numbe o adequa e places o he measu ing o low a e a ailable (i any a e a ailable a all), bu whe e he p essu e a he discha ge pipe o he obse ed pump can be measu ed. This simpli ied me hod can ind applicabili y in ins alla ions in emo e u al egions whe e limi ed esou ces a e a ailable. The esul s show ha he calcula ed alues o he low ob ained by he p esen ed me hod de ia e g ea ly in ela ion o he measu ed alues p o ided by he po able ul asonic lowme e , up o 60% a one o he measu ing poin s. Howe e , in ela ion o he measu ed alues p o ided by he pe manen ly ins alled lowme e he disc epancy is signi ican ly lowe (0.6–6.8%). Keywo ds: pumps; p essu e d op; low es ima ion; accu a e measu emen ; pipelines; wa e - wo ks; lowme e 1. In oduc ion In he absence o a lowme e o due o i s inaccu acy, he low a e a he discha ge sec ion o he pipeline ollowing he obse ed pump can be oughly es ima ed i he wa e p essu e can be measu ed ins ead. Ve y o en, i is p ac ically impossible o selec an adequa e place o a lowme e due o he p esence o many elemen s in a wa e pumping s a ion, such as al es and elbows whe e he pipeline changes i s di ec ion. The p oblem o inco ec measu emen s o he discha ge low a e in wa e wo ks can be easily sol ed i a sec ion o he pipe wi h an adequa e leng h wi h no low dis u bances is o eseen a he discha ge side o he obse ed pump. To sol e he p oblem, in his p ac ical echnical no e an al e na i e, simpli ied app oach is gi en o a ough es ima ion o he low a e a he discha ge sec ion o he pipeline o hose pumps whe e he lowme e is absen o when he eading om an exis ing lowme e is un eliable due o an un a o able pipeline con igu a ion o due o any o he eason [ 1 – 7 ]. A pump is a machine ha is used o ans e quan i ies o liquids om one place o ano he , and he e i s low-p essu e cha ac e is ic is used o es ima e wa e low a e a he discha ge side o wa e pumping s a ions. The p esen ed simpli ied app oach can be adap ed o any o he liquid, including c ude oil whe e a special applica ion can be ound in o sho e ins alla ions wi h limi ed places a ailable o measu emen . In p ac ice, he e a e si ua ions when he e a e no lowme e s ins alled in pumping s a ions (especially in emo e low-income egions), which is especially common when i Wa e 2021,13, 796. h ps://doi.o g/10.3390/w13060796 h ps://www.mdpi.com/jou nal/wa e Wa e 2021,13, 796 2 o 15 comes o pumping s a ions o smalle capaci y. In such cases, po able lowme e s a e used o es ima e he low a e, i.e., he amoun o liquid pumped in a ce ain pe iod o ime, bu choosing he place o hei ins alla ion is no easy. In ce ain ins alla ions wi h pumps, o make measu emen s, i is easie and less cos ly o ins all only a manome e (in al eady exis ing ins alla ions, his will p e en addi ional cu ing o he pipeline o ins all a lowme e ). I he place a which a low me e should be ins alled is no p ope ly chosen in he design phase p ope ly chosen in he design phase, he p oblem can be sol ed by a adical app oach, which in ol es he exca a ion o a pa o he pipeline ha is o he wise unde g ound. Howe e , his adical app oach in ol es signi ican cos s and ca ies he isk o acciden s. The p oposed app oach o low a e es ima ion has a gene al cha ac e and can be applied in any pumping s a ion wi h a subme ged pump (in a ank o a well) p o ided ha : 1. I has a pump uni wi h an in-ad ance known ac ual H(Q) cu e gained om lab- o a o y es ing (possible disc epancy be ween he design sys em cu es a ailable om manu ac u e s and he on-si e one is equen and he e o e such cu es om ca alogues should be e-e alua ed i possible), and, 2. The p essu e can be measu ed a he discha geside o he obse ed pump. Res ic ions include a lack o equipmen o egula e he speed o he o o s, and he use o wo o mo e pumps in a pa allel con igu a ion, which means ha hei pe o mance canno always be de e mined (especially ue when he non- e u n al es a he pumps a e no ully igh ened). Such a si ua ion o en occu s in small emo e pumping s a ions whe e he ope a ing egime is no ully espec ed ( he diame e o he suc ion pipe is no always he same as he discha ge pipe diame e when, due o he isk o ca i a ion, a la ge diame e o he suc ion pipe is usually used). In he absence o pe manen measu emen s o low in wa e wo ks, o whe e accu acy is doub ul, he mos commonly used p ac ice is o compa e he esul s ha can be ob ained om se e al di e en po able con ol me e s ( hese a e, as a ule, po able ul asonic me e s) [ 8 – 16 ]. We will also es ou app oach in his manne . As i will be p esen ed, he esul s es ima ed ollowing he ecommenda ion om his p ac ical echnical no e a e mo e eliable compa ed o hose ob ained using po able lowme e s in sys ems wi h a complex geome y o pipeline ollowing he pump [17–21]. Based on one p ac ical example om Se bia, he heo e ical backg ound will be p e- sen ed u he in he ex . This simpli ied me hod can ind applica ion in ins alla ions in emo e, low-income egions whe e limi ed places o measu emen a e a ailable (i any a e a ailable a all). Simila ough app oxima e me hods o es ima ion o wa e low using local p essu e loss measu emen s a e no known o he au ho s, bu inaccu acies o lowme e s a e no a e [22,23]. 2. The Desc ip ion o he P oposed App oach To apply he simpli ied app oach p oposed in his wo k o low- a e es ima ion, i is necessa y o ha e a pump wi h in-ad ance p ecisely de e mined H(Q) cu e and o ha e a manome e ins alled a he discha ge side o he pump be o e he al e o low egula ion [ 24 , 25 ]. I is no ad isable o ely on he ca alogued cha ac e is ics o he pump, especially o olde pump models. E en wi h he pump uni s o he same ype and manu ac u ed in he same yea , he ope a ing cha ac e is ics will no be he same and will depend on hei eal condi ion such as he numbe o ope a ing hou s, he wea o impelle s, he condi ion o bea ings, he numbe o o e hauls and losses in elec ic mo o s, e c. Figu e 1shows a gene al a angemen o elemen s equi ed o he applica ion o he p oposed indi ec low a e es ima ion in a pump s a ion wi h subme sible pumps ( he lowme e s depic ed in ed a e no p esen a all o a e possibly inaccu a e due o he unsui able place o placemen in a complex pipeline con igu a ion). The example o he placemen o a po able lowme e shown in Figu e 1is a ypical example o an Wa e 2021,13, 796 3 o 15 inapp op ia e posi ion in which a signi ican e o in low measu emen occu s (high measu emen unce ain y). Wa e 2021, 13, x FOR PEER REVIEW 3 o 16 lowme e s depic ed in ed a e no p esen a all o a e possibly inaccu a e due o he unsui able place o placemen in a complex pipeline con igu a ion). The example o he placemen o a po able lowme e shown in Figu e 1 is a ypical example o an inapp o- p ia e posi ion in which a signi ican e o in low measu emen occu s (high measu e- men unce ain y). Figu e 1. The layou o he elemen s equi ed o low a e es ima ion. Rega ding he scheme om Figu e 1, one should no o ge abou he p essu e loss in he e ical sec ion o he pipeline— he p essu e measu ed a i s op is lowe han a he pump head. Taking in o accoun he complexi y o he pipeline, he equi alen cha ac e is ics o he pump should be e alua ed h ough he analysis o he indi idual sys em o pipes on which he pump is ins alled. In such a case, i is di icul o alk abou he compliance o noncompliance o he measu ed cha ac e is ics o hose gi en by he pump manu ac u e . In p ac ice, he e a e si ua ions whe e lowme e s a e no ins alled in pumping s a- ions, which is especially common when i comes o pumping s a ions o smalle capaci y (usually wi h wo pump uni s ha do no wo k in a pa allel con igu a ion, bu whe e one o hem is used as a backup pump). In such cases, po able lowme e s a e used o es ima e he low a e, i.e., he amoun o liquid pumped in a ce ain pe iod, while he choice o he posi ion o hei ins alla ion is no easy. I he e a e no manholes p epa ed in ad ance, i is necessa y o exca a e he g ound a ound he pipeline. In such si ua ions, his is no a common p ac ice, bu a he he lowme e is placed in any accessible place. Fo he low- a e es ima ion, he p essu e can be exp essed in [Pa] (in [ba ], whe e 1 ba = 105 Pa) o as a p essu e head in a uni o leng h [m], whe e hese wo o ms a e ela ed as 𝑝 =𝜌·𝑔·𝐻, whe e 𝑝 is p essu e [Pa] measu ed by he manome e a he dis- cha ge side (exac ly abo e he pump), 𝜌 is he densi y o he wa e ~1000 kg/m3, g is g a - i a ional cons an ~9.81 m/sec2, while 𝐻 is p essu e head [m]. 𝐻 is he co ec ion in [m], which depends on he heigh di e ence be ween he posi ion o he manome e and he wa e le el in he ank. I he wa e le el in he ank is cons an du ing he expe imen , he eloci y a he suc ion side is 𝑉 =0 [m/s]. The eloci y a he discha ge side 𝑉 de- pends on he pipeline diame e and he low a e, which a e unknown a iables a he beginning. This p oblem can be sol ed ei he by he implemen a ion o i e a i e analysis, o by p ope choice o he posi ion o he manome e (as i is shown in Sec ion 3.2.1). Ne- glec ing local losses om he poin o luid suc ion o he poin o p essu e measu emen , o al head H in [m] can be es ima ed using Equa ion (1): Figu e 1. The layou o he elemen s equi ed o low a e es ima ion. Rega ding he scheme om Figu e 1, one should no o ge abou he p essu e loss in he e ical sec ion o he pipeline— he p essu e measu ed a i s op is lowe han a he pump head. Taking in o accoun he complexi y o he pipeline, he equi alen cha ac e is ics o he pump should be e alua ed h ough he analysis o he indi idual sys em o pipes on which he pump is ins alled. In such a case, i is di icul o alk abou he compliance o noncompliance o he measu ed cha ac e is ics o hose gi en by he pump manu ac u e . In p ac ice, he e a e si ua ions whe e lowme e s a e no ins alled in pumping s a ions, which is especially common when i comes o pumping s a ions o smalle capaci y (usually wi h wo pump uni s ha do no wo k in a pa allel con igu a ion, bu whe e one o hem is used as a backup pump). In such cases, po able lowme e s a e used o es ima e he low a e, i.e., he amoun o liquid pumped in a ce ain pe iod, while he choice o he posi ion o hei ins alla ion is no easy. I he e a e no manholes p epa ed in ad ance, i is necessa y o exca a e he g ound a ound he pipeline. In such si ua ions, his is no a common p ac ice, bu a he he lowme e is placed in any accessible place. Fo he low- a e es ima ion, he p essu e can be exp essed in [Pa] (in [ba ], whe e 1 ba = 10 5 Pa) o as a p essu e head in a uni o leng h [m], whe e hese wo o ms a e ela ed as pdis =ρ·g·H , whe e pdis is p essu e [Pa] measu ed by he manome e a he discha ge side (exac ly abo e he pump), ρ is he densi y o he wa e ~1000 kg/m 3 ,gis g a i a ional cons an ~9.81 m/sec 2 , while H is p essu e head [m]. Hg is he co ec ion in [m], which depends on he heigh di e ence be ween he posi ion o he manome e and he wa e le el in he ank. I he wa e le el in he ank is cons an du ing he expe imen , he eloci y a he suc ion side is Vsuc = 0 [m/s]. The eloci y a he discha ge side Vdis depends on he pipeline diame e and he low a e, which a e unknown a iables a he beginning. This p oblem can be sol ed ei he by he implemen a ion o i e a i e analysis, o by p ope choice o he posi ion o he manome e (as i is shown in Sec ion 3.2.1). Neglec ing local losses om he poin o luid suc ion o he poin o p essu e measu emen , o al head H in [m] can be es ima ed using Equa ion (1): H =pdis ρ·g+Hg+V2 dis 2·g(1) Wa e 2021,13, 796 4 o 15 To es he app oach o indi ec es ima ion o pump low discha ge p oposed he e, he al e a he discha ge side o he pump should be ully open. Fu he , he al e needs o be g adually closed in disc e e s eps, which changes he alues o he low and subsequen ly o he p essu e. The e o e, o each achie ed s a iona y ope a ing poin , he alues o he p essu e pdis om he manome e should be eco ded. Based on Equa ion (1) and g aph in Figu e 2, i is possible o es ima e he low a e Qes a he discha ge side o he obse ed pump. The cu e in Figu e 2 ela es he o al head H and he low a e Q and has o be ob ained om he manu ac u e ’s ca alogue o p e e ably om a labo a o y es in ad ance. The possibili y o disc epancy be ween he labo a o y cha ac e is ics and cha ac e is ics om he ca alogue is some hing ha exis s in eali y, especially o an olde pump, which has been in se ice o a long pe iod o ime and has been de ined by alid echnical s anda ds (such as [ 26 ]). Depending on he ype o pump equi ed, mino o majo de ia ions om he ac o y cha ac e is ic a e pe mi ed. The echnical s anda d, EN ISO 9906:2012 [ 26 ], allows ela i ely la ge disc epancies be ween he ope a ing cha ac e is ics o he pumps he ca alogue cha ac e is ics. Wa e 2021, 13, x FOR PEER REVIEW 4 o 16 𝐻=𝑝 𝜌·𝑔+𝐻+𝑉  2·𝑔 (1) To es he app oach o indi ec es ima ion o pump low discha ge p oposed he e, he al e a he discha ge side o he pump should be ully open. Fu he , he al e needs o be g adually closed in disc e e s eps, which changes he alues o he low and subse- quen ly o he p essu e. The e o e, o each achie ed s a iona y ope a ing poin , he al- ues o he p essu e 𝑝 om he manome e should be eco ded. Based on Equa ion (1) and g aph in Figu e 2, i is possible o es ima e he low a e 𝑄 a he discha ge side o he obse ed pump. The cu e in Figu e 2 ela es he o al head 𝐻 and he low a e 𝑄 and has o be ob ained om he manu ac u e ’s ca alogue o p e e ably om a labo a o y es in ad ance. The possibili y o disc epancy be ween he labo a o y cha ac e is ics and cha ac e is ics om he ca alogue is some hing ha exis s in eali y, especially o an olde pump, which has been in se ice o a long pe iod o ime and has been de ined by alid echnical s anda ds (such as [26]). Depending on he ype o pump equi ed, mino o majo de ia ions om he ac o y cha ac e is ic a e pe mi ed. The echnical s anda d, EN ISO 9906:2012 [26], allows ela i ely la ge disc epancies be ween he ope a ing cha ac e - is ics o he pumps he ca alogue cha ac e is ics. Figu e 2. Indi ec de e mina ion o low 𝑄 a he measu ing poin based on he cu e, which ela es o al head 𝐻 and low 𝑄. The e o e, he co esponding low 𝑄 can be de e mined indi ec ly o each meas- u ing poin om he known 𝐻(𝑄) cu e, (wi h sa is ac o y measu emen unce ain y) o each measu ing poin o he p essu e 𝑝 ob ained om he manome e , as shown in Figu e 2 ( ecalcula ed o 𝐻). Figu e 2. Indi ec de e mina ion o low Qes a he measu ing poin based on he cu e, which ela es o al head H and low Q. The e o e, he co esponding low Qes can be de e mined indi ec ly o each mea- su ing poin om he known H(Q) cu e, (wi h sa is ac o y measu emen unce ain y) o each measu ing poin o he p essu e pdis ob ained om he manome e , as shown in Figu e 2( ecalcula ed o H). The ollowing simple algo i hm, shown in Figu e 3, should be used o es ima e he low a e using he p oposed app oach. Wa e 2021,13, 796 5 o 15 Wa e 2021, 13, x FOR PEER REVIEW 5 o 16 The ollowing simple algo i hm, shown in Figu e 3, should be used o es ima e he low a e using he p oposed app oach. Figu e 3. A simple algo i hm o es ima ion o discha ge low. 3. A P ac ical Example The pumping s a ion obse ed in which he me hod has been es ed has had a long his o y o ques ionable measu emen s o low due o he complex geome y o he pipeline wi h an insu icien leng h o pipe whe e a lowme e can be ins alled. Simpli ied diag am o he measu ing pump s a ion is shown in Figu e 4 ( he op iew). Figu e 4. Simpli ied diag am o he pump s a ion. Due o a se ious mis ake du ing he cons uc ion p ocess, he main discha ge pipeline made o s eel DN700 is no in acco dance wi h he o iginal p ojec and has h ee elbows a sho dis ances. Pumps a e subme sed in he wa e ank, which is placed benea h he loo o he pump s a ion. The wa e le el in he ank is held a a cons an alue. Du ing he mode niza ion o he pump s a ion ha has been ca ied ou ecen ly, he old pumps we e aken ou and eplaced wi h wo new subme sible pumps (G und os SP 270-3A G). Figu e 3. A simple algo i hm o es ima ion o discha ge low. 3. A P ac ical Example The pumping s a ion obse ed in which he me hod has been es ed has had a long his o y o ques ionable measu emen s o low due o he complex geome y o he pipeline wi h an insu icien leng h o pipe whe e a lowme e can be ins alled. Simpli ied diag am o he measu ing pump s a ion is shown in Figu e 4( he op iew). Wa e 2021, 13, x FOR PEER REVIEW 5 o 16 The ollowing simple algo i hm, shown in Figu e 3, should be used o es ima e he low a e using he p oposed app oach. Figu e 3. A simple algo i hm o es ima ion o discha ge low. 3. A P ac ical Example The pumping s a ion obse ed in which he me hod has been es ed has had a long his o y o ques ionable measu emen s o low due o he complex geome y o he pipeline wi h an insu icien leng h o pipe whe e a lowme e can be ins alled. Simpli ied diag am o he measu ing pump s a ion is shown in Figu e 4 ( he op iew). Figu e 4. Simpli ied diag am o he pump s a ion. Due o a se ious mis ake du ing he cons uc ion p ocess, he main discha ge pipeline made o s eel DN700 is no in acco dance wi h he o iginal p ojec and has h ee elbows a sho dis ances. Pumps a e subme sed in he wa e ank, which is placed benea h he loo o he pump s a ion. The wa e le el in he ank is held a a cons an alue. Du ing he mode niza ion o he pump s a ion ha has been ca ied ou ecen ly, he old pumps we e aken ou and eplaced wi h wo new subme sible pumps (G und os SP 270-3A G). Figu e 4. Simpli ied diag am o he pump s a ion. Due o a se ious mis ake du ing he cons uc ion p ocess, he main discha ge pipeline made o s eel DN700 is no in acco dance wi h he o iginal p ojec and has h ee elbows a sho dis ances. Pumps a e subme sed in he wa e ank, which is placed benea h he loo o he pump s a ion. The wa e le el in he ank is held a a cons an alue. Du ing he mode niza ion o he pump s a ion ha has been ca ied ou ecen ly, he old pumps we e aken ou and eplaced wi h wo new subme sible pumps (G und os SP 270-3A G). Be o e he ins alla ion, one o he new pumps, ma ked as P1 in Figu e 4, had been addi ionally es ed by he manu ac u e ’s labo a o y. Wa e 2021,13, 796 6 o 15 To e i y he accu acy o he simpli ied app oach p oposed he e in p ac ice, low measu emen s in he obse ed pumping s a ion using lowme e s we e pe o med (in u he ex Qmes ) and hen hose measu ed alues we e compa ed o he es ima ed alues (in u he ex Qes ). Besides, he exac cu e o he obse ed G und os SP 270-3A G, which ela es o al head H and low Q was de e mined in he manu ac u e ’s labo a o y ( he es ing o he pump in he manu ac u e ’s acili y is shown in Figu e 5, while he esul s a e shown in Table 1). In he speci ic si ua ion p esen ed in his pape , he eal cha ac e is ics o he pump eco ded in he labo a o y di e om hose om he manu ac u e ’s ca alogue. Fu he mo e, some imes i is no possible o ha e a s able equency o 50 Hz, so he ac ual cu e om he labo a o y, which ela es he o al head H and he low Q should be ecalcula ed o he ac ual condi ions in he obse ed wa e pumping s a ion [ 27 ]. As we will show in he ollowing case, he ope a ing equency was se o 49 Hz, o show how o ecalcula e a cu e designed o 50 Hz. Wa e 2021, 13, x FOR PEER REVIEW 6 o 16 Be o e he ins alla ion, one o he new pumps, ma ked as P1 in Figu e 4, had been addi- ionally es ed by he manu ac u e ’s labo a o y. To e i y he accu acy o he simpli ied app oach p oposed he e in p ac ice, low measu emen s in he obse ed pumping s a ion using lowme e s we e pe o med (in u - he ex 𝑄) and hen hose measu ed alues we e compa ed o he es ima ed alues (in u he ex 𝑄). Besides, he exac cu e o he obse ed G und os SP 270-3A G, which ela es o al head 𝐻 and low 𝑄 was de e mined in he manu ac u e ’s labo a o y ( he es ing o he pump in he manu ac u e ’s acili y is shown in Figu e 5, while he esul s a e shown in Table 1). In he speci ic si ua ion p esen ed in his pape , he eal cha ac e is ics o he pump eco ded in he labo a o y di e om hose om he manu- ac u e ’s ca alogue. Fu he mo e, some imes i is no possible o ha e a s able equency o 50 Hz, so he ac ual cu e om he labo a o y, which ela es he o al head 𝐻 and he low 𝑄 should be ecalcula ed o he ac ual condi ions in he obse ed wa e pumping s a ion [27]. As we will show in he ollowing case, he ope a ing equency was se o 49 Hz, o show how o ecalcula e a cu e designed o 50 Hz. Figu e 5. Tes ing o SP 270-3A G pump in he labo a o y. Table 1. Values o he cu e ha ela es o al head and low o he SP 270-3A G pump measu ed in he labo a o y a 50 Hz and ecalcula ed o 49 Hz. 50 Hz 𝑄 [dm3/s] 0 11.67 59.88 75.84 90.08 𝐻 [m] 145.38 138.89 97.47 86.2 71.96 49 Hz 𝑄 [dm3/s] 0 11.44 58.68 74.32 88.28 𝐻 [m] 139.62 133.39 93.61 82.79 69.11 The ollowing equipmen was used o he es in he pumping s a ion: 1. A subme sible pumping uni G und os SP 270-3A G wi h a a ed powe o 110 kW, Figu e 5. Tes ing o SP 270-3A G pump in he labo a o y. Table 1. Values o he cu e ha ela es o al head and low o he SP 270-3A G pump measu ed in he labo a o y a 50 Hz and ecalcula ed o 49 Hz. 50 Hz Q[dm3/s] 0 11.67 59.88 75.84 90.08 H[m] 145.38 138.89 97.47 86.2 71.96 49 Hz Q[dm3/s] 0 11.44 58.68 74.32 88.28 H[m] 139.62 133.39 93.61 82.79 69.11 The ollowing equipmen was used o he es in he pumping s a ion: 1. A subme sible pumping uni G und os SP 270-3A G wi h a a ed powe o 110 kW, 2. The low was measu ed using a pe manen ly ins alled ul asonic lowme e Siemens SITRANS F a he main discha ge pipeline a he obse ed pump s a ion (addi ionally a po able ul asonic lowme e TDSH100 was used), Wa e 2021,13, 796 7 o 15 3. The p essu e was measu ed using an IDROSCAN digi al manome e which was ins alled on he discha ge side o he pump (addi ionally, an analogue manome e was ins alled), 4. The equency o he powe supply o he d i e mo o was egula ed using a Mi subishi F740 egula o , and 5. The low was egula ed using he al e ins alled a he s eel discha ge pipe DN 200 a e he pump P1. All equipmen used in ou expe imen s has been p ope ly es ed using all common echnical no ms and s anda ds equi ed o such de ices [28]. 3.1. De e mina ion o Subs i u e Cha ac e is ics The pu pose o his subsec ion is o show how he accu a e H(Q) cu e o he obse ed G und os SP 270-3A G was de e mined. 3.1.1. Measu ing in he Manu ac u e ’s Labo a o y and he Recalcula ion o he Ac ual F equency o Powe Supply The measu ing in he manu ac u e ’s labo a o y: The ac ual H(Q) cu e o he ob- se ed pump SP 270-3A G was de e mined expe imen ally in he manu ac u e ’s labo a o y and he esul s a e alid o powe supply equency o 50 Hz ( ela ed lows and he p es- su e ob ained in disc e e s eps, which ha e been used o cons uc he cu e a e gi en in Table 1). Labo a o y es s a e expensi e, bu hey a e no manda o y and do no ep esen wha he au ho s sugges in e e y si ua ion. In ce ain si ua ions, especially when i comes o pumping uni s o highe powe , he p ice o such es s may be negligible when compa ed o he possibili ies ha he use can ge wi h he help o such es s. The ac is ha pump manu ac u e s usually do no ag ee o p o e he pe o mance o pumping uni s a he ins alla ion si es o such pumps, because hey canno gua an ee he accu acy o he measu ing equipmen in he pumping s a ions whe e he obse ed pumps ha e been ins alled. Ins ead, hey p e e es ing in an independen o he manu ac u e ’s labo a o y. Also, he cha ac e is ics o pump uni s change du ing se ice li e. In si ua ions whe e he e a e lowme e s ins alled in pumping s a ions, i is no complica ed o pe iodically pe o m measu emen s a he ins alla ion si e o check and/o co ec he ope a ing cha ac e is ics o pumping uni s. This can usually be done as a pa o planned main enance ac i i ies in he pumping s a ions so ha i does no inc ease unning cos s. This way, he deg ee o de e io a ion o he ope a ing cha ac e is ics o he pumping uni s can be moni o ed. This is pa icula ly impo an because hei e iciency can be educed o such an ex en ha i would be necessa y o epai and/o o eplace hem. The obse ed pumping s a ion in which he me hod was es ed has had a long his o y o ques ionable measu ing o low due o he complex geome y o he pipeline wi h insu icien leng h o pipe whe e a lowme e could be ins alled. The ins alled pumps a e old and due o ha d exploi a ion, hei cha ac e is ics we e al e ed compa ed o hose om he ca alogue. The e o e, he old pumps we e aken ou and eplaced wi h new pumps which ha e been addi ionally es ed by he manu ac u e ’s labo a o y ( es ing o he pump in he manu ac u e ’s acili y is shown in Figu e 5, while he esul s a e shown in Table 1). Recalcula ion o he ac ual equency o he powe supply: Fo an illus a ion o he p oposed es ima ion o he low in gene al condi ions, du ing he es in he wa e pumping s a ion whe e he pump has been ins alled, he equency has been se o 49 Hz using a Mi subishi F740 egula o and consequen ly, he cu e, which ela es o al head H and low Q o such condi ions has been ecalcula ed. The co ec ed alues ha e been calcula ed using Equa ion (2) and a e also p esen ed g aphically in Figu e 6(based on he da a poin s om Table 1). H49 =49 50 2·H50 Q49 =49 50 ·Q50 ), (2) Wa e 2021,13, 796 8 o 15 Wa e 2021, 13, x FOR PEER REVIEW 8 o 16 calcula ed using Equa ion (2) and a e also p esen ed g aphically in Figu e 6 (based on he da a poin s om Table 1). 𝐻 =49 50·𝐻 𝑄 =49 50·𝑄 ⎭ ⎬ ⎫ , (2) S a is ical calcula ions in he shown case a e based on a limi ed numbe o measu e- men poin s om Table 1. Al hough his may be insu icien o a ho ough analysis whe e he numbe o hese poin s should be inc eased, o p ac ical analyses, i e poin s can be su icien especially in cases whe e mo e da a is no a ailable such as in his case. Figu e 6. The expe imen ally de e mined cu e which ela es p essu e head and low o he SP 270-3A G pump ecalcula ed o 49 Hz. 3.1.2. Reg ession Model and S a is ical Analysis To acili a e he use o he da a om Table 1, he o al head and he low o he pump SP 270-3A G in ou expe imen can be p esen ed g aphically as gi en in Figu e 6. The co ec ed g aph o 49 Hz is also gi en in Figu e 6, while he ela ed cu e based on e- g ession analysis is gi en in Equa ion (3). To a oid eading om he cu e p esen ed in Figu e 6, i is be e o use he eg es- sion o mula as gi en in Equa ion (3), which gi es he low as he unc ion o he o al head o he obse ed pump; he da a om he labo a o y o 50 Hz and ecalcula ed al- ues o 49 Hz a e in Table 1. 𝑄 =−0.0018·𝐻−0.8643·𝐻+156.77 (3) The da a om he measu emen ha was used o p oducing o Equa ion (3) is gi en in Table 1. The ela ion based on he inpu da a o Table 1 was i ed by eg ession analysis using S a g aphics Cen u ion, a s a is ical s a is ics package ha pe o ms and explains, in plain language, bo h basic and highly ad anced s a is ical unc ions. We ha e ied se - e al eg ession models, and we es ed hem using Pea son co ela ion and R-Squa ed alue coe icien o de e mina ion [29,30]: Figu e 6. The expe imen ally de e mined cu e which ela es p essu e head and low o he SP 270-3A G pump ecalcula ed o 49 Hz. S a is ical calcula ions in he shown case a e based on a limi ed numbe o measu e- men poin s om Table 1. Al hough his may be insu icien o a ho ough analysis whe e he numbe o hese poin s should be inc eased, o p ac ical analyses, i e poin s can be su icien especially in cases whe e mo e da a is no a ailable such as in his case. 3.1.2. Reg ession Model and S a is ical Analysis To acili a e he use o he da a om Table 1, he o al head and he low o he pump SP 270-3A G in ou expe imen can be p esen ed g aphically as gi en in Figu e 6. The co ec ed g aph o 49 Hz is also gi en in Figu e 6, while he ela ed cu e based on eg ession analysis is gi en in Equa ion (3). To a oid eading om he cu e p esen ed in Figu e 6, i is be e o use he eg ession o mula as gi en in Equa ion (3), which gi es he low as he unc ion o he o al head o he obse ed pump; he da a om he labo a o y o 50 Hz and ecalcula ed alues o 49 Hz a e in Table 1. Qes −49 =−0.0018·H2−0.8643·H+156.77 (3) The da a om he measu emen ha was used o p oducing o Equa ion (3) is gi en in Table 1. The ela ion based on he inpu da a o Table 1was i ed by eg ession analysis using S a g aphics Cen u ion, a s a is ical s a is ics package ha pe o ms and explains, in plain language, bo h basic and highly ad anced s a is ical unc ions. We ha e ied se e al eg ession models, and we es ed hem using Pea son co ela ion and R-Squa ed alue coe icien o de e mina ion [29,30]: • The coe icien o de e mina ion R-Squa ed alue deno ed as R 2 equals o 1.0 would indica e a pe ec i , while an R-Squa ed alue o 0.0 would indica e he opposi e case; • The Pea son co ela ion coe icien is a s a is ic ha measu es he linea co ela ion be ween wo a iables and has a alue be ween +1 and − 1, whe e a alue o +1 is a o al posi i e linea co ela ion, 0 is no linea co ela ion, and − 1 is o al nega i e linea co ela ion. Wa e 2021,13, 796 9 o 15 In ou pa icula case, a linea model is sligh ly mo e sui able o he poin s om Table 1, bu we use he squa ed model because i is mo e gene al and sui able o mos cases. Fo example, he linea model Qes −49 = 180.147 − 1.26628 ·H , shows he In e cep 180.147 and he Slope − 1.26628 as p edic o s. These a iables a e s a is ically signi ican because hei p- alues equal 0.000, which a e < 0.05. I also means ha he e is a s a is ically signi ican co ela ion be ween Qes −49 and H a he 95% con idence le el (de ails o he s a is ical analysis a e gi en in Table 2). Table 2. Compa ison o al e na i e models ob ained by he S a g aphics Cen u ion so wa e using Pea son co ela ion and R-Squa ed alue coe icien o de e mina ion. Model Co ela ion R-Squa ed Linea −0.9991 99.82% Squa ed-H −0.9980 99.60% Squa ed-Qes −49 ecip ocal-H 0.9978 99.56% Squa e oo -H −0.9977 99.53% Loga i hmic-H −0.9945 98.91% Squa ed-Qes −49 loga i hmic-H −0.9920 98.41% Squa ed-Qes −49 squa e oo -H −0.9866 97.34% Recip ocal-H 0.9822 96.47% Squa ed-Qes −49 −0.9799 96.03% Squa e oo -Qes −49 squa ed-H −0.9760 95.26% Squa e oo -Qes −49 −0.9663 93.37% Double squa ed −0.9643 92.98% Double squa e oo −0.9592 92.01% Squa e oo -Qes −49 loga i hmic-H −0.9504 90.33% Squa e oo -Qes −49 ecip ocal-H −0.9269 85.92% Besides, i is possible o use he poin s om Figu e 6and Table 1 alid o he equency o powe supply o 50 Hz o cons uc he cu e and he ela ed unc ion, while in ha case he alues o he measu ed low and he p essu e om he nex wo subsec ions whe e he equency was 49 Hz, should be ecalcula ed o 50 Hz, see Equa ion (2). 3.2. Measu emen in he Obse ed Pumping S a ion The measu emen s in he obse ed pumping s a ion we e pe o med o compa ison wi h he es ima ed alues ob ained using he shown simpli ied me hod. The p essu e mea- su emen in his subsec ion is used as one o he inpu pa ame e s and is essen ial o he me hod o low es ima ion desc ibed in his echnical no e. Howe e , low measu emen s in his subsec ion a e used only o compa ison. The equency o he powe supply du ing he measu emen a he wa e pumping s a ion was se o 49 Hz. 3.2.1. P essu e Measu emen The p essu e change, in he sec ion be ween he pump and he al e o he egu- la ion o low, was moni o ed by IDROSCAN digi al manome e wi h measu ing ange 0–50 ba (wi h a eading esolu ion o 0.01 ba and wi h a decla ed nonlinea i y ± 0.2%). The IDROSCAN digi al manome e was placed di ec ly on he discha ge side o he pump, oge he wi h he analogue manome e (Figu e 7). Because o he posi ion o he manome- e s, some undesi able a ia ion o low can occu which can in oduce a ce ain e o o p essu e measu emen due o incomple ely s abilized low. Howe e , bo h manome e s showed he iden ical alues o he measu ed p essu e. I should be men ioned ha due o he speci ic placemen o he manome e (i is moun ed in a special socke on he elbow o he discha ge pipeline, exac ly abo e he pump), he wa e eloci y a he poin o measu - ing is locally conside ed o be Vdis ≈ 0 [m/s]. Thus, he measu ed p essu e is somewha highe han he eal s a ic p essu e and includes he dynamic p essu e. Due o he heigh di e ence be ween he posi ion o he manome e and he wa e le el in he ank du ing ou expe imen , co ec ion Hg = 1.6 m ( ela ed o Figu e 1) is in oduced in o Equa ion (1).