EFFECT OF SUCKER-ROD PUMPING UNIT WALKING BEAM OSCILLATION FREQUENCY ON ASYNCHRONOUS ELECTRIC DRIVE

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1 Vol. 6, No. 1, 16 COMPUTATIONAL PROBLEMS OF ELECTRICAL ENGINEERING EFFECT OF SUCKER-ROD PUMPING UNIT WALKING BEAM OSCILLATION FREQUENCY ON ASYNCHRONOUS ELECTRIC DRIVE Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna Lviv Polytchnic National Univsity, Ukain Malya A., Kaluzhnyi B., Andishyn A., Molna K., 16 Abstact: Th pocss of oil xtaction quis continuous monitoing of oil wlls opation. To impov th fficincy of oil wlls, it is ncssay to st th optimal mod of oil pumping unit opation in which th at of liquid pumping cosponds to that of its inflow. Many oil wlls a stipps and thfo a opatd intmittntly. Application of automatd contol systms quis not only liabl data on th oilxtaction quipmnt status, but also dtmination of stictions which ais fom th conditions of o-f pfomanc of th lctic div systm. This can only b don on th basis of mathmatical modlling. Th mthod and algoithm dvlopd to comput opating mods of suck-od pumping units (SRPU) allow th walking bam oscillation fquncy to b dtmind dpnding on th oil fomation flow at, as wll as th stictions gading th ang of its gulation dfind by toqu and hat ovload of th moto. Th computation algoithm is undlain by th fin mathmatical modls of th asynchonous moto (AM) and suck od pump, and th mthod of computation of piodic dpndncis of th unit opating mod coodinats by solving a bounday-valu poblm. Ky wods: suck-od pumping unit, asynchonous lctic div, oscillation fquncy contol, stady-stat mod, static chaactistics. 1. Intoduction Suck-od pumping units (SRPU) a usd in most oil filds. A suck od pump (Fig. 1) is powd by an asynchonous moto (AM). Ensuing fficint and liabl opation of th SRPU lctic div is on of th most challnging tasks. Th spcificitis of its opation includ a piodically vaiabl load, whos law of vaiation changs within a wid ang duing th wll opation, and a piodically vaiabl toqu. An impotant facto affcting th law of vaiation of th AM shaft toqu is suck od pump balancing. Adjustmnt of th dp-wll pumping quipmnt and th mods of its opation must ag with th wll flow at, which dcass as th wll is opatd. A paticula impotanc is attachd to th optimization of stipp wlls opation [1,, 1]. Fig. 1. A suck-od pumping unit. It is impotant to nsu th ncssay chang in th mod of th suck od pump opation so that it can cospond to th oil inflow at [4, 8]. As th toqu fom th AM oto shaft is tansfd to th cank via a duction ga and a blt ga, th walking bam oscillation fquncy can b manually changd in a disct way by changing thi duction atio. Howv, th most ffctiv appoach is using contolld lctic divs [3, 5, 7, 1]. Th availabl diagnostic facilitis fo monitoing th undgound quipmnt status [3, 4, 6, 7] nabl liabl SRPU load cuvs to b obtaind, but th softwa fo automatic contol of oil pumping units dos not mt th cunt pactical nds. Fo any contol to b implmntd it is ncssay to stablish th lationship btwn input and output vaiabls of th contol objct. Th complxity of this task fo SRPU lctic divs stms fom two facts. Fist, th input vaiabl is psntd not by a scala valu of th toqu, but by its functional piodic dpndnc. Scond, th lation btwn th foc acting upon th walking bam in th point of ods suspnsion, and th AM shaft toqu is dfind by a complx non-lina kinmatic lationship [6, 7], which tansfoms th piodic law of vaiation of th foc acting on th walking bam in th point of suspnsion of th ods connctd to th pump into th law of vaiation of th AM shaft toqu (Fig. ). It should b addd that th AM of th SRPU lctic div continuously opats in a dynamic mod and fatus a non-lina dpndnc btwn th AM load toqu and lctomagntic toqu. Lviv Polytchnic National Univsity Institutional Rpositoy

6 Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna Fig.. Piodic dpndncis of a lativ valu of th foc Р * = Р/Р мах in th point of suspnding th ods and lctomagntic toqu * M of th moto.

2 6 Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna Fig.. Piodic dpndncis of a lativ valu of th foc Р * = Р/Р мах in th point of suspnding th ods and lctomagntic toqu * M of th moto. Th poblm of nsuing th ffctiv opation of th SRPU, including discpancy btwn th oil pumping at and oil inflow at, can only b solvd on th basis of a complx mathmatical modl of th moto, suck od pump and contol systm in thi intlations. Th fist stp is stablishing lationships btwn a dynamogam, which dtmins th piodic law of vaiation of th foc in th point of ods suspnsion, fquncy of walking bam oscillations and duction atio btwn th AM shaft and duction ga shaft. Solving this poblm will allow th mthods of SRPU contol to b impovd and stictions stmming fom th spcificitis of SRPU lctic div opation to b dtmind, thby making it possibl to nhanc ngy fficincy and liability of th unit as wll as to xtnd its tunaound intval. Th sach aims to dvlop a mathmatical modl and algoithm nabling th dtmination of th AM oto spd, which cosponds to th wll flow at and pmissibl ang of its adjustmnt, basd on th known piodic law of th load catd by th pump.. Mathmatical modl On volution of th cank cosponds to a full cycl of up-and-down movmnt of th plung and, spctivly, to a chang of th load toqu M c (α) = M c (α+π), i.. th toqu vaiation piod is qual to th cank otation piod. Th plung pump poductivity can b dtmind using th xpssion q λπd S =, (1) 4p k () t () t wh p is th numb of moto pol pais; is th otational spd of th oto; D is th plung diamt; S is th plung tavl; λ is th volum fficincy of th pump dtmind as th atio btwn th i thotically possibl volum of th liquid and its al on, which in pactic is somwhat low [5] du to its lak fom th cylind, and falls into th ang,6 λ,8; k і = k ш k p is th duction atio btwn th AM shaft and cank, which is qual to th poduction of duction atios of th blt ga k ш and th duction ga k p. Sinc th load toqu is a piodic vaiabl, vaiation of q(t) will also b govnd by th piodic law. Thfo, th volum of oil xtactd p cycl of th SRPU opation can b calculatd as a piod avag valu T 1 Qc = q() t dt. () T Dividing th cunt oil inflow at by th oil pumping at p opation cycl givs th piod avag otational spd of th AM oto, which nsus th balanc btwn th inflow and pumping of th liquid. Th implmntation of such a lationship, howv, is associatd with a numb of stictions on th AM opation in th SRPU systm both in tms of ovload capacity of th moto, and with gad to its hat load. Establishing ths stictions is a complx non-lina poblm, which can b solvd using mathmatical modlling of th lctomchanical systm of th SRPU lctic div considing such factos as a satuation-causd non-lina chaact of lctomagntic lationships btwn its lctic cicuits, non-lina kinmatic lationships of th suck od pump and a vaiabl momnt of intia of th moving pats. Th otational spd of th oto at th st law of vaiation of th AM shaft toqu M c (t) is found fom th diffntial quation (DE) of movmnt of th SRPU mchanical systm, which, taking into account th vaiabl momnt of intia of th unit J, has th fom d p dj = ( M M c () t ), (3) dt J J wh M is th AM lctomagntic toqu; J is th momnt of intia of th moving pats coctd fo th moto shaft, which is dtmind on th basis of th momnts of intia of th unit componnts pfoming otational o tanslational movmnts and dpnds on th angl of otation α of th cank J (α) = J (α+π), and, thfo, is a function of th angl of oto otation, which in tun is a function of tim. On th x and y axs, th lctomagntic toqu of AM is dtmind using th fomula M =,5 p ( ψ i ψ i ) 1. x y y x Lviv Polytchnic National Univsity Institutional Rpositoy

3 Effct of Suck-Rod Pumping Unit Walking Bam Oscillation Fquncy 7 To dtmin th vaiabls in this fomula, th systm of DE of AM lctomagntic balanc is solvd: dψ = u Ω ψ Ri, (4) dt wh ( u,,,) * u = sx usy ; ψ = ( ψ,,, ) * sx ψ sy ψ x ψ y ; i = i i, i, i a th vctos of voltag, ( ) * sx, sy x y cunt and flux linkag of th cicuits (upp indx * mans tansposition); R = s is th diagonal matix in which s, a th sistancs of th oto and stato windings, spctivly; Ω s = ;, a th angula fquncis of th AM supply voltag and movmnt of th oto, spctivly. Systm of DE (4) maks it possibl to dtmin th vctos ψ and i fo a st valu of th vcto u and a st angula spd of th oto movmnt, taking into considation th AM magntic path satuation. To do this, computation of flux linkag of th cicuits and matix of lctomagntic paamts lis on using magntization cuvs fo th main magntic path and th paths of lakag fluxs of th stato and oto cicuits [9]. 3. Algoithm of computing a stady-stat mod In a stady-stat mod, du to a cyclic chaact of th unit opation, pocsss in th lctomchanical systm of th SRPU lctic div chang accoding to th piodic law dtmind by a complt cycl of th suck od pump opation. Howv, its tim piod is unknown, and its angula piod is dtmind by a complt volution of th cank and is qual to Т=π ispctiv of th cank shaft otational spd. Thus, th solution to th systm of DE (3), (4) of lctomagntic balanc is a totality of piodic dpndncis of th coodinats within a piod dtmind by on volution of th cank. Dtmination of ths dpndncis by intgating th systm of DE (3), (4) in th tim domain bfo th pocss achs th stady stat is unasonabl, and th most ffctiv way of thi finding is to solv a bounday-valu poblm, which nabls ths dpndncis to b obtaind using a minimum amount of computations. To do this, lt us plac th tim coodinat t in quations (3), (4) with th angl of cank otationα, dψ u Ωψ Ri =, (5а) d pki dj = ( M M c ), (5b) J J wh k is th angula spd of th cank. To shotn th dsciption of th algoithm of solving th poblm as a bounday-valu on, DE systm (5) is psntd by on vcto quation y( x, α ) = f ( u, y, x, α ) (6) α wh f = k ψ i y = ; x = ; ( u Ωψ Ri )/ k pki M M c J J J ( ) ' To solv th poblm as a bounday-valu on, DE a to b tansfomd into algbaic ons. Accoding to [6], on can us appoximation of stat vaiabls by th 3 d od splins, which povid high accuacy fo a small numb of nodal points on th piod. Th splin appoximation of th coodinats on th gid of n nods of th piod sults in an algbaic countpat of systm (6) in th fom of a non-lina algbaic quation of th (m= 5n) th od H Y X F Y, X =, (7) ( ) ( ) wh Н is a m m sizd matix of tansition fom th continuous chang in th y -vcto coodinats to thi nodal valus, whos lmnts a dtmind by a gid of nods of th piod (6); (, X = x ) * 1 xn, F = f f a th vctos consisting of nodal valus ( ) * 1, n of th spctiv vctos coodinats. Systm (7) of non-lina quations is a disct flction of non-lina DE systm (6) appoximating it on th piod T. Th unknown vaiabl is th vcto X mad up of th vctos of nodal valus of AM cicuit cunts and otational spd of th AM oto, and th Jacobi matix is F Y F W = H Y. X X 4. Algoithm of computing th chaactistics. Systm (7) of th mn th od finit quations allows us not only to comput a stady stat, but also to study. Lviv Polytchnic National Univsity Institutional Rpositoy

8 Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna th ffct of vaiation of any coodinat χ chaactizing this stat, fo instanc, th amplitud o fquncy of th supply voltag, momnt of intia, tc.

(8) dχ χ Fo diffnt coodinats χ, DE systms (8) will diff only in th vcto of th ight pats, which nabls solution of th poblms of computation of diffnt static chaactistics using th sam algoithm.

4 8 Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna th ffct of vaiation of any coodinat χ chaactizing this stat, fo instanc, th amplitud o fquncy of th supply voltag, momnt of intia, tc. To achiv this, th systm is diffntiatd with spct to this paamt [11], which sults in th DE systm = F dx W c. (8) dχ χ Fo diffnt coodinats χ, DE systms (8) will diff only in th vcto of th ight pats, which nabls solution of th poblms of computation of diffnt static chaactistics using th sam algoithm. Intgation of DE systm (8) with spct to th vaiabl χ as a paamt using th numical mthod givs a multi-dimnsional static chaactistic of th piodic pocss as a totality of th stady-stat mods (vctos X ) cosponding to diffnt valus of χ in th ang fom χ 1 to χ. Using th known dynamogam, th algoithm dvlopd to comput chaactistics maks it possibl to dtmin stady-stat dynamic opation mods of th SRPU pmissibl with spct to ctain indicatos. Changing th oil flow at quis adjustmnt of th oil-pumping at, which is achivd by stting up appopiat spds of th walking bam oscillation. Howv, as oth calculations show, th cank otational spd cannot always b changd within th quid ang, as this can caus th AM ovload with spct to both hat and maximum load toqu. In od to dtmin th pmissibl ang of adjustmnt of th oil pumping at and fomulat th stictions, it is ncssay to cay out a pliminay study, which can only b don by mans of mathmatical modlling. As an xampl, Fig. 3 psnts piodic dpndncis of th activ pow, and Fig. 4 dmonstats an ffctiv valu of th cunt computd accoding to th abov-discussd algoithm fo diffnt valus of th cank otation fquncy, which cospond to th dynamogam fo th 4АР16S4У3 (Р n =15kW, U n =38/V) moto stting in motion th 7СК8-3,5-4 suck od pump (Fig. ). Fig. 5 and Fig. 6 show th static chaactistics obtaind by pocssing th computd piodic dpndncis of th spctiv coodinats, which allow dtmination of th utmost pmissibl conditions of gulation sulting fom th limitations of th moto opation accoding to th maximum piod avag valu of pow (Fig. 5) and cunt (Fig. 6), as wll as th ovload capacity with spct to th toqu (Fig. ). As shown in Fig. 5 and Fig. 6, fo th dynamogam in Fig., th pmissibl otational spd of th AM oto is th on at which th cank otational spd dos not xcd 1 pm. Fig. 3. Rlativ valu of th activ pow Р consumd by th moto vsus th angl α fo vaious valus of th cank otational fquncy. Fig. 4. Rlativ valu of th AM cunt vsus th angl α fo vaious valus of th cank otational fquncy. Fig. 5. Rlativ valu of th activ pow vsus th cank otational fquncy. Fig. 6. Rlativ valu of th cunt vsus th cank otational fquncy. Lviv Polytchnic National Univsity Institutional Rpositoy

5 Effct of Suck-Rod Pumping Unit Walking Bam Oscillation Fquncy 9 4. Conclusions Th dvlopd computation algoithm nabls dtmination of th walking bam oscillation fquncy which cosponds to th continuous opation of SRPU dpnding on th oil fomation flow at, as wll as maks it possibl to stablish stictions gading th ang of its gulation dtmind by th toqu and hat ovload of th moto. Th algoithm lis on th fin mathmatical modls of th asynchonous moto and suck od pump and th mthod of computation of piodic dpndncis of SRPU mod coodinats basd on solving a bounday-valu poblm. Th high-spd softwa pogams dsignd on th basis of th dvlopd algoithm can b applid fo altim analysis of th SRPU opation, which can b usd fo cating ffctiv intllctual contol systms. Rfncs [1] O. Akulshyn, On stablishing th mods of dpwll od pumping units, povidd P bb < P sat, Naftova i gazova pomyslovist, no. 5, pp. 31, Kyiv, Ukain, 4. (Ukainian) [] Z. Dshi. Study of pow balanc tchnology on bam pumping unit, in Poc. Intn. Conf. IEEE Masumnt, Infomation and Contol (ICMIC), vol., pp , 13. [3] А. Shagyv, А. Timushva, L. Shagyva, and А. Gishkin, Automatd monitoing of wlls pocssing - th fist stp to intllignt contol systms, Nftyanoy khozyaistvo, no. 11, pp , Moscow, Russia,. (Russian) [4] Т. Aliv and О. Nusatov, Tchniqus and diagnostic tools fo dp-wll oil-pumping quipmnt, Nftyanoy khozyaistvo, no. 9, pp. 78 8, Moscow, Russia, (Russian) [5] V. Baskiy, D. Kudyumov, and A. Kolslnyk, On fild xpinc in application of th automatd lctic div in th contol station of RENN dpwll od pumping unit, Vstnik NTU KhPI Poblmy avtomatiziovannoho lktopivoda. Toiya i paktika, no. 1, vol. 1, pp. 6 9, Khakiv, Ukain,. (Russian) [6] B. Kaluszhnyi and A. Malya, Estimato of th foc in th polishd od of a dp-wll pumping unit, Tkhnichna lktodynamika, Spcial issu, vol. 4, pp. 79 8, Kyiv, Ukain, 6. (Ukainian) [7] A. Malya and B. Kaluzhnyi, Automatic contol and monitoing systm of oil xtaction pocss: monogaph. Lviv, Ukain: Lviv Polytchnic National Univsity, 1. (Ukainian) [8] A. Malya Mathmatical modlling of wok of th od of a dp-wll oil-pumping unit, Naftova i gazova pomyslovist, no. 3, pp , Kyiv, Ukain, 8. (Ukainian) [9] R. Filts, Mathmatical foundations of th thoy of lctomchanical tansducs. Kyiv, Ukain: Naukova dumka, (Russian) [1] L. Tagiova, Automation of contol pocss of oil poduction fom maginal wlls basd on dynamic modls, Abstact of Docto of Engining disstation (majo ), Ufa, Russia, 8. (Russian) [11] M. Yakovlv, To th issu of solving systms of non-lina quations by mans of diffntiating by paamt, Zhunal Vychislitlnoy Matmatiki i Matmatichskoy Fiziki, vol. 4, no. 1, pp , Moscow, Russia, (Russian) ВПЛИВ ЧАСТОТИ ГОЙДАНЬ БАЛАНСИРА ШТАНГОВОЇ НАФТОВИДОБУВНОЇ УСТАНОВКИ НА РОБОТУ АСИНХРОННОГО ЕЛЕКТРОПРИВОДУ Андрій Маляр, Богдан Калужний, Андрій Андреїшин, Крістіан Молнар Процес нафтовидобутку нафти потребує постійного моніторингу роботи обладнання свердловин. Для підвищення ефективності роботи нафтових свердловин необхідно встановити оптимальний режим роботи нафтовидобувної установки, за якого відбір рідини відповідає її притоку. Значна кількість свердловин мають невеликий дебіт, а тому працюють у режимі періодичної експлуатації. Для застосування автоматизованих систем керування необхідно мати достовірну інформацію не тільки про стан нафтовидобувного обладнання, але й визначати обмеження, які витікають з умов надійної роботи системи електроприводу. Це можливо здійснити лише на основі математичного моделювання. Розроблений метод і алгоритм розрахунку режимів роботи штангових глибиннопомпомпових нафтовидобувних установок дає змогу визначати частоту гойдань балансира залежно від зміни дебіту пласта, а також обмеження щодо меж її регулювання, які визначаються перевантаженням двигуна за моментом та нагріванням. В основу алгоритму розрахунку покладено математичні моделі асинхронного двигуна і верстата-гойдалки високого рівня адекватності і метод розрахунку періодичних залежностей координат режиму роботи установки на основі розв язування крайової задачі. Lviv Polytchnic National Univsity Institutional Rpositoy

3 Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna Andiy Malya Docto of Scinc, Pofsso, Dpatmnt of

Scintific intsts: mathmatical modlling of lctomchanical systms, study of automatd contol systms of oil pumping

Bohdan Kaluzhnyi PhD, Associat Pofsso, Dpatmnt of Scintific intsts: mathmatical modlling of lctomchanical

modlling of lctomchanical systms, modlling of nual ntwoks.

6 3 Andiy Malya, Bohdan Kaluzhnyi, Andiy Andishyn, Kistian Molna Andiy Malya Docto of Scinc, Pofsso, Dpatmnt of Elctic Div and Computizd Elctomchanical Systms, Lviv Polytchnic National Univsity. Scintific intsts: mathmatical modlling of lctomchanical systms, study of automatd contol systms of oil pumping units. Bohdan Kaluzhnyi PhD, Associat Pofsso, Dpatmnt of Elctic Div and Computizd Elctomchanical Systms, Lviv Polytchnic National Univsity. Scintific intsts: mathmatical modlling of lctomchanical systms, sach into lctic div of oil pumping units. Andiy Andishyn PhD studnt, Dpatmnt of Elctic Div and Computizd Elctomchanical Systms, Lviv Polytchnic National Univsity. Scintific intsts: mathmatical modlling of lctomchanical systms, modlling of nual ntwoks. Kistian Molna Studnt at th Institut of Pow Engining and Contol Systms Lviv Polytchnic National Univsity Institutional Rpositoy

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