Journal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article

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1 Avalabl onln Journal of Chmcal and Pharmacutcal sarch, 4, 6(5):66-73 sarch Artcl SSN : CDN(SA) : JCPC5 Gap lmnt mthod and ts applcaton on forc analyss of tubng strngs Lu ka #, Song Mngxng *, X and Zhang Xuhong # # Ptrolum ngnrng Collg, Northast Ptrolum nvrsty, Hlongjang Daqng, Chna * Daqng Drllng ngnrng nsttut of chnology, Hlongjang Daqng, School of Ptrolum ngnrng, Chna nvrsty of Ptrolum, Bjng Campus, Bjng, Chna ABSAC A statc forc modl s st up for analyzng th dual layr contact btwn tubng strngs faturng ts actual work condtons. Dual layr gap lmnt thory dscrbs th frctons whn th tubng strngs ar contactd, wth ts ral contact ach nod of tubng strngs rflcts, th ovrall balanc quaton and ts rqurmnts for solutons can b gvn. Basd on th forc analyss, a scton of tubng strng s addd on th bottom of th orgnal strngs for rducng th frctons, whch a pr-addd forc s put undr th artfcal bottom hol that could rduc th avrag forc of th tubng strngs and longat th lf span of tubng strngs. Kywords: ubng Strng; Forc Analyss; Gap lmnt; Contact; Lf Span NDCN Brokn tubng strngs and off-cntr wars ar on of th common problms th pumpng unt fac and s dffcult to addrss durng th ol producton. h factors nfluncng th forcs of tubng and suckr rods ar many but lmtd to th wll gomtry, th qualty of producd lqud, th placmnt of stablzr and varanc of condtons undr th hol, tc. h forc of tubng strngs s rally complx, whn t s n upward strok, th xtractd suckr rod gts contactd wth th nnr layr of suckr rod n bndd wllbor, and th tubng s n contact wth th nnr layr of tubng undr th racton forc of suckr rod; whn n downward strok, th bottom of suckr rod s bnd and dformd undr th forc of pump, and vn sprally dformd whch gts contactd wth th nnr layr of tubng, thus th tubng would b contactd wth th nnr wall of casngs. t s obvously dffcult to undrstand th nonlnar quston of forc among th suckr rod, tubng and casng. gardng to th forc analyss of tubng strngs undr th wll, rsarchrs of natonalts hav proposd many forc modls, such as classcal dffrntal quaton mthod[], crossbar bnd contnuous bam[], wghtd rsdual mthod [3], ntal paramtrs[4,5], fnt dffrntal mthod[6-8], fnt lmnt mthod[9], whl ths thors may not solv th contact problm among th suckr rod, tubng strng and casng. hs papr taks th statc forc modl and Dual layr gap lmnt thory to analyz th forc among th thr. MHD AND HCAL QAN. SAC FC MDL S S F ANALYZNG H DAL LAY CNAC H SCK D, BNG SNG AND CASNG A forc analyss modl s st, as shown n fgur, through th analyss of th suckr rod, tubng strng and casng undr work condtons. hn constructng th modl of fgur, th whol tubng strng from th wllhad to th bottom s undr th followng hypothss: () th strng and accssors ar lastc dformd; () th nnr wall of wllbor and strngs ar stff and round ; (3) th contact wth th suckr rod, tubng strng and casng s undr random stat, and ts contact dformaton s wthn th scop of lastc dformaton and thr ar racton forc and frctons at th contact; (4) all dynamc factors ar nglctd; (5) th axs of wllbor s a 3-D curv n th spac and 66

2 Lu ka t al J. Chm. Pharm. s., 4, 6(5):66-73 th locaton of wllbor axs s dtrmnd by th wll profl or survyd data of wll dpth, dvatd angl and azmuth that ar calculatd by th spln functon. hr ar som modfcatons on th rqurmnts of boundars: th wllhad s smplfd wth a buld-n nd; whn th tubng strng s anchord, th bottom s smplfd by a fxd hng sttng and a fr nd whn t s not. h boundary of fr mov of suckr rod, tubng strng and casng ar rlatvly smplfd as boundary of frctons. h contact frcton s dtrmnd by th balanc stat of Dual layr systm of suckr rod, tubng and casng. h man load ar th wght of suckr rod and tubng, th nrta forc of suckr rod, th racton forc of wllhad, buoyancy of ol and normal racton, frcton of rod and tubng at th contact pont, pston forc at th bottom of suckr rod and dffrntal lqud prssur nsd and outsd of rod and tubng. Suckr rod ntrnal layr gap l mnt xtrnal layr gap lmnt y z ubng strng Casng Fgur. Statc forc analyss modl and gap lmnt modl of suckr rod, tubng strng and doubl layr contact of strngs DAL LAY CNAC GAP LMN ANALYSS F SCK D, BNG SNG AND CASNG Dual layr fnt lmnt thory can b usd to dscrb th contact frcton btwn tubng strngs accordng to to th work of tubng. And fnt lmnt s normally adoptd to sparat th rod and tubng basd on th statc forc analyss modl along th axs nto svral spatal bam unts, th nod of ach unt s st as Dual layr contact frcton gap lmnt, th suckr rod, tubng and casng strngs ar untd as a whol through ths. h gap lmnt of contact frcton n vard angls s a vrtual unt consstng lqud or gas shapd as a thck round crcl, th xtrnal boundary of gap lmnt contacts wth th casng and nnr boundary wth th outr wall of tubng strng; th unt that th outr boundary of th gap lmnt of nnr layr conncts wth th nnr wall of tubng strng and nnr boundary conncts wth outr wall of suckr rod has followng physcal faturs: th nnr layr btwn tubng strngs s not n contact would not nflunc th mov of tubng and ts comprssv stffnss rachs zro; whn n contact, th gap lmnt at nods would b compltly comprssd, th nnr and outr boundary of gap lmnt s tangnt at th contact pont, ts comprssv stffnss quals a crtan numbr or a numbr that s larg nough that could prvnt th ntrvnton btwn tubng strngs, whch th sld of tubng strngs s sn on th surfac of sdwall wth contact forc, frcton forc, torqu and drag ar gnratd.. VALL BALANCD QANS h ovrall coordnat of tubng strng s st up and ach spatal unt has partal coordnats. h rlaton of nodal dsplacmnt vctor btwn partal coordnats and ovrall coordnats s: { δ } [ ]{ δ }, () { δ } s nodal dsplacmnt of partal coordnat ; [ ] s th matrx of coordnat transformaton; { } dsplacmnt of ovrall coordnat. δ s nodal 67

3 Lu ka t al J. Chm. Pharm. s., 4, 6(5):66-73 h coordnat transformaton of nodal dsplacmnt vctor btwn partal coordnat and ovrall coordnats s { F } [ ]{ F }, () { F } s nodal vctor of a tubng strng n partal coordnat; { } coordnat. F s nodal vctor of a tubng strng n ovrall y z n n z y Fgur. h dformaton of gap lmnt wth dual layr contact systm chart h spatal bam unt of sparatd tubng strng faturs tnsl prssur, countr bndng and rsstanc aganst torsonal rgdty, lastc potntal nrgy of ach unt can b xprssd as followd: p L { ε } [ ]{ δ } { ε} [ D ]{ ε} d L { u} { q} d L { δ } { F } B, L, (3) L s th unt lngth ;{ ε } s stran vctor; [D] lastc matrx; { q } s load vctor;{ } [B] s stran matrx, thus th stffnss matrx quaton basd on th mnmum potntal thory can b xprssd as: [ ] { δ } { } F (4) u s nodal dsplacmnt vctor; K, (5) [ K ] s th unt stffnss matrx of a tubng strng n partal coordnat [ K ] [ B] [ D] [ B] d l. (6) L h transformaton from th nodal dsplacmnt and nodal vctor of partal coordnat to thos of n th ovrall coordnat can calculat th unt stffnss matrx [ K of tubng n ovrall coordnat and that of n partal coordnat: [ K ] [ ] [ K ] [ ] ], (7) bvously, th suckr rod and tubng strng ar not th sam dformd objcts; ach of thm taks on dffrnt load and changs rspctvly, and t s n th contact ara that ths two would b ntractd and ths papr taks mor mphass on that part usng th gap lmnt thory. 68

4 Lu ka t al J. Chm. Pharm. s., 4, 6(5): H GAP LMN F DAL LAY FCN N VAD ANGLS hn t s takng th statc analyss of suckr rod, tubng and casng dual layr systm, th gap lmnt dual layr systm s st at th nods of bam unt. Dual layr gap lmnt and bam unt of th partal coordnat X Y Z ar n th sam radus of th rng, as llustratd n fgur. And dsplacmnt drcton of n (th azmuth s th suckr rod gnratd n th ) n rlaton to th nnr layr gap lmnt of th tubng strng, th ntal gap lmnt of nnr gap lmnt s, th gap lmnt aftr dformaton s, so (8) ε (9), ε s stran of nnr lay gap lmnt, th stffnss rgdty of nnr layr gap lmnt s A C A, B thus th contact s n G potntal nrgy of nnr layr gap lmnt s:, nnr layr contact frcton s X and lastc A () f () X n n G ε C ε () f s th frcton coffcnt of nnr layr, usng th C and B that s n th sam ordr of bam unt, th unt stffnss rgdty matrx quaton of suckr rod bam unt of nnr layr gap lmnt s: [ K ] [ K ] + [ B ] [ C ][ B ] B wth zro nto a matrx [ C ] and [ ] (3) As can b ncludd from th abov, th unt stffnss rgdty matrx quaton of tubng strng bam unt of xtrnal layr gap lmnt s: [ K ] [ K ] + [ B ] [ C ][ B ] + [ B ] [ C ][ B ] (4) of whch th comprssv rgdty of tubng strng n xtrnal layr gap lmnt s, B, A, C A s th ntal gap of xtrnal gap lmnt, s th gap aftr t s dformd, s th dsplacmnt of th tubng strng n th xtrnal layr gap lmnt along a sphrcal drcton ).h frcton of nnr layr s f, th stran forc of xtrnal layr G n (azmuth s n, frcton of nnr layr X ar : A (5) f (6) X h ovrall balancd quaton of suckr rod, tubng strng and casng strngs through th transformaton of coordnats and suprposton prncpl can b calculatd by: 69

5 Lu ka t al J. Chm. Pharm. s., 4, 6(5):66-73 [ ]{ δ} { F} K, (7) [K ],{ δ } and{ F } s th stffnss rgdty, nodal dsplacmnt and nodal vctor of ovrall coordnats. Durng th procss of solvng th quaton of(7),th contact condton of suckr rod, tubng strng and casng through Dual layr contact systm may b classfd nto 5 catgors and 9 knds:whch ar fr mod ( <, < ) sngl layr contact mod(, < ;or <, ) Dual layr contact mod (, ) sngl layr ntrud mod ( >, < ;or >, ;or <, > ;or, > ;)and Dual layr ntrud mod ( >, > ). h ral contact mod s classfd nto 3 catgors and 4 knds, whch s fr mod, sngl layr contact mod ( knds) and Dual layr contact mod. h contact mod of ach nod may b on of th abov. h quatons ar: Fr mod: mε n n n + n < mε m < m ε m m s th postv valu. Sngl layr contact mod: mε m m < m ε m (8) (9) m s postv valu, computaton. < mε m mε m m + + s th contact angl of nnr layr gap lmnt of + and through tratv () 7

6 Lu ka t al J. Chm. Pharm. s., 4, 6(5): s th contact angl of xtrnal layr gap lmnt of + and through tratv computaton. Dual layr contact mod: n + n + mε m m m ε m m () h gap lmnt s ntroducd nto (7) and ts answr must b calculatd through tratv computatons to mak all nods mt th rqurmnts of quatons from (8) ~ ()..3 CALCLAN F QVALN SSS AND SNGH CHCKF SCK D AND BNG SNG h gnralzd dsplacmnt of suckr rod and tubng strng could b calculatd through loop traton of (7), and on whch t s basd to calculat th axal forc N and N, flxural torqu M y M z M y and M x, sharng forc Q y Q z Q y and normal strss and sharng strngth ar : Q z on any scton of suckr rod and tubng strng, thus th maxmum suckr rod: x N A M τ n x ± M y + M z () tubng strng: x N A M τ n x ± M y + M A A z n and (3) n ar scton ara, moduls of bndng scton and torsonal scton of suckr rod and tubng strng, of whch ± taks + whn th axal forc s postv and vc vrsa. h quaton of sharng strngth nglcts th scton sharng strngths and normal strss s th man strss on th scton, thus th maxmum absolut valu of normal strss on th scton s th dangr scton and pont of maxmum normal strss on dangr scton s th dangr pont, and t s on th outr dg of dangr scton. n addton, th hoop strss and radal strss gnratd by th nnr prssur p and xtrnal prssur p ar: suckr rod: r p p (4) 7

7 Lu ka t al J. Chm. Pharm. s., 4, 6(5):66-73 suckr rod: r α p α max( p + α α, p ) p (5) α d D,s th rato of nnr and outr damtr of tubng strng. wo of prncpal strss at th scton can b calculatd from th prncpal strss quaton: max + x x ± ( ) + τ mn (6) max + x x ± ( ) + τ mn (7) quvalnt strss of suckr rod and tubng strng ar: max(,, ) mn(,, ) (8) 4 3 r max mn r max mn max(,, ) mn(,, ) (9) 4 3 r max mn r max mn h strngth chck condtons of suckr rod and tubng strng ar: [ ] 4 (3) [ ] 4 (3) 3 CALCLAN F AL CASS ubng strngs of 3 wlls ar calculatd basd on th abov thors. h layr tmpratur of 3 wlls s around 65, dpth s 45~5 m, pump damtr s 38mm. o prov th accuracy, th calculaton s n tabl, from whch th maxmum dscrpancs of survyd valus compard to th calculatd valus of polshd rod load s 3.33%, lss than 5%, whch mans th modl ths papr hypothss s rght and can b usd n fld. abl Comparson of Calculaton sults of Polshd od Load of 3 lls ll ll ll ll 3 Strok upwards downwards upwards downwards upwards downwards Survyd load at kn Polshd rod load,kn latv rror,% gardng to th strng brakng, th bst mthod s to mprov th dformaton condton of strngs and th ky s to rduc th strss ampltud and maxmum man strss of strngs. Currntly t s not possbl to rduc th maxmum strss ampltud and maxmum man strss du to th spcal work condton suckr rod has. hl to th tubng strng, a scton of strng can b addd at th bottom of tubng strng for puttng pr-strss on th artfcal bottom to rduc th maxmum man strss of tubng strng by mans of th calculaton, and prvnt th rlatv dsplacmnt of strngs at bottom nd from movng, rduc th strok loss and mprov ol pumpng ffcncy. h calculaton of dformd condton aftr changs ar mad to th strngs s analyzd n abl. From th abl, th maxmum man strss bfor th chang s 5.57MPa, maxmum strss ampltud s.7mpa; th maxmum man strss aftr th chang s 5.9MPa, whch s rducd by 6.38%, and maxmum strss ampltud s ncrasd by 6.5% to 4.3MPa. t should b notd that th maxmum strss ampltud s ncrasd but th strss nflunc acts from th vcnty of wll hol bfor th chang to bottom of wll hol aftr th chang, and ts man strss of th maxmum strss ampltud on th scton s % of th maxmum man strss 7

8 Lu ka t al J. Chm. Pharm. s., 4, 6(5):66-73 aftr changs ar mad, whch gratly hlps rduc th fatgu strss; th maxmum quvalnt strss droppd to 3.63MPa from 56.7MPa, lowrd by 6.4%, and s almost th sam as th maxmum strss at th dangr pont aftr upward and downward strok hav takn plac, and dynamc strss has sn droppd drastcally compard wth that of bfor th chang, ths papr taks th masurs that could mprov th dformd condton of tubng strngs and ways of lastng th lf span of tubng strng. abl Dformaton of ubng Strngs of 3 lls bfor Chang ll No. ll ll ll 3 Avrag Structur Strok Prcomprsson kn Maxmum bndng strss MPa Maxmum quvalnt strss MPa Maxmum strss ampltud MPa Maxmum man strss MPa Bfor th upwards chang downwards aftr th upwards chang downwards bfor th upwards chang downwards aftr th upwards..6 3 chang downwards bfor th upwards chang downwards aftr th upwards chang downwards bfor th chang aftr th chang ducd by Prcnt 6.38% 6.4% -6.5% 6.38% Acknowldgmnts Projct supportd by Hlongjang Postdoctoral sarch Startup of Chna No. LBH-Q338. CNCLSN ()A gap lmnt modl of dual layr contact frcton n vard angls through th forc analyss of suckr rod, tubng strng and casng s st up, th calculaton of strss of suckr rod and tubng strng whl takng nto account of th thr s gvn n ths papr. ()h maxmum dscrpancy of survyd valus compard to th calculatd valus of polshd rod load s 3.33%, mnmum s.67%, ts man dscrpancy s 8.%, lss than 5%, whch mans th modl ths papr hypothss s rght and can b usd n fld. (3)hl to th tubng strng, a scton of strng can b addd at th bottom of tubng strng for puttng pr-strss on th artfcal bottom to rduc th maxmum man strss of tubng strng by mans of th calculaton, whch could rduc th maxmum man strss of tubng strngs and ncrass th lf span of tubng strng. FNCS [] A Lubnsk, Drllng and Producton Practc AP, 95:78-4. [] YN Su; XP ang; ZX Chn, Practc of Mchancs, 4, 6():4-44. [3] YN Su; XP ang; ZX Chn, Mchancs n ngnrng, 4, 6():4-44. [4] CD Xu; Mchancs and Practc, 98, (4):-5. [5] D Darng; CA Ahlrs, J. of nrgy s. ch, 99, :-. [6] J Xu; DF Hou, Journal of Janghan Ptrolum nsttut, 993, 6:56-6. [7] B Bradly, Journal of Ptrolum tchnology, 975:679~688. [8] FJ Fshr, SP 57. [9] M Yang; DL Gao; BG Xu, Ptrolum Drllng chnqus, 99,9: